Growth, Employment, Inequality, And the Environment Unity of Knowledge in Economics Volume II

Growth, Employment, Inequality, and the Environment

Growth, Employment, Inequality, and the

Environment

Unity of Knowledge in Economics: Volume II

Adolfo Figueroa

growth, employment, inequality, and the environment

Copyright © Adolfo Figueroa, 2015.

All rights reserved.

First published in 2015 byPALGRAVE MACMILLAN®in the United States—a division of St. Martin’s Press LLC,175 Fifth Avenue, New York, NY 10010.

Where this book is distributed in the UK, Europe and the rest of the world, this is by Palgrave Macmillan, a division of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS.

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ISBN: 978–1–137–50696–2

Library of Congress Cataloging-in-Publication Data

Figueroa, Adolfo. Growth, employment, inequality, and the environment : unity of

knowledge in economics / Adolfo Figueroa. volumes cm Includes bibliographical references and index. ISBN 978–1–137–50266–7 (vol. 1 : hardback : alk. paper)— ISBN 978–1–137–50696–2 (vol. 2 : hardback : alk. paper) 1. Economics. 2. Capitalism. I. Title.

HB71.F497 2014330—dc23 2014041730

A catalogue record of the book is available from the British Library.

Design by Newgen Knowledge Works (P) Ltd., Chennai, India.

First edition: May 2015

10 9 8 7 6 5 4 3 2 1

To Yolita Vásquez, beloved wife and great partner

Contents

List of Figures and Table ix

Part I The Long Run: Growth and Distribution

Chapter 1 Toward a Unified Theory of Capitalism 3

Chapter 2 Education and Human Capital Formation 11

Chapter 3 The Epsilon Society: A Dynamic Model 29

Chapter 4 The Omega Society: A Dynamic Model 43

Chapter 5 The Sigma Society: A Dynamic Model 57

Chapter 6 Unified Theory of Capitalism: A Growth and Distribution Model 69

Part II The Very Long Run: Economic Growth and the Environment

Chapter 7 Economic Growth under Environmental Stress 97

Chapter 8 Land Resources and Food Supply 133

Chapter 9 Economic Growth and Quality of Society 153

Part III The Political Economy of the Unified Theory

Chapter 10 Science-Based Public Policies 177

Bibliography 203

Index 211

Figures and Table

Figures

2.1 Relations between education and human capital, by social groups A, X, and Z, in sigma society 17

2.2 Income (y) and education (E) relationships, by social groups A, X, and Z, in sigma society 22

3.1 Steady state equilibrium in epsilon society 313.2 Human capital accumulation in epsilon society 343.3 Interactions between technological adoption and

human capital in epsilon society 353.4 Growth frontier and transition dynamics in epsilon

society 373.5 Effect of higher investment ratio on the growth frontier

in epsilon society 394.1 Growth of output per worker in omega society 494.2 Inequality changes in the growth process in omega society 545.1 Growth of output per worker in sigma society 615.2 Inequality changes in the growth process in sigma society 656.1 Growth of output per worker in the capitalist system 776.2 Levels of income inequality in the capitalist system 806.3 Income inequality changes in the growth process in the

capitalist system 827.1 Economic process with depletion of mineral resources 1027.2 Economic process with linear depletion and pollution 1097.3 Economic process with nonlinear depletion and pollution 1127.4 Output growth effect upon depletion and pollution

under linear relations 1207.5 Effect of mineral resource-saving technological change

on depletion and pollution under linear relations 121

x l Figures and Table

7.6 Economic growth as an evolutionary process 1258.1 Food market: Population effect upon food scarcity 1378.2 Combined effects of technological change and soil erosion

upon labor productivity in food production 1428.3 Food market: Limits to food supply in the very long run 1448.4 Land resources as a limiting factor of economic growth 1479.1 Economic growth and quality of life 158

Table

6.1 Income per worker and growth rates in the capitalist system, 1960–2008 87

PART I

The Long Run: Growth and Distribution

CHAPTER 1

Toward a Unified Theory of Capitalism

The principal aim of this book is to understand the production and distribution process in the countries of the First World and the Third World, which constitute the capitalist system, considered

separately first, and then as a whole. To that end, this study presents three partial theories of capitalism: epsilon, omega, and sigma, which are dis-cussed in volume 1 of this book in chapters 4–7. The partial theories when considered separately do in fact explain the basic short-run features of the First World and Third World.

Good partial theories, however, do not necessarily imply a good uni-fied theory. Consider, for instance, the general theory of relativity and the quantum theory in physics. The former explains the large physical world, whereas the latter explains the small subatomic physical world. Thus, they explain these two physical worlds, when considered separately, but they can-not explain the physical world taken as a whole. These theories are contra-dictory to each other, that is, they both cannot be true at the same time; hence, a unified theory of physics—the theory of everything—is the funda-mental problem being researched on today (Hawking, 1996).

A similar challenge appears in this book now. The task before us is to construct a unified theory of capitalism. This chapter starts the construc-tion of the unified theory by summarizing the findings of the partial theo-ries. Then the set of primary assumptions that is consistent with that of the partial theories is formulated. Finally, the dynamic model of the unified theory is constructed, which attempts to explain the economic growth pro-cess in the capitalist system, which has the following endogenous variables: output growth and distribution.

4 l Growth, Employment, Inequality, and the Environment

Partial Theories: A Summary

According to income levels, the capitalist system is categorized into the rich and the poor, which are called First World and Third World, respectively. How does each type of capitalist society function?

A scientific explanation of the capitalist system started with the con-struction of partial economic theories. Several assumptions were been made for that purpose. First, the capitalist system is composed of three types of societies. The criteria to make this distinction are based on dif-ferences regarding two initial conditions: factor endowments and initial inequality. The former separates societies that are overpopulated from those that are underpopulated; the latter separates those that began to function as capitalist economies with highly unequal societies from those that functioned with a lesser degree of inequality. Second, the essential factor underlying the differences in the initial inequality is the distribu-tion of political entitlements among individuals, which separates societies that are socially homogeneous (having one class of citizens) from those that are not (having several classes of citizens). Three abstract capitalist societies have been constructed in the form of partial theories of the sys-tem, which include:

Epsilon society: underpopulated and socially homogeneous, intended to explain the First World.Omega society: overpopulated and socially homogenous, intended to explain the Third World with weak or no colonial domination legacy.Sigma society: overpopulated and socially heterogeneous, intended to explain the Third World with strong colonial domination legacy.

From a historical perspective, as shown in chapter 2 (volume 1), the Third World countries can be divided into two groups: those that have a strong legacy of European colonial domination and those that do not. While the omega theory intends to explain the latter type of countries, the sigma the-ory refers to the former type. Empirically, the majority of Third World countries correspond to the sigma type society. The First World is composed of the European countries and some countries of the New World (Australia, Canada, New Zealand, and the United States), which, strictly speaking, were not colonies, but were rather settlement systems. Epsilon theory seeks to explain the First World.

The three partial theories have been submitted to the falsification pro-cess using static short-run models and confronting them against the four short-run empirical regularities on production and distribution, as listed in

Toward a Unified Theory of Capitalism l 5

chapter 2 (volume 1). Epsilon theory predicts the two empirical regularities of the First World: Fact 1, the existence and persistence of unemployment, and Fact 4, the relation between nominal and real variables (chapter 4, vol-ume 1). Omega theory predicts the two empirical regularities of Third World countries in general: Fact 2, existence and persistence of unemployment and underemployment, and Fact 4 (chapter 5, volume 1). Finally, sigma the-ory has been able to predict the three empirical regularities of Third World countries with strong colonial legacy: Fact 2, Fact 4, and Fact 3, which refers to existence and persistence of income inequality between ethnic groups—a colonial legacy (chapter 6, volume 1).

So far, these theories resemble well the realities they intend to explain. However, there are many more empirical regularities of capitalism to be explained, Facts 5–7. This will be undertaken in the following chapters.

In light of the partial theories’ results, some additional comments on the nature of these three groups of capitalist countries are presented here. As to differences among these groups of countries in the short run, the following are worth mentioning:

a. Capitalist societies show a class structure in epsilon and omega, but they include an underclass in sigma, the second-class citizens.

b. Capitalist societies operate with devices for labor-effort extraction, which differ according to the type of society. Unemployment plays that role in epsilon and underemployment in omega and sigma.

c. In overpopulated societies, capitalism includes subsistence sectors. The role of subsistence sectors is to make capitalism socially viable in such a context.

d. In capitalist societies, people act motivated by self-interest. However, they behave differently in each type of society, which is due to the presence of different institutions. Capitalists use different devices for labor-effort extraction, as mentioned before. Governments supply universal public goods in epsilon and omega, but also include local public goods with differences in quantities and qualities for the dif-ferent classes of citizenship in sigma. Workers react differently when there is excess labor supply and an excessive degree of inequality and thus generate different degrees of social disorder.

e. Market and democracy, the basic institutions of capitalism, operate distinctly in different types of capitalist societies. The market system operates as if it has solved a system of equations based on which prices and quantities are determined in all societies, but the particular sys-tem of equations that need to be solved vary by the type of society. In particular, the conditions of labor market equilibrium are different in


an epsilon society compared to those in omega and sigma societies. Democracy operates through voting rights in all cases, but the degree of participation of citizens in public policies is higher in epsilon and omega than in sigma.

f. In conclusion, the three societies that constitute the capitalist system operate differently. Social actors are guided in their actions by a com-mon motive (self-interest), but they behave differently, according to the type of society in which they live. There are qualitative differences among these societies, especially between epsilon and sigma.

As to similarities, the following are easily drawn from the theoretical models:

i. General equilibrium with excess labor supply is the outcome in all types of capitalist societies. The form of the excess labor supply var-ies according to the type of society: unemployment in epsilon soci-ety and underemployment in omega and sigma societies. However, excess labor supply plays the same role in all societies: it is the device for labor-effort extraction, which ensures high labor productivity and high profits. Labor markets operate with efficiency wages, which implies inequality among homogeneous workers: the market real wage rate (always above the Walrasian wage rate) is always above the real average income of the unemployed or underemployed. Inequality among homogeneous workers is the general labor-discipline device. Hence, excess labor supply (and the corresponding inequality among homogeneous workers) is essential for the functioning of capitalism.

ii. General equilibrium with excess income inequality, and the corre-sponding social disorder, is another trait of capitalism. The higher the initial inequality, the higher the level of income inequality and social disorder. Therefore, income inequality and social disorder are higher in sigma than in the other societies.

iii. The exogenous variables that explain production and distribution in the short run are common to the three types of societies and include: factor endowments, initial inequality in the individual distribution of economic and political assets, and international terms of trade and international interest rates.

The three partial theories explain the short-run functioning of the three corresponding types of capitalist countries that constitute the capitalist sys-tem. Up to now, they are valid partial theories. The task ahead consists of constructing the corresponding unified theory of the capitalist system.


Foundations of the Unified Theory of Capitalism

In the construction of a unified theory, we follow the Moore Principle, named after E. H. Moore, an American mathematician. According to this princi-ple, the existence of analogies between central features of partial theories leads to the existence of a unified theory, which will represent the central features of those partial theories (cited in Samuelson, 1947, p. 3).

In order to become a unified theory, therefore, the partial theories must give rise to common central features, as Moore’s principle requires. In terms of the alpha-beta method, the “central features” correspond to alpha proposi-tions; hence, the requirement is equivalent to finding a common set of alpha propositions in epsilon, omega, and sigma theories. This common set, if it exists, would then constitute the alpha propositions of the unified theory; if it did not, there would not be unified theory. In a way, the requirement is that there should exist a common set of alpha propositions that constitute a logical system.

The common primary assumptions of epsilon, omega, and sigma socie-ties (presented in chapters 4, 5, and 6 of volume 1) are easily identifiable. The corresponding unified theory can then be expressed as the following set of alpha propositions:

α(C) (1). Institutional context: (a) Rules: People participating in the eco-nomic process are endowed with economic and political assets; eco-nomic assets are subject to private property rights; people exchange goods subject to the norms of market exchange, which include the norm that nominal wages cannot fall; the market system operates in Walrasian and non-Walrasian markets, in which the labor market is of the latter type. The political regime is democratic. (b) Organizations: firms, households, and the government.

α(C) (2). Initial conditions: There are different types of capitalist societies based on two initial conditions: factor endowments and the initial inequality in the distribution of economic and political assets among individuals. Factor endowments make capitalist societies underpop-ulated or overpopulated. Initial inequality makes capitalist societies class-societies (constituted by capitalists and workers) and socially homogeneous or heterogeneous.

α(C) (3). Economic rationality of agents: Consistent with the institu-tional context of capitalism, individuals act motivated by self-interest. Capitalists seek two particular objectives, hierarchically ordered: first, maintenance of class position and, second, maximization of profits. In the labor market, workers seek to maximize wages and minimize


effort, while capitalists seek to minimize wages and maximize effort. Due to this conflict in labor relations, capitalists use excess labor sup-ply as the device to extract effort from workers. Individuals have a limited tolerance for inequality.

This set of alpha proposition constitutes the common alpha proposition of the partial theories epsilon, omega, and sigma; moreover, this set is a logical system, as there are no logical inconsistencies between them. Therefore, this set constitutes the alpha propositions of the unified theory of the capitalist system. The symbol “C” stands for capitalism as a whole. The three abstract capitalist societies (epsilon, omega, and sigma) are now partial theories of the unified theory.

This set of alpha propositions can be seen as the core of the theoretical system, which includes the partial theories and the unified theory.

Models that were able to explain the short-run economic process in each type of capitalist society, taken separately, were presented in chapters 4–7 (volume 1). In order to explain the capitalist system taken as a whole, a static short-run model of the unified theory is needed. However, it is not devel-oped here for strategic reasons. The particular features of the capitalist sys-tem that still need to be explained include the empirical differences between the First World and the Third World, which were shown in chapter 2 (vol-ume 1) as Facts 5–7. Why do poor and rich countries coexist in the capitalist system? Why are rich countries more equal societies than poor countries? These questions mostly refer to empirical regularities over time: the existence and persistence of differences in income levels and in the degree of inequality between the First World and the Third World. The answer calls for dynamic models of the unified theory.

This analytical challenge will be approached as follows: First, dynamic models that are logically consistent with the static models of the partial the-ories (chapters 4 to 7 in volume 1) will be constructed; second, the dynamic models will be transformed into a dynamic model of the unified theory; third, the predictions of this unified dynamic model will be confronted against Facts 5–7.

Constructing a Dynamic Model of the Unified Theory

In order to make the unified theory falsifiable (in the sense of Popperian epistemology), a particular dynamic model will be constructed by intro-ducing auxiliary assumptions that are consistent with the primary assump-tions of the theory. The objective of the dynamic model is to explain the economic growth process, in which output growth and the distribution of


output among social groups are the endogenous variables. Because the three types of societies (epsilon, omega, and sigma) constitute the capitalist sys-tem, dynamic models of each society will first be constructed, then trans-formed into a unified dynamic model by introducing auxiliary assumptions that refer to the essential interactions between the three abstract societies.

The long-run dynamic model of the unified theory be used in the follow-ing chapters include the following auxiliary assumptions:

The three societies produce one good only (called good B). International ●l

trade is thus ignored, but there will be free capital mobility between societies.Investment is independent of savings in each society, for the model ●l

assumes an open economy with perfect capital mobility.Effective full employment equilibrium initially prevails in the labor ●l

market. The implication is that money supply is neutral; hence, the short-run effects of nominal variables upon real variables can be ignored. Only one labor market exists in each society. General equilib-rium of markets in each type of society is thus reduced to two markets: good B (Walrasian) and labor market (non-Walrasian), in which the labor market constitutes the core of the general equilibrium.The economic process is dynamic and the objective is long-run analy-●l

sis. The interactions between the economic process and the biophysical environment are ignored in this analysis.

According to the unified model, there are two basic endogenous variables, which are output per worker and income distribution over time. Therefore, the exogenous variables will determine the trajectory of these two variables for each society taken separately and for the capitalist system taken as a whole. This is the content of Part I of this book, which begins with this chapter.

Later on, in Part II, the biophysical environment will be internalized into the economic growth process. Another endogenous variable will be part of the process: the degree of degradation of the biophysical environment. The two first laws of thermodynamics will be introduced into the economic process, resulting in a shift in the process from dynamic to entropic and evolutionary (as qualitative changes accompany growth). Hence, in the eco-nomic growth process, the same exogenous variables of the dynamic model determine the trajectory of the following endogenous variables: output per worker, degree of inequality, and the limits (periods) to economic growth. Finally, the entropic model will include another endogenous variable in the economic process: quality of society. In the economic growth process,


therefore, the same exogenous variables will determine the trajectories of four endogenous variables: output per worker, degree of inequality, limits to growth, and degree of quality of society.

The unified theory will seek to explain the quantitative and qualitative changes of the economic growth process, its social relations and its relations with the biophysical environment, and its direct effects on human life and its side effects. Economic growth takes place under environmental distress now, which has consequences for the quality of life of present and future generations, and even for the fate of the human species. Economics will have to cope with these fundamental problems of our time.

If challenges as big as these have to be answered in a few chapters, it be at the cost of great simplification. The dynamic model of the unified theory is constructed at a very high level of abstraction, as indicated by the auxiliary assumptions of the dynamic model listed above. This journey starts with the study of human capital accumulation, which is developed in the next chapter.

CHAPTER 2

Education and Human Capital Formation

Human capital refers to production skills embodied in workers. According to standard economics, human capital plays an impor-tant role in the economic process; on the one hand, human cap-

ital is as important as machines and technology in the production process; on the other hand, higher human capital implies higher labor productivity and higher incomes for workers; higher human capital also requires higher schooling years, which give workers the basic capacity to learn skills.

Up to now, human capital has been considered to be a constant in the static models of epsilon, omega, and sigma theories. The aim of this chap-ter is to develop an economic theory of human capital formation through education. Then the theory will be submitted to the falsification process through the corresponding model.

Education as Economic Process

People are not born with human capital. People need to invest in acquiring it through education. Hence, to understand human capital differences we must understand the education system. Education refers to formal schooling. Other forms of human capital accumulation, such as on the job training, is ignored while formulating this theory. The terms “school” and “student” will refer to each of the levels of formal education (primary, secondary, tech-nical, and university).

Education is seen as a process, the outcome of which is general knowl-edge and human capital. The concept of process analysis that was introduced


in chapter 1 (volume 1) is then applied to education. There are elements that enter into the educational process, elements that emerge from it, and a mechanism that transforms exogenous into endogenous elements.

According to the different disciplines that seek to explain the process of human learning (such as psychology, biology, and neuroscience), students should be endowed with cognitive capacities essential for learning via the education process. Humans are born with multiple talents, as per the so-called multiple intelligence theory (Gardner, 1999). Although humans are naturally diversified in their talents, the composition is not homogeneous among individuals; thus, some are more talented in art, others in science, and so on. Therefore, individuals are genetically different (not unequal) from each other in talents they are endowed with.

Genetic cognitive or learning capacities in humans can be considered as exogenously determined (the effect of nature). However, these initial capac-ities and their paths are not given once and for all; they are developed over time to different degrees, depending upon the social environment in which individuals live (the effect of nurture). The important distinction made by Rousseau (1755) refers exactly to these two factors. Rousseau distinguished two types of inequalities among individuals: the natural, referring to the gifts of nature, natural endowments, and the random mechanism; and the artificial, referring to inequalities originating in the functioning of society.

Due to the nurture effect, an individual’s cognitive capacities at each level of education may be considered as endogenously determined. In the modern literature of neuroscience, this is known as the brain plasticity the-ory, and it is usually stated as follows:

The brain is not a computer that simply executes predetermined pro-grams. Nor is it a passive gray cabbage, victim to the environment influ-ences that bear upon it. Genes and environment interact to continually change the brain, from the time we are conceived until the moment we die. (Ratey, 2002, p. 17)

Of the two factors that affect the development of cognitive skills in individ-uals, the essential factor in this theory will be the social environment, or the social class, to which they belong. The genetic endowments at birth, being randomly distributed, will be considered a less important factor, particularly when we come to aggregate individuals into social classes or groups, that is, the theory will assume that all individuals are born equal.

A primary assumption of this theory is that, in any capitalist society, human capital accumulation through the education process is not uniform for all social groups, but it depends upon the position of the social groups

Education and Human Capital Formation l 13

in the distribution of economic and political assets in society. The alpha proposition of the theory of human capital accumulation can be stated as follows:

α (C). The theory of formal education: In capitalist societies, the education process is not uniform for all social groups; hence, human capital accu-mulation by social groups takes place under separate and hierarchical education processes, according to the position of the social groups in the distribution of economic and political assets in the society.

This general theory attempts to explain the process of human capital forma-tion in the three types of capitalist societies: epsilon, omega, and sigma.

A Model of the Education Theory

A model of the education theory can be constructed by introducing three auxiliary assumptions. First, the societies under study will include the three types of capitalist societies together with the social groups that were defined in the models we have been studying so far. Second, students participating in the education process will be endowed with unequal cognitive skills or capacities, depending on the social group to which they belong. Nutrition, health, and early intellectual stimulation are the main channels through which the wealthy can develop higher levels of learning capacity in their children when compared to the poor. Third, language proficiency, which is also associated with the socioeconomic level of households, is another factor that brings in inequality in developing cognitive skills,.

Language as a factor in the education process needs some elaboration. There exist language disparities among individuals. This is shown in vari-ous aspects of language, such as vocabulary, syntaxes, ways of speaking, and writing and reading skills. In unequal societies, language disparities become language inequality. According to sociolinguistic theory, language inequal-ity is due mostly to social environmental factors than to genetic factors (cf. Hudson 1996, p. 204).

Capitalism is a class society and thus a hierarchical one. In such a society, the language of the dominant social group would also the dominant lan-guage. Therefore language inequality becomes more significant than lan-guage disparity. The language problem would be more important in sigma societies, where the hierarchical features are more marked. (Recall that the sigma society is constituted by X-workers and Z-workers, who are first- and second-class citizens.) Given the segregation that exists in sigma, the com-mand in the use of the dominant language would be unequal between social


groups of society; thus, the problem of heteroglossia would appear as another form of language inequality.

Heteroglossia is a concept that comes from sociolinguistic theory and refers to the existence of variations in the usage of a given language. In sigma society, where the usage of the dominant language has a hierarchy, from the one that is considered correct and socially superior (the native language of the dominant social group) to the incorrect and socially inferior one, which is utilized by the subaltern population, and usually learned as a second lan-guage, these variations would increase. This is reflected in the different accents and proficiency in the dominant language usage that we observe in the real world. Given the existence of “white Spanish,” “mestizo Spanish,” and “indigenous Spanish” spoken in Latin America, language becomes a social marker: “Let me hear how you speak and I will tell who you are.” This social marker refers of course to the dominant language, which is a second language for Z-populations.

Neuroscience research has shown that we lose flexibility in forming new language connections in our brains by the age six or seven. Hence, second languages learned after these ages are stored within neural systems that are distinct from those for the native language. By contrast, people who grow up bilingual from birth store their native and second languages in the same neural area (Ratey, 2002, p. 278). Social segregation would then cause the problem of heteroglossia.

Inequalities in language skills among social groups imply unequal cog-nitive skills in the children. There are at least two reasons for this: the het-eroglossia effect and the oral language effect. The first has to do with the unequal command on the dominant language, a result of segregation. The second is based on the theory that abstract and complex thoughts are not only language-dependent, but also complex-language-dependent. The phi-losopher John Searle stated this theory as follows:

Some thoughts are of such complexity that it would be empirically impos-sible to think them without being in possession of symbols. Mathematical thoughts, for example, require a system of symbols. . . . Complex abstract thoughts require words and symbols. (Searle, 1995, p. 64)

The implication of this theory is that written language allows people to work with more abstract and complex thoughts than does oral language alone. Therefore, oral language societies show disadvantages in cognitive skills compared to written language societies. In the case of sigma society, Z-populations’ children will be limited in the learning of abstract and com-plex thoughts because they come from an environment of illiteracy. This is


the first effect of language on cognitive skills, the illiteracy effect. However, because they come from an oral culture as well, where the aboriginal lan-guage is not written, those limitations will be reinforced. This is the second effect, the oral culture effect. Hence, Z-populations’ children will have, on average, a lower cognitive skills than those of X-populations. Inequalities in learning capacities will exist even between illiterate families, depend-ing on whether they live in epsilon society or sigma society. Students who come from an illiterate social environment within a written culture will be less handicapped in learning skills compared to those coming from an oral culture.

The assumption that language is a factor of formal education is applica-ble to all types of capitalist societies, not only to sigma societies. This can be stated as follows: the inequality in the endowment of economic and political assets among individuals leads to linguistic inequality, which in turn leads to inequality in cognitive capacities of students. A hypothesis coming from sociolinguistic theory goes even further: “Linguistic inequality can be seen as a cause of social inequality, but also as a consequence of it, because language is one of the most important means by which social inequality is perpetu-ated from generation to generation” (Hudson, 1996, p. 205).

In sum, the model of the theory of formal education assumes that in cap-italist societies, in which households are endowed with unequal economic and political assets, students participating in the educational process will be endowed with unequal learning capacities. This is part of the underlying mechanism through which exogenous variables affect endogenous variables in the education process, as will be shown next.

Transforming Education into Human Capital

In the education process, which produces both general knowledge and human capital, the model will assume that school inputs are the exogenous variables, whereas learning capacities of students and educational technol-ogy are mechanisms that transform the inputs into different types of output. Again, for the sake of simplicity, the endogenous variables of the education process will be reduced to human capital.

Consider for a moment that all schools are homogeneous. Even under this condition, for a given number of years of education, the children of the wealthy will accumulate more human capital than the children of the poor due to the initial inequality in learning capacities. Also, children will not have the same number of years of schooling. The accumulation of human capital requires financing. Rich households have greater financing capacity than poor households, which allows them to finance more years


of schooling. Then, the income effect on investing in human capital is pos-itive: the quantity of human capital demanded will positively depend upon the level of household income. Consequently, on average, the children of rich households will accumulate a higher level of human capital than the children of the poor households on two accounts: more years of schooling and a higher level of learning in each year of schooling.

If the assumption that schools are homogeneous is now abandoned, dif-ferences in school quality will be another factor under consideration. The effect of a such difference is that children of rich households attend schools of higher quality (private schools), while the children of poor households attend schools of lower quality (public schools). Private schools are more equipped with material inputs, technology, and quality of teachers when compared to public schools. The children of rich households will therefore acquire, on average, not only more schooling years but also a higher level of human capital for every year of schooling when compared to the children of poor households. In any case, the transformation of education into human capital will operate differently for different social groups.

It should be clear that this model of investment in human capital assumes that there is no one-to-one relation between schooling years and human capital in society. The same years of schooling may correspond to different levels of human capital, depending on the social group. The general rela-tion between schooling years and human capital levels produced is certainly positive; however, this relation is not unique, but will take different paths depending on the type of capitalist society.

Figure 2.1 represents the transformation of education into human capital in sigma society. There is a positive relation between years of education and levels of human capital accumulation for a given generation; however, this relationship is separate for each social group, and also hierarchical between the three social groups that we introduce in the sigma model (chapter 6, volume 1). The implication is that if the schooling years were the same, the human capital accumulated would be the highest for the social group A (the capitalist class, which includes high executives as partners) and the lowest for the group Z, with the group X in between. However, the years of educa-tion between social groups are not the same; the highest is for group A, the lowest for group Z, with group X in between.

The transformation of education into human capital, therefore, trav-els along separate and hierarchical trajectories, indicating the differ-ences in both the quality of students and the quality of the schools. The Z-population will have access to public schools of the lowest quality (say public rural school), while the A-population will study in exclusive private schools, and the X-population in public schools of a better quality than


the Z-population schools (say, urban public schools). There is segregation in the school system. The economic and political elites in sigma society do not care for the quality of public schools because their own children’s education is not affected by that. Therefore, the difference in trajectories also reflects this particular form of functioning of democracy in the sigma society. Citizens of different classes have access to public goods of different categories. Therefore, transformation of education into human capital does not take the same form, along the same trajectory, for all social groups, in sigma society.

In epsilon and omega societies too, which are socially homogeneous soci-eties, transformation from education into human capital will operate along hierarchical trajectories. In these societies, the Z-population does not exist; therefore, Figure 2.1 would now show only two curves, one for social group A and the other for group X, but still separate and hierarchical, reflecting the social class structure of these societies.

These relationships imply that in any type of capitalist society, the educa-tion process is not conducive to equalization in the human capital of social groups. The poor and the rich accumulate human capital along different and hierarchical paths. Even if the social groups reached equalization in schooling years, it would not imply equalization in human capital.

A

X

Z

O m n r

H

G

F

Years of education

Human capital

Figure 2.1 Relations between education and human capital, by social groups A, X, and Z, in sigma society.


In sum, the model predicts that in every type of capitalist society (epsi-lon, omega, or sigma), children will inherit the relative position of their par-ents in the human capital distribution. In the education process, the initial human capital gaps between social groups are not eliminated endogenously. Because there exist ceilings to education years, inequality in education years between social groups may become equalized, but human capital will not. Thus, the education process is not human capital equalizing. In the process of human capital accumulation, there is path dependency, that is, initial socioeconomic conditions of households do matter.

Formal education produces human capital—production skills embod-ied in workers. But this is not the only mechanism to accumulate human capital. After formal education, workers accumulate human capital contin-uously induced by the new technologies, and skills learning will take the form of on-the-job training and others. Assume that human capital learned through these nonformal systems of education will maintain the same order of human capital acquired in the formal school system. Years of schooling and socioeconomic status are therefore the basic determinants of differences in human capital among individuals.

Transforming Human Capital into Income

The question now is to explain the process by which human capital is trans-formed into income. The model of human capital accumulation presented here will now be integrated into the models of epsilon, omega, and sigma theories.

Wages and Human Capital in Labor Markets

Given that human capital and schooling are not equivalent, do firms buy education or human capital in the labor market? Consistent with their ratio-nality of profit maximization, firms will buy human capital in the labor market, which is the relevant factor for productivity and profits. Each level of human capital (not level of education) will then constitute a particular labor market. Furthermore, in a competitive labor market, wage rates will be uniform for the same level of human capital, not for the same level of education.

The observation that firms pay different average wage rates to workers with equal years of schooling does not constitute a case of wage discrimina-tion, as the literature sometimes describes it. According to our theoretical models, wage discrimination exists if, and only if, different levels of market wage rates correspond to workers with similar human capital levels.


Could market wage discrimination for a given human capital exist? As Gary Becker (1971) argued, market competition will tend to eliminate wage discrimination. If firms hire the workers who are more expensive, then they are not minimizing costs. However, there may be cases in which market equilibrium with wage discrimination does exist.

Consider a sigma model in which X-workers and Z′-workers (a subgroup of Z-workers) have equal levels of human capital. Why would Z′-workers be paid less than X-workers in the market? The origin of this discrimi-nation could come from factors other than human capital, such as eth-nic prejudices. Firms could have little confidence on the competence of Z′-workers; hence, hiring these workers will imply higher transaction costs for the firm and market wage rate would be lower just to compensate those costs. This wage discrimination would tend to operate only in the short run. In the long run, as Becker said, market competition will tend to elim-inate discrimination.

Therefore, the empirical prediction of the sigma model is that the low wages of Z-workers relative to those of X-workers originate mainly from differences in human capital endowments rather than from practices of wage discrimination. Profit-maximizing firms will have incentives to pay the same wages for equal human capital level, which rules out discrimina-tion. Differences in human capital in turn originate in forms of exclusion in the education process. As shown earlier, this exclusion takes two forms: exclusion from good-quality education (less human capital per equal years of education) and exclusion from the quantity of education (less years of schooling).

According to this model, labor markets operate on the basis of human capital, not schooling years. Labor productivity depends on the former, not on the latter. Hence, profit-maximizing firms will generate hierarchical labor markets based on the human capital level of workers, in which wage rates will be higher in labor markets for higher human capital levels. The impli-cation is that profit-seeking firms cannot suffer from “school-years illusion” or “credential illusion.” Therefore, in the labor market, those X-workers and Z-workers that have the same years of education will not get the same wage rate: Z-workers will be paid less because they have lower human capital level. This difference cannot be attributed to wage discrimination practices in the labor market.

The Role of Social Networks

Labor markets operate with excess labor supply in all types of capitalist soci-eties, as shown in the models developed in chapters 4–6, volume 1. The


mechanism of exclusion from the labor market was assumed to be random in those models. Now introduce the assumption that the mechanism of exclusion is not random, but based on social networks.

Social networks also constitute assets, which are distributed among indi-viduals according to the initial distribution of economic and political assets: It is low for the poor and high for the rich. The reason is that exchange of favors within a social network takes the form of reciprocity, which requires similar wealth levels among its members. Given the same level of human capital, X-workers who have high social networks will be more likely to get selected for wage employment than Z′-workers. Hence, differences in socio-economic background will have an additional effect in generating income differences among workers with the same level of human capital, as the probability of getting wage employment (and avoiding self-employment) depends on that background.

Social networks also play a role in doing business. Capitalists and the self-employed in small businesses use their (different) social networks, which give them more advantages while conducting business deals with the owners of large firms. Credit and insurance markets are quasi-Walrasian markets (Figueroa, 2011), as they operate with inclusions and exclusions of buyers. Inclusion-exclusion in the credit and insurance markets is based upon dif-ferences in wealth and in social networks, which again prove to be more advantageous to the wealthy.

For example, according to the sigma model, the income gap between social groups X and Z does not come from the fact that professionals of group Z receive a market wage rate that is lower than that of group X (wage discrimination), but from the fact that the proportion of Z-workers who are professionals is lesser, among them those with a high level of human capital is also less, and their social network effect is smaller than that of the X workers. In addition, the social group A will have higher human capital and higher social network than the X-workers and Z-workers. This model predicts that the income differences between social groups A, X, and Z will be more than proportional to differences in their years of education.

The overall conclusion is that the education process does not lead to income equalization because the system is neither human capital equaliz-ing nor social network equalizing. This conclusion is valid for any type of capitalist society. Given the exogenous variable initial inequality in the dis-tribution of economic and political assets, there are no mechanisms that can modify this result; neither the market nor democracy, the basic institutions of capitalism, can do that.


Beta Propositions

Given the short-run general equilibrium (chapters 4–6, volume 1), in which prices and quantities have been determined, we can now explain the dif-ferences in personal incomes assuming that the education endowments of social groups are exogenously given. First, consider the sigma model. The structural equations of the education model and the corresponding reduced form in a sigma society can be written as follows:

h = F (E, S), Fi > 0, where S = (Z, X, A) (2.1)y = G (h, S), Gi > 0 (2.2)y = Φ (E, S), Φi > 0 (2.3)

Equation (2.1) shows the transformation of education (E) into human cap-ital (h) for each of the three social groups contained in the qualitative var-iable S, social background. The effects of these variables are positive. The second equation shows the transformation of human capital into income (y) for each social group. Equation (2.3) is the reduced form of the system: it shows the transformation of education into income for each social group. Income increases with years of schooling, and given the number of years of schooling, it increases with the order of the social background. The degree of the initial inequality (δ) is held constant and underlies the structure of the qualitative variable S.

Figure 2.2 shows the reduced form equation and thus the empirical pre-diction of the model. Income level is measured in the vertical axis and years of education in the horizontal. Line Z shows the increase in income associ-ated with the increase in education for the Z-population of the same gener-ation. Line X corresponds to X-population and line A to A-population. The income-education curve is separate and hierarchical by social groups. The same number of years of education implies different income levels, depend-ing upon the social background.

Furthermore, the endowment of the number of years of schooling varies among social groups. For the current generation, let these endowments of education be given by point m, n, and r, reflecting difference in the initial wealth among social groups Z, X, and A; therefore, the income gap among social groups is due to differences in education (E) and social status (S), that is, incomes increase more rapidly relative to years of schooling, as shown by the rising line L. This is the short-run general equilibrium situation.

Exogenous increases in schooling years in each social group will shift the line L outward. Incomes will not be equalized as each social group


moves along different paths. Even if only Z-workers increased the aver-age years of schooling exogenously, incomes will not be equalized among social groups; moreover, even if Z-workers and X-workers had the same schooling years exogenously of the social group A, their incomes will not be equalized. Therefore, the school system is not income equalizing because it is not human capital equalizing; it is not social network equal-izing either.

Note that group A refers not only to the capitalist class, but also includes high-ranking executives as their partners. Given that the proper capitalist class is very small, group A’s education refers mostly to the schooling years of the high-level executives. There is another reason why the school system cannot be income equalizing: the income of the capitalists comes mostly from property. Education operates as a mover for workers alone; but workers will not be able to equalize their income to the level of the economic elites or become part of their social network through education. This is what the education model predicts.

Considering the short-run general equilibrium in epsilon and omega models, equations (2.1)–(2.3) will remain the same, except that S = (X, A). Figure 2.2 would show only two lines, and curve L would have only two

A

Z

X

y

E

r´

n´

m´

rnmO

L

Figure 2.2 Income (y) and education (E) relationships, by social groups A, X, and Z, in sigma society.


points. However, the role of education in the determination of personal income would be similar to that of sigma society.

Figures 2.1 and 2.2 allow us to define analytically the content of the equal opportunity principle in the education process: A unique education-human capital-income path should exist in society. In a sigma society, for example, equal opportunity means that the three curves A, X, Z are some-how reduced to only one, that is, it implies the shifting of the X and Z curves onto curve A. Only then, the same years of education would imply the same human capital level and the same income for all social groups.

This would need intervention through public policies. In a sigma society, governments do not have the incentive to carry out such policies. Z-workers are second-rate citizens and thus have no political voice to push governments toward this policy. Governments act motivated by maximizing votes in the next elections, that is, in the short run. Accordingly, governments will seek to supply workers’ children with more years of education, inaugurating more school buildings, which is politically more profitable in the short run. This policy will imply maintaining the separate trajectories for different social groups.

Can workers get equal education opportunity policies through collec-tive action? Collective action is subject to several constraints. The Olsonian problem of the free rider behavior is one of them (Olson 1965). In particular, Z-workers are too poor to finance collective actions for such complex set of development policies. Finally, Z-workers are socially excluded; they are second-rate citizens, with no political voice, which makes collective action less likely to succeed. Therefore, the trajectories shown in figures 2.1 and 2.2 are indeed the equilibrium situation in sigma society.

In the case of epsilon and omega societies, governments and the people will interact to implement policies of equal opportunity; the democratic sys-tem is more participatory because citizenship degree is homogeneous (only classes A and X). Education may take the form of public service for all; if private firms also supply education service, credit markets become less restrictive to finance education, which goes toward creating equal opportu-nity policies. Nevertheless, the initial inequalities in the endowments of eco-nomic assets (including here physical capital ownership and social networks) will not allow the curve X to get shifted onto the curve A. Then workers will advance in years of education, but along different paths.

The exogenous variable of the model in each type of capitalist society is the initial inequality in asset endowments among individuals (δ). As long as inequality in the distribution of economic and political assets remains constant, the differentiated paths will also remain unchanged. If this initial inequality were reduced, then the effect of the socioeconomic background


of the student would also be reduced; the education process would still fol-low different paths, but along closer paths between social groups. A stronger reduction in the initial inequality, such as citizenship equalization in sigma society, may transform the social structure of three groups to two, as sigma society would become omega society.

The models of education theory in epsilon, omega, and sigma societies, under short-run general equilibrium, when education endowments are exog-enously determined, predict the following empirical relations:

1. Income differences between social groups will be more than propor-tional to the difference in years of schooling (curve L in figure 2.2).

2. Learning levels are hierarchical. They are higher in schools attended by students from a higher socioeconomic background.

3. A higher degree of concentration in economic and political assets will increase the income gaps in points 1 and 2.

Empirical Consistency: The Capitalist World

The empirical predictions derived from the model of the theory of education must be confronted now against the facts shown in the international empir-ical literature. However, the available data are very limited.

Regarding beta proposition (1), a study on Peru, a sigma society, which is based on the national household survey of 2003, found that education levels varied by social groups, and the differences were statistically significant, in which the indigenous population represented social group Z, the mestizo social group X, and the white social group A. The mean years of schooling among adult populations were 7.6, 11.4, and 14.2 respectively, which implies differences of 1.5 and 1.2 times; differences in mean income were 1.9 and 2.0 times (Figueroa, 2010, Table 3, p. 122). This result is consistent with the prediction that income differences between groups are higher than dif-ferences in years of schooling. However, this is just a single observation and has no statistical value to refute or accept the model. This beta proposition will be pending refutation until more evidence that is empirical becomes available.

As to prediction (2), the surveys of Program for International Student Assessment (PISA) provide a relevant database for international compari-sons. This survey measures learning levels at school using the performance of 15-year-old students (having similar years of schooling) in reading, math-ematics, and science tests applied in the OECD countries and other partici-pating countries. The 2009 results (OECD, 2010) showed a big gap between the First World and the Third World. From the 16 Third World countries,


only South Korea and Singapore (omega societies) showed average marks that are comparable to those of the First World; in the other 14 countries (sigma societies), the marks were well below the average.

If the comparison was made between students of the OECD countries with students from the elites in the Third World, the gaps would possibly be less significant. Then the observed differences would come mostly from the presence of students of social group Z in the Third World, which greatly reduces the national average. Although the report does not present this test, it states: “Socio-economic background of students and schools does appear to have a powerful influence on (test) performance” (p. 5). Prediction (3) is pending data availability.

Biologist Jared Diamond (1999) has included written language as one of the explanatory factors for Western superiority. In trying to explain why the Spaniards conquered the Incas and Aztecs, and it did not happen the other way around, he includes written language. He says, “Writing marched together with weapons, microbes, and centralized political organizations as a modern agent of conquest” (p. 216). This empirical fact is in accord with the prediction of the model about the significance of written language over oral languages. The colonial legacy of language inequalities is thus consis-tent with the data showing low test performance in the Third World, as shown by the PISA data. European colonialism has created a hierarchy of languages and cultures in the capitalist system.

Given that the available information, even though limited, does not con-tradict the predictions of the model, there is no reason to reject the theory at this stage of our investigation, and we may accept it provisionally until more evidence that is empirical or a better theory appears.

Conclusions

An economic theory of human capital formation based on the workings of formal education has been presented in this chapter. The basic assumption of this theory is that the education process is not uniform in the capitalist society. The initial inequality in the distribution of economic and political assets among individuals creates social classes and citizenship classes, which in turn leads to separate and hierarchical paths of education-human capital-income for every social group.

A model of this theory has been included in a short-run general equi-librium situation of the three types of capitalist societies. The exogenous variables are education endowments and initial inequality. Changes in edu-cation endowments, maintaining the initial inequality constant, do not lead to human capital equalization or to social network equalization; hence, the


model predicts that the education system is not income equalizing. The empirical evidence tends to be consistent with this prediction, although available data are limited. Even though these facts are now limited, there is no reason to reject the theory, and we may accept it at this stage of our research, although only provisionally, until new empirical evidence or a bet-ter theory appears.

Dynamic models are needed to study the education process when edu-cation and human capital accumulation are endogenously determined. However, introducing the simple assumption that schooling years depend upon real income of households, it follows that the rich accumulate more human capital than the poor. Higher income leads to higher schooling and a higher level of human capital, which in turn lead to higher incomes, and so on. This leads to a dynamic equilibrium situation: the education process operates in this manner, along different paths for the rich and the poor, period after period, as long as the exogenous variable (initial inequality in economic and political assets) remains unchanged. In any type of capital-ist society, therefore, the education process tends to reproduce the initial inequality of society. Models that are more complex are presented next, but this relation will still hold true.

The static model is able to provide a definition of equality of opportu-nity in the educational process: the education-human capital-income rela-tionship is meant to travel along a unique trajectory for all social groups. But, this is certainly not what happens in the real world. Particularly in the Third World, governments publicize high rates of school enrolment among the poor, but hide the fact that these children are traveling along different paths when compared to the children of wealthy families. The rationality of maximization of votes for the next elections could hardly lead governments to apply the equal opportunity policies, which is a long-term endeavor, with effects beyond the next election period. Their actions reveal their prefer-ences: governments just do not have the incentives to do it.

Differences in the quality of schools reflect differences in the position of households in the initial inequality. (This is similar to the low quality of public health and transportation services, when the elites attend private clin-ics and travel in their private cars.) The model presented here thus explains why the formal education system is not income equalizing.

The education process produces two types of output: human capital and general knowledge, including here knowledge about social norms and citizenship. The education system does not lead to human capital equal-ization, as shown in this chapter. In addition, the education process in the Third World seems to reproduce implicitly the social norms of citizen-ship inequality as well. Education does not tend to equalize citizenship.


This is ref lected in the culture of inequality that is observed in the Third World.

As indicated in chapter 2 (volume 1), Facts 6 and 7 refer to the existence and persistence of differences in income levels and in the degrees of income inequality between the First World and the Third World. The three partial theories were able to explain the prevalence of differences. Epsilon has the highest income level, sigma the lowest income level, and omega lies some-where in between, which is due to their differences in factor endowments, including here human capital. Sigma society has a higher degree of income inequality than the others due to their differences in the initial inequality. The persistence question calls for long-run and dynamic models of output growth and distribution in which physical and human capital accumulation will be endogenous. These dynamic models for epsilon, omega, and sigma societies taken separately, together with a unified model for the capitalist system taken as a whole, will be presented in the following chapters.

CHAPTER 3

The Epsilon Society: A Dynamic Model

This chapter will start with the study of growth and distribution in the capitalist system. Long-run dynamic models for each type of society will be constructed. Environmental interactions with the economic

process will be ignored in these models. We discuss the epsilon dynamic model in this chapter.

Epsilon is an underpopulated and socially homogeneous capitalist society. As shown in chapter 4 (volume 1), the static general equilibrium implies pos-itive rates of unemployment because unemployment constitutes the device for labor-effort extraction. The initial condition of the dynamic model that follows assumes general equilibrium with effective full employment, where unemployment rate is just the necessary rate. Money is thus neutral. Hence, the labor market alone constitutes the core of general equilibrium.

Output Growth in Epsilon Society

In order to derive more operational relations, the dynamic model will assume a production function of the Cobb-Douglas type. In the capitalist sector, the only sector in the epsilon economy, the production function will take the following form:

Y = Kα (AL)1–α, 0<α<1 (3.1)

The term Y is total (net) output, K is the stock of physical capital, A is the level of technology, and L is the quantity of workers employed. This production


function assumes constant returns to scale. Labor-augmenting technological change is also assumed, which means that technology increase raises output in a way that is equivalent to an increase in the quantity of labor. Capital goods are measured in units of good B, the only good produced in this society (but the subscript b will be dropped for simplicity).

Technological change is exogenously determined and grows at the rate equal to g, that is, assume ΔA/A=g. However, technology adoption is endog-enous and depends upon the level of human capital of workers (h). The assumption is that workers need high skills to use more advanced capital goods and practices in which new technologies are incorporated. Then

A = f (h), f ′>0 (3.2)

Substituting in equation (3.1), and just simplifying equation (3.2) to the linear form A=τh, and letting τ=1, equation (3.1) becomes

Y = K α (hL)1–α, 0<α<1 (3.3)

In this equation, h is the average skill of the L workers, and hL is then total human capital. The same quantity of workers will produce more output if their average human capital is higher, for more human capital allows them to adopt new technologies (increases A).

At this point, the model will follow the standard textbook procedure, which is to find the dynamic equilibrium in the form of steady state equilib-rium. The following variables are thus introduced and defined as follows:

k ≡ K/hL = (1/h) (K/L) = (1/h) k (3.4)y ≡ Y/hL = (1/h) (Y/L) = (1/h) y = k α (3.5)

The term k indicates the ratio of physical capital to human capital and y is output per human capital; in addition, k is capital per worker and y is output per worker.

The steady state condition is that Δ k = 0. If it were not zero, the value of k would keep changing until steady state is attained. This condition can then be written as

Δ k / k = ΔK/K – Δh/h – ΔL/L = 0 (3.6a)ΔK/K = Δh/h + ΔL/L,

where physical capital accumulation takes the form

The Epsilon Society: A Dynamic Model l 31

ΔK/K ≡ I/K = eY/K, 0<e<1 (3.6b)

Here letter I means net investment and e is the investment rate. The invest-ment ratio e may be equal to the domestic savings ratio, but it is not necessary because, in an environment of perfect mobility of capital, domestic invest-ment could be higher or lower than domestic savings. Then

e Y/K = Δh/h + ΔL/Le y/ k = Δh/h + ΔL/Le y = (g + n) k (3.7)

where g is the growth rate of human capital per worker (equal to the growth rate of technology in equilibrium, as will be shown next) and n the growth rate of population or workers. This equation indicates the steady state condi-tion of the dynamic model.

Figure 3.1 shows the steady state condition. The quantity of physical cap-ital that society is willing to add is represented by the curve M, whereas the quantity of physical capital required to keep the amount of physical capital per human capital constant is represented by the curve N. The steady state condition implies that both curves must cross each other, which occurs at point E , and indeed Δ k =0. The equilibrium values k* and y* are derived from the equilibrium condition. The values of the two endogenous variables

R

N [g + n]

M [E,e]

y

F~

*~y

E~

k~*~

k

Figure 3.1 Steady state equilibrium in epsilon society.


are in equilibrium as they will be repeated period after period, as long as the exogenous variables remain unchanged.

The steady state condition implies that the quantity of physical capital that society is willing to add in each period must be equal to the quantity that society requires in order to maintain constant physical capital per skilled worker (K/hL). As seen in equation (3.6a), this constancy implies additional capital in two parts. The first part would be as if the skill level were fixed, which then implies that additional capital should grow at the same rate as population, at the rate n; the second part includes the fact that skills grow at rate g, which implies that additional physical capital needed to keep physical capital per skilled worker constant should grow at the rate n+g.

Equilibrium is stable. If the value k were below that of equilibrium, then society would be accumulating more physical capital than is required and thus the ratio of physical capital per human capital would increase, produc-ing higher output per human capital, and physical capital would increase further, and so on, until the equilibrium is reached. In a similar manner, if the value k were above that of equilibrium, then society would be accumulating less physical capital than is required and thus the ratio of physical capital to human capital would decline and through the adjustments the equilibrium value would be reached.

Any initial value of y that is below equilibrium will therefore reach the equilibrium value y* spontaneously. This is the transition dynamics. Moreover, in this model, the higher the gap with equilibrium, the higher the growth rate and the higher speed of convergence to equilibrium (Barro and Sala-i-Martin, 2004, Chapter 1, Appendix). This relation may be called the conver-gence theorem.

By solving equation (3.7), and using equation (3.5), we get the following equilibrium values of the steady state endogenous variables:

k * = (e/g+n)1/1–α (3.8a)y* = k α = (e/g+n)α/1–α (3.8b)

The latter equation can be written in terms of output per worker (y) as follows:

y*(t) = y* h(t) = (e/g+n)α/1–α h*(t) (3.9)

This equation shows the dynamic equilibrium of output per worker, which is determined by the dynamic equilibrium of the accumulation of human capital.


How does accumulation of human capital take place?Higher human capital implies that workers have learned higher skills that

enable them to use modern machines and practices. The model will assume two mechanisms for learning skills. First, education or schooling years (E) increases human capital, for this is where the basic knowledge (numeracy and literacy) to learn skills is built up, as shown in chapter 2 of this volume. Without schooling no skills can be learned to operate new machines, and we would have only raw labor, that is, hL=L. Second, skills are learned outside for-mal education (on the job training) because there is much to learn due to the continuous increase in technology. If technology remains unchanged, there would be nothing new to learn, and thus no new skills would be needed, and more education would be useless. The economist Theodore Schultz (1975) suggested that the value of education as human capital depends upon the supply of new technologies.

Combining both mechanisms for accumulating human capital, the model assumes that workers learn skills according to the following relation

h = f (E, A), fi>0 (3.10)

The term A here denotes the index of the most advanced capital goods and productive practices invented to date. Call it the technology frontier. According to this equation, given E, skill learning is tied to the growth of technological knowledge; given A, learning skills depends upon schooling years. Following the procedure suggested by Jones (1998, Chapter 6), this equation can also be written as follows:

Δh = f (E, A, h), fi>0 (3.11)

The increase in skills depends not only on E and A, but also on the initial level of h. Dividing by h, we assume the following relation:

Δh/h = F (E, A/h), Fi>0, Fii<0 (3.12)

The growth rate of skill learning is higher, the higher is the value of E, and the higher is the value of A/h. The latter term denotes the gap between the tech-nology frontier and the initial level of h, which shows the gap to be learned. The effect of both factors upon the growth rate of human capital is then posi-tive, but subject to diminishing returns.

Figure 3.2 depicts the model of dynamic human capital accumulation. Curve CD represents equation (3.12) and the equilibrium situation is given


by point P, with (A/h)* as the equilibrium value, at which human capital has the same growth rate as that of technology (g). The equilibrium gap will be repeated period after period, as long as the exogenous variable (E) remains unchanged.

This equilibrium condition is stable. If (A/h)>(A/h)*, then g<Δh/h, which implies that (A/h) will decline, and the adjustment process will restore the equilibrium position. Similar adjustment would occur if (A/h)<(A/h)*. An increase in E will shift the curve CD to C′D′ and point P′ will be the new equilibrium position, with (A/h)*′ as the new equilibrium value. The gap between the technological frontier and society’s capacity to adopt new tech-nology thus decreases. Society is closer to the technology frontier. An increase in E moves the equilibrium from (A/h)* to (A/h)*′. Nevertheless, at the new equilibrium, human capital will still grow at the same rate of technology change; hence, E has level effect, but not growth effect.

From the process of technological adoption, equation (3.2) above, let the initial condition of human capital level be h0, which implies

A0 = f (h0) (3.12a)

Then equation (3.12) becomes

Δh/h = G (E, A/A0), Gi>0 (3.13)

D´ [E´ ]

D [E ]

∆h/h

C´

∆A /A

C

(A/h)*´ (A/h)*

P´ P

A/h

Figure 3.2 Human capital accumulation in epsilon society.


Thus, the growth of human capital depends upon the gap between the most advanced technology (A) and the current technology level in use (A0), which was adopted with the current skill level (h0). The higher the gap in technol-ogy, the higher the growth rate of human capital because there is a lot of learning to happen. To recall, the model assumes that the growth rate of tech-nology (g) is exogenously determined. Given E, the steady state condition implies that the ratio A/h must remain constant, and equal to (A/h)*, which implies Δh/h = ΔA/A = g.

It should be noticed that this model deals with two processes: first, the technological adoption process—equation (3.12a)—in which adoption of new technologies depends upon the skill level of workers; and second, the skill accumulation process—equation (3.13)—in which the increase in skills depends upon the increase in the technology frontier. The interaction between the two processes is thus a feature of the model.

Figure 3.3 shows these two processes. Line G represents equation (3.12a), assuming a linear function, whereas line F represents equation (3.13), for a given value of E. Technological adoption moves along line G and skill accu-mulation along line F. At the initial value h0, the technology level that can be adopted is A0 (point M); so the technological gap is A/A0. If A remains

A

SGN1

N

h

R

M1M

F [E ]

h1h 1́

A1́

h0

A´

A0

A1

O

A

F´ [E´]

Figure 3.3 Interactions between technological adoption and human capital in epsi-lon society.


constant, point M will be the equilibrium situation and will be repeated period after period. If A increases exogenously to A′, learning of skills will increase (proportionally) to point N1, which implies h1, for there will be more new knowledge to learn; with h1 more new technology will be adopted by society, reaching point M1, which implies reaching the new level A1. In this process, the gap between society’s technology and the technology frontier remains unchanged, that is, A/A0=A′/A1.

What keeps society from reaching the technology frontier? The answer is given by equation (3.10). Learning skills do not depend on the availability of new technology alone, they also depend on the schooling years, for edu-cation provides the basic tools to learn skills (e.g., numeracy and literacy). Consider again the point N1 in figure 3.3 as the equilibrium point in human capital accumulation. If E increases, then the capacity to learn new skills will increase, which implies that line F will shift outward to line F′; thus the new equilibrium will be at point S, which implies a much higher level of human capital (h1′), with which society will be able to adopt a higher technology level (A1′). The technological gap will then be reduced (A′/A1′<A′/A1). From the new equilibrium point S, both technology and skills will grow at the same rate. Therefore, change in E has level effect, but not growth effect; the latter is determined by the growth rate of technology (g). In sum, the limit to reach the technology frontier is given by the level of formal education of workers.

From the relations shown in figure 3.3, it follows that the dynamic equi-librium of human capital can be written as

h*(t) = f (E; g, t), fi>0 (3.14)

Substituting equation (3.14) into equation (3.9), we get

y*(t) = F (n, e, E; g, t), F1<0, and Fi>0 otherwise (3.15) = F (y0*; g, t), Fi>0

Equation (3.15) represents the dynamic equilibrium of output per worker. The curve over time described by this equation is be called the growth frontier curve.

Figure 3.4 represents the dynamic model of epsilon. The dynamic equi-librium is given by the curve MN. The equilibrium value of y* shown in fig-ure 3.1 is now mapped into curve MN. Curve MN is the growth frontier of epsilon. This curve has two types of determinants: those that determine the curve level and those that determine the slope of the curve, its growth rate. The exogenous variables n, e, and E have level effects, as they determine the value of the intercept (y0*), marked as point M, whereas g has a growth effect,


as it determines the growth rate of MN. Output per worker grows endoge-nously over time.

The growth rate of output per worker along the frontier curve is then

Δy*/y* = ΔA/A ≡ g = Δh/h = ΔA0/A0 (3.16)

Note that ΔA/A ≡ g means that the growth rate of technological change is constant and equal to g. The effect of g is significant in determining the growth rate of output per worker, which in the steady state or dynamic equi-librium is equal to the growth rate of human capital per worker and equal to the growth rate of technology adoption. So, along the curve MN, the tech-nology gap (A/A0) will remain constant.

Beta Propositions

The dynamic equilibrium is stable, as shown by the steady state stability in figure 3.1. If output per worker is for some reason out of its dynamic equilib-rium, there will be a spontaneous adjustment to reach the equilibrium path. This adjustment trajectory is the transition dynamics. Suppose the initial output per worker is y0, such that y0<y0*. Then, the time path of y(t) showing the transition dynamics can be written as follows:

y (t) = f (y0*, y0, g, t), fi >0, y0 < y0*, t ≤ t* (3.17)Δy/y = F (g, y0*/y0)>g, Fi >0, y0 < y0*, t ≤ t* (3.18)

N [g]

N´

M

O t

[e,n,E ] y *

[k 0] y0

y

Figure 3.4 Growth frontier and transition dynamics in epsilon society.


The transition dynamics is also shown in figure 3.4 by the curve starting at y0 and ending at point N′, which lies on the growth frontier. This curve has a positive slope and grows at a rate that is, on average, higher than that of the growth frontier. This is obvious: if the initial value y0 grows at the same rate as that of the frontier it will never catch up; so it will have to grow faster. Moreover, the higher the gap y*/y0, the higher is the growth rate of the transi-tion dynamics. This comes from the convergence theorem mentioned earlier. It is as if the point of catching up took place at approximately the same time on the frontier, independent of the starting point; so if the starting point is farther from y0*, it would have to travel at a higher speed.

Comparative dynamics can easily be determined from equations (3.15) and (3.16), together with the help of figures 3.1 and 3.4. It follows that:

1. Higher e causes higher income level (y*): The growth frontier curve will be shifted upward. An increase in e implies new equilibrium values of k* and y*, that is, both will increase (as can be seen figure 3.1), which implies a higher growth frontier curve. As can be seen in figure 3.5, the initial growth frontier curve is MN, in which the value of variable e is constant. If e increases at period t ′, then the growth frontier curve (dynamic equilibrium curve) will be shifted upward to M′N′, main-taining the same growth rate. Now situation C is out of equilibrium, so output per worker will move spontaneously toward the new equilib-rium (frontier M′N′); hence, CD′ corresponds to transition dynamics. Higher investment rate has only a level effect upon the growth frontier, but it is followed by a temporary growth at a rate that is higher than that of the frontier.

2. Lower n causes higher income level (y*): A fall in n has the same effect as an increase in e, as shown in figure 3.5. Therefore, CD′ will also represent the transition dynamics.

3. Higher E causes higher income level (y*): The growth frontier will be shifted upward. As shown in figure 3.2, more years of education will have only level effect and no growth effect. Segment CD′ will repre-sent the new transition dynamics in this case too.

4. Lower y0 causes higher growth rate in output per worker: A lower initial output per worker will imply a higher gap between this value and that of the frontier and, according to the convergence theorem, the tran-sition dynamics will move at a higher growth rate. In short, poorer epsilon societies will grow faster than richer epsilon societies.

In sum, the individual effects of the exogenous variables upon income level and the growth rate have been solved and the partial derivatives have given


the necessary justification. These are the beta proposition or the causality relations of the epsilon model.

Distribution in the Economic Growth Process

What Happens with Income Distribution along the Growth Process in Epsilon Society?

In the epsilon model, there are only two social groups: capitalists and workers. What part of national income goes to each group corresponds to the functional distribution question. The average profit of the capitalist class and the average wage rate of the workers correspond to the personal distri-bution question. Both functional and personal distributions determine the overall degree of income inequality in society, which is shown by the standard Lorenz curve and the corresponding Gini coefficient measures.

In the competitive market model, prices are uniform, including wage rates. Firms seeking profit maximization will pay a uniform real wage rate (w), which is equal to the marginal productivity of labor (∂Y/∂L). From the Cobb-Douglas production function—equation (3.1)—shown before, this condition can be written as follows:

w = ∂Y/∂L = (1 – α) y (3.19)

D´

M´

O t

y* ´

y

My* C

t´

D

N [g]

N´ [g]

Figure 3.5 Effect of higher investment ratio on the growth frontier in epsilon society.


In this type of production function, the marginal productivity of labor is a constant fraction of the average labor productivity; so the market real wage rate is a constant fraction of output per worker. This result implies that labor share is a constant fraction of national income:

W/Y = w L/y L = w/y = (1 – α) (3.20)

The share of profits in national income can be written as

r = ∂Y/∂K = α Y/K (3.21)P/Y = r K/Y = α (3.22)

The first equation in this set says that the rate of return of capital (r) is equal to the marginal productivity of capital, which is constant because the ratio Y/K will remain constant as a dynamic equilibrium condition. The second equation says that the profit share is also a constant.

In sum, each factor of production will receive its marginal productivity. It is another property of the Cobb-Douglas production function that if each factor of production is paid its marginal productivity, the total output will be exhausted (Euler’s theorem). Therefore, these four equations can be taken as equilibrium conditions in the distribution of income. It will prevail under any solution of the market system, including dynamic equilibrium.

How about personal distribution? The real wage rate (w) is also the aver-age income of workers. The average real profit of capitalists (p) is defined as follows: p=rK/L′, where L′ is the population of capitalists. The model will assume that capitalists also receive wages for they work in their firms. If they lose their capital, they can still get wage incomes. The model also assumes that L′ is a small proportion of L (say, around 1 percent) and concentrates most of the ownership of physical capital (say, 90 percent). Thus, the distri-bution of the remaining 10 percent of profits among the 99 percent of the population will not alter the results of overall income distribution.

The growth rates of both average incomes will be

Δw/w = Δy/y (3.23)p = r K/L′ (3.24a)Δp/p = ΔK/K – ΔL′/L′= ΔY/Y – ΔL/L = Δy/y (3.24b)

The first equation is derived from equation (3.20) and says that the average wage rate grows at the same rate as output per worker. The second and third say that this is the same with the growth of average profits going to capitalists,


assuming that the population of capitalists and the population of workers grow at the same rate. Although the profit rate (r) is constant, the amount of capital increases in the process of growth, which explains the growth in the average income of capitalists.

In the process of economic growth of this epsilon model, therefore, the personal income distribution will also remain constant. This holds true for the dynamic equilibrium (along the growth frontier curve) and also for the transition dynamics. In each case, the wage rate will grow at the same rate as output per worker in both cases, which implies constant functional distribution.

Consider the following example to illustrate the process of growth and distribution, as shown in figure 3.4. Along the growth frontier, total output grows (say at 50 percent per decade) at the same rate of capital stock (50 per-cent) and thus the growth rate of human capital (30 percent) and labor sup-ply (20 percent) combined is also 50 percent. Output per worker will then grow at 30 percent per decade.

Suppose the society has a current output per worker that is below that of the frontier. Then in the transition dynamics to the frontier, capital stock will grow at a higher rate (say 70 percent per decade) and, due to diminishing returns, it will decline over time until it reaches the value of 50 percent (the stability condition, shown in figure 3.1); thus output per worker will grow at the average rate of 40 percent in the transition dynam-ics. Because the real wage rate is equal to a constant fraction of output per worker, it will grow at the same rate of output per worker, that is, at the rate of 40 percent in the transition dynamics and at 30 percent along the growth frontier curve. Income distribution remains unchanged in both cases.

Therefore, income inequality (D) will remain unchanged in the economic growth process, given the initial inequality in the distribution of economic and political assets (δ). This is the only exogenous variable in the model. What are the mechanisms that prevent the change in the initial inequality along the growth process? Two mechanisms have been shown in the growth process: the private property rule of inheritance and the human capital accu-mulation, as they both depend upon the initial inequality. The capitalist class has other mechanisms as well to protect their membership in the privileged position, which include the following: (a) the wealth size advantage, which implies capacity to invest in high-risk projects, access to credit and insurance markets, and influence on government policies; and (b) social networks con-stituted by wealthy people for protection against uninsurable risks (Figueroa, 2008). Therefore, the initial inequality will not be endogenously altered in the growth process; thus, the initial inequality is an exogenous variable in the


dynamic epsilon model. This assumption will also be applied to the omega and sigma societies later on.

What is the effect upon income inequality when the initial inequality (δ) changes exogenously? Personal inequality does depend upon the distribution of assets among individuals, for a given functional distribution. Profits accrue to the owners of physical capital only. If the concentration of physical capital ownership increases even further, because, say, some small capitalists lost their property exogenously, that is, these properties were transferred to big capi-talists, then the asset inequality will be more concentrated, and total profits will go to a smaller group of capitalists, and inequality in personal income distribution will increase, which implies an increase in income inequality (D). Thus

D = G (δ), G ′>0 (3.25)

Beta propositions on income inequality can then be derived from the epsi-lon dynamic model. They are: (1) as long as the initial inequality remains fixed, income inequality will remain also fixed in the growth process, along the growth frontier curve and along the transition dynamics curve; (2) the initial inequality will remain unchanged in the growth process through sev-eral mechanisms, including private property inheritance and human capital accumulation, that is, there is no mechanism to alter the initial inequality in the growth process endogenously; and (3) exogenous changes in the initial inequality will have a positive effect upon income inequality: it will be shifted to a higher level.

CHAPTER 4

The Omega Society: A Dynamic Model

Omega is an overpopulated and socially homogenous capitalist soci-ety. As shown in chapter 5 (volume 1), the marginal productivity of the total labor supply is near zero. Thus, the Walrasian real

wage rate would be near zero, which is socially unviable. The labor market cannot operate as Walrasian and thus it will be non-Walrasian. The eco-nomic structure of the omega model includes a capitalist sector together with a subsistence sector. Part of the labor force is employed in the capitalist sector and receive wages; the rest, the excess labor supply, is unemployed or self-employed in the subsistence sector.

The static general equilibrium conditions were two. First, general equi-librium solution is sequential: the subsistence sector size is determined once the equilibrium in the capitalist sector has been determined. Self-employment in the subsistence sector is thus residual, whereas unemploy-ment is residual-residual. Second, the labor market operates with efficiency wages, which implies that the market wage rate must be higher than the opportunity cost of wage earners, which is given by the marginal income in the subsistence sector. This gap constitutes the device for labor-effort extraction.

In order to understand the growth and distribution process in omega society, consider initially the static equilibrium, as shown in figure 5.1(c) (chapter 5, volume 1). The labor market equilibrium is given by point E. The demand curve for labor has the stock of capital as an exogenous variable. Suppose the capital stock increases exogenously in this society. The effect will be to shift the demand curve HR upward (similar to the effect of an


increase in the international terms of trade) and, say, cut the effort extrac-tion curve m*n*; hence the new equilibrium will lie on the effort extraction curve. This is the effective full employment equilibrium situation, in which money will become neutral.

As more capital is accumulated, the demand curve will be shifted outward again and thus the new equilibrium situations will move along the effort extraction curve. Given the labor supply curve, as the labor demand curve shifts outward, the subsistence sector will decrease and will ultimately be eliminated. The omega society will become an epsi-lon society with a sufficiently large exogenous injection of physical capital. The question is, however, whether omega will become epsilon endogenously.

Output Growth in the Omega Society

In order to construct an omega growth model, the first task is to con-struct the growth frontier curve of omega society. The steady state equi-librium would imply solution at point m* (instead of point E) in figure 5.1 ( volume 1). This is the initial situation from which the dynamic equilibrium can proceed. Nevertheless, this is just to say that steady state implies absence of the subsistence sector or, equivalently, that the growth frontier is that of the epsilon society. Therefore, figure 3.1 (volume 2) can be utilized to repre-sent the growth frontier of omega society. The pending question before us is to explain the transition dynamics.

The Capitalist Sector

The production function for the capitalist sector of omega can be written as follows:

Q = Kα(hDh)1-α, 0<α<1 (4.1)

The steady state equilibrium will be similar to that shown in the case of epsilon society. Figure 3.1 shown in the previous chapter for the case of epsilon will also apply to omega. The quantity of capital that society is able to increase in each period must be equal to the quantity needed to keep the physical capital per skilled worker constant, that is, the growth rate of capital should be equal to the sum of the growth rate of population and the growth rate of skills (n+g).

The capitalist growth frontier will have the same characteristics we found in the epsilon model, which are re-written here just for convenience:

The Omega Society: A Dynamic Model l 45

q*(t) = F (e, n, E; g, t), F2<0, Fi>0 (4.2) = F (q0*; g, t), Fi>0Δq*/ q* = g = ΔA/A = Δh/h = ΔA0/A0 (4.3)

The first equation in this set indicates the determinants of the growth fron-tier curve. Given the initial value of the frontier (y0*) and given the growth rate (g), the value of output per worker will move with the passage of time along this particular trajectory. This equation then shows the dynamic equi-librium of the model. The second equation says that the growth rate of the frontier curve is determined by the growth rate of the technological frontier (g), which is equal to the growth rate of human capital and also equal to the growth rate of new technologies adopted in omega. These three rates are equal, which implies that the technological gap between the technology frontier and the adopted remains constant along the growth frontier curve.

In order to understand the transition dynamics of the capitalist sector in a simple way, we start with the effective full employment equilibrium in the labor market (at point g in figure 5.1(c), chapter 5, volume 1). Then, an exogenous increase in capital stock will shift the labor demand curve upward. Because there is excess labor supply, but the labor market adjustment is with the labor supply, the quantity of wage employment can increase and the real wage rate needs to increase as well. As more physical capital is introduced into the capitalist sector, the labor market equilibrium will move along the effort extraction curve, as indicated before. There are several implications for the dynamic model now: unemployment can be ignored, money will be neutral in the economic process, and the labor market will constitute the core of the general equilibrium.

In the transition dynamics, the growth rate of physical capital will be higher than that of human capital and population, taken together. Hence, the ratio of physical capital per human capital in the capitalist sector will tend to increase until it reaches the equilibrium situation, that is, figure 3.1 (this volume) also applies to the omega model. For initial values below the equilibrium ratio of physical capital to human capital, society will endogenously move to the equi-librium situation (stability condition). The only difference is that in the tran-sition dynamics, together with quantitative changes in the growth process, there exist qualitative changes, as the subsistence sector is now shrinking.

From equation (4.1), the following relations can be derived for the tran-sition dynamics:

ΔQ/Q = α ΔK/K + (1 – α) (Δh/h + ΔDh/Dh) (4.4)ΔDh/Dh = c n, c ≥ 1 (4.5)ΔK/K = g + c n (4.6)


The symbols g and n stand for the growth rate of human capital (h) and that of total labor force (L). When c=1, when all the labor force is equal to wage employment, we have the steady state equilibrium, that is, the capitalist sec-tor moves along the growth frontier curve. When c>1, we have transition dynamics, in which the value of c approaches the value of 1.

Based on equation (4.4), consider the following examples of growth rates (say, percentage per decade), in which t* represents the period in which the growth frontier is reached. The parameters are g=0.30 (which is also equal to that of human capital), labor supply, n=0.20, and α=0.5. Then:

In period one, capital stock grows faster than (A+Dh), which is the stability condition. Suppose wage employment grows at 30 percent, then total output will grow at, say, 70 percent. As a result average labor productivity grows at 40 percent (i.e., 70–30), which also applies to marginal labor productivity. Thus, the real wage rate also grows at 40 percent. The implication is that the share of employment in the capitalist sector increases and that of the sub-sistence sector falls. In period two, the growth rate of K declines, due to the effect of diminishing returns in the production function. Wage-employment also declines to 25 percent. The result is that total output will grow at 60 per-cent, which implies a growth of average and marginal labor productivity at the rate of 35 percent. Real wage rate will also grow at 35 percent.

Finally, the transition dynamics reaches the growth frontier curve at period t*. The growth rate of K is 50 percent, the combined growth of A and L=Dh is also 50 percent (30 percent + 20 percent); therefore total output also grows at 50 percent. Thus, the average and marginal productivity of labor grow at the rate of 30 percent, which is equal to the growth rate of the tech-nological frontier (A). The subsistence sector has been eliminated. The real wage rate grows at the rate of 30 percent. These growth rates will be repeated period after period as long as the exogenous variables remain unchanged.

In the transition dynamics, physical capital accumulation in the capital-ist sector has to accomplish two tasks. First, it must absorb the excess labor supply, which implies the continuous increase in capital per worker (capital deepening), and then equip the growing population with the same capital

K A Dh Q q w

t1 80 30 30 70 40 40

t2 70 30 25 60 35 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t* 50 30 20 50 30 30


per worker (capital widening). Therefore, the growth rate of employment in the capitalist sector must be higher than that of the population, if the cap-italist sector is to absorb the excess labor supply over time. Second, this is assuming that the skill level remains fixed, but it will also grow. Then the growth of physical capital must take into account this component and pro-ceed at a higher rate than n+g.

Omega society, at the initial position, shows excess labor supply, and the desire to increase physical capital is also higher than what is needed and this increases the ratio of physical capital per skilled worker. The difference with epsilon is that the increase in this ratio will not be as large as it was in epsilon because part of the excess labor supply must be added to the new population to be equipped; it is as if in the initial position of omega the value of (g+cn) was higher than in epsilon (g+n). The consequence is that, starting from the same initial conditions, omega society will take more time to reach the steady state equilibrium than epsilon.

In terms of the growth frontier curve, the capitalist sector of omega will accumulate physical capital at a rate that is higher than (g+n) in the transi-tion dynamics; once the frontier has been reached, capital accumulation will proceed at a rate equal to (g+n), just as in the epsilon model.

The Subsistence Sector

The omega society is nothing else but an epsilon society with a subsistence sector. The only difference is that omega being an overpopulated society, transition dynamics implies the coexistence of the capitalist sector with the subsistence sector. So there is a role for the subsistence sector in the growth process of the capitalist sector. Hence, the subsistence sector needs to be included into the transition dynamics.

The production function of the subsistence sector can be written start-ing from the type of production function utilized for the capitalist sector as follows:

V = F (Ks, As, Ls) = Ksα (As Ls)1–α (4.7)

As = f (hs), f ′>0 (4.8)Assuming that Ks

α = 1, the production function becomesV = F (hs, Ls) = hs β Ls

1–β, where 0<β<1 (4.9)Ls = L – Dh (4.10)

The model thus assumes that the subsistence sector is endowed with little capital, which is constant; so this factor can be ignored. If the subsistence


production unit were able to accumulate physical capital, then it would become a capitalist firm. To simplify, the model will assume a dynamic pro-cess in which labor absorption of the self-employed comes from the growth in the capitalist sector. Then the essential factors in the production process include technology (As), the adoption of which depends upon human capital per worker (h), and on total labor (Ls). V is total output in the subsistence sector, in which the production function is also subject to constant returns to scale and diminishing returns to the labor factor.

Comparing the production function of the two sectors, it follows that the level of total output for equal quantities of labor will be higher in the capi-talist sector. The gap is due not to differences in human capital per worker (h), which is homogeneous in both sectors, but to the lack of physical capital in the subsistence sector. As an initial condition, the model will assume that output per worker is also higher in the capitalist sector.

So far, the level of human capital in the subsistence sector has remained unchanged. But the model will assume that the self-employed also learn new skills. The model will assume that skill learning will follow the same path as in the capitalist sector, but through a different mechanism. Skill learning can be obtained through on the job training in the capitalist sector because workers are mobile between sectors. In addition, the model will assume that workers will seek to learn those skills by any means at their disposal, and thus avoid being left behind in the labor market and remain employable in the capitalist sector. Hence, labor will remain homogeneous in the process of growth.

In the transition dynamics, the growth rate of output per worker in the subsistence sector (v=V/Ls) can then be written as follows:

Δv/v = β (Δh/h – ΔLs/Ls) (4.11a)ΔLs/Ls = n – ΔDh/Dh < 0 (4.11b)Δv/v = β [ΔAs/As + (ΔDh/Dh – n)] (4.11c) = β [(ΔA/A + (ΔDh/Dh – n)] = β [(g + (ΔDh/Dh – n)] < g.

The first equation says that the growth rate of output per worker in the subsistence sector will be equal to a fraction of the difference between the growth rate of human capital per worker minus the growth rate of self-employed workers, which is in turn equal to the growth rate of labor supply minus the growth rate in wage employment, as shown in the second equation. The third equation consolidates the first two and, in addition, assumes that the level of human capital increases at the same growth rate


of technological change (g), and then shows that the growth rate of out-put per worker in the subsistence sector will be positive, variable, and less than g.

The Aggregate Growth Process

Figure 4.1 displays the growth process in omega society. Let curve N*R* be the growth frontier of the capitalist sector. In addition, let q0 be the initial output per worker in the capitalist sector and v0 in the subsistence sector. As in the case of the epsilon model, the growth process in the capitalist sector implies a trajectory, the transition dynamics, represented by the segment NJ. Once point J has been reached, at time t*, both the excess labor supply and the subsistence sector have been eliminated; the structure of the economy is now composed of the capitalist sector alone, which will grow along the frontier. The growth rate along the segment NJ is higher than that of the frontier.

At what rate does the output per worker in the subsistence sector grow? This was shown above in equation (4.11). The first component in the bracket says that this rate will be smaller than that of technological change (g), whereas the other component being a negative number makes the total value even smaller than g. Then the average growth rate of the subsistence sector may be represented by the curve SS′, which grows at a slower rate than that

O

y

tt*

R*

J

[q*] N*

S´

[q0] N

[y0] H

[v0] S

Figure 4.1 Growth of output per worker in omega society.


of the frontier of the capitalist sector. Hence, in the transition dynamics, the following inequality prevails:

Δq/q = Δw/w > Δq*/q* = g > Δv/v (4.12)

On the other hand, the firms’ objective of profit maximization imposes the constraint that the market real wage rate must be higher than the oppor-tunity cost of wage earners. This condition implies that the growth rate of the real wage rate should be equal to or higher than that of the marginal productivity of labor in the subsistence sector, which is equal to the growth rate of the average productivity counterpart. This constraint is satisfied, as shown in equation (4.12).

In the aggregate, at what rate would the national income per worker grow?

Let the initial national income per worker be equal to y0, which is the weighted average of both sectors. The weights are the shares of labor in each sector. In the process of growth, these weights change, for the share of labor in the subsistence sector declines over time. The growth rates in the tran-sition dynamics, segment NJ, implies an increasing weight of the capitalist sector (λ(t), where λ′>0), until it becomes equal to one at point J. Therefore, the segment HJ shows the path of national income per worker. Along this path, the average growth rate of national income per worker (y) is higher than that of the output per worker in the capitalist sector (q), for it will arrive at the same point J, but from a lower initial point. After point J is reached, after a period t*, omega society travels along its growth frontier curve, which is given by the growth frontier of the capitalist sector.

Consider again the example shown earlier. The growth frontier of the capitalist sector implies a growth rate of 50 percent per decade of total out-put, 50 percent of capital stock growth rate, 30 percent of technological knowledge, and 20 percent of labor supply. This is a steady state, which implies equal growth rates of q* and w (30 percent). In transition dynamics, the capitalist sector initially has a higher growth rate of capital stock, say 80 percent, and technological progress is still 30 percent. However, wage-employment is endogenous. If this rate took the value of 30 percent (consis-tent with the stability condition), then the share of wage-employment would increase and that of the subsistence sector would shrink. In this case, the growth rate of q is 40 percent, but it is not a steady state. In the following periods, the capitalist sector will grow at lower rates (35 percent), and so on, until it reaches the frontier, as in the example shown above; so the average growth rate in the transition period will be above 30 percent, say 34 percent. The average (and marginal) productivity of labor in the subsistence sector


grows at a rate smaller than g (30 percent). National income per worker would then grow at an average growth rate in the transition period that is higher than that of the capitalist sector (34 percent), as it starts at a lower level (y0<q0) but reaches the same destination and in the same period (t*).

Beta Propositions

What are the determinants of the output per worker over time in omega society? The growth frontier is that of the capitalist sector as in the epsilon society, which was rewritten above as equations (4.2) and (4.3). For the tran-sition dynamics, the trajectories can be written as follows:

Capitalist sector:

q (t) = f (q0*, q0, g, t), fi >0, q0 < q0*, t ≤ t* (4.13)Δq/q = f (q0*/q0, g) > g, such that fi >0, q0 < q*, t ≤ t* (4.14)

Subsistence sector:

v (t) = f (v0, g, t), fi>0, t ≤ t* (4.15)Δv/v = g′< g, t ≤ t* (4.16)

Aggregate:

y0 = λ0 q0 + (1 – λ0) v0 (4.17)y (t) = F [e, n, E, q0, v0; λ(t), A(t)], F2<0, Fi>0, t ≤ t* (4.18)= F (q0*, y0, g, t), Fi>0, y0 < q*, t ≤ t* (4.19)Δy/y = F (q0*/y0, g)>g, such that Fi>0, y0 < q*, t ≤ t* (4.20)

In the transition dynamics, given the level (q0*) and the growth rate of growth frontier (g), the initial national income per worker (y0) will move toward the frontier at a growth rate that is higher than that of the fron-tier; moreover, the growth rate will be higher the higher is the gap (q0*/y0), which is determined by the gap (q0*/q0); we can thus invoke the convergence theorem.

In sum, the omega model predicts the following relation between growth rates of national income per worker and that of the other variables as follows:

Δy/y > Δq/q > Δq*/q* = g > Δv/v (4.21)


In the transition dynamics, the growth rate of national income per worker is higher than that of output per worker of the capitalist sector, which in turn is higher than that of the output per worker of the subsistence sector. This relationship may seem strange, in which the average grows at the higher rate compared to its two components, but remember that weights of the sectors are not fixed by variables over time. Finally, when the transition dynam-ics reaches the growth frontier, national income per worker will reduce its growth rate to the value g. These relationships constitute the dynamic equi-librium of the omega model and are shown in figure 4.1.

The exogenous variables include e, n, E, g, and the initial conditions include y0 and v0. With the help of figure 4.1, the effects of changes in the exogenous variables upon the trajectory of the transition dynamics, which are observable, can be summarized as follows:

1. Higher e or lower n will cause faster growth rate of y: The growth fron-tier curve will be shifted upward. The same initial national income per worker will have a trajectory toward the new frontier that is fur-ther away, which implies a higher gap between the new two initial conditions, and thus a higher growth rate. The subsistence sector will be eliminated sooner, that is, t* will occur sooner.

2. Higher E will cause faster growth rate of y: The growth frontier will be shifted upward. Higher average schooling years of the labor force will have a level effect, not a growth effect. The schooling effect will also increase the output level of the subsistence sector, but not its growth rate. The initial value of the national income per worker will be higher. In the capitalist sector, the transition dynamics will grow at a higher rate to reach the new frontier. This behavior of the capi-talist sector will lead the trajectory of the national income per worker to grow at a faster rate.

3. Lower initial value q0 will cause faster growth rate of y: A lower value of the initial output per worker of the capitalist sector implies a higher gap with the frontier. Hence, transition dynamics will make the capi-talist sector grow at a faster rate (convergence theorem). This behavior of the capitalist sector will lead to a faster growth rate of the aggregate output per worker. Consequently, we can draw the following empiri-cal prediction. Poorer omega societies will grow faster than richer omega societies.

Hence, the signs of the partial derivatives of the two equations (4.19) and (4.20) are now justified. These are the beta propositions or the causality rela-tions of the omega model.


Income Distribution in the Economic Growth Process

Along the growth frontier, the omega society behaves just like the epsilon society. Hence, income inequality will remain unchanged in the growth process.

We now need to know the changes in income inequality along the tran-sition dynamics. The omega model has two social classes but three social groups that participate in national income distribution: capitalists, wage earners, and the self-employed. The initial average incomes of these groups follow that order. The change in the overall income inequality will be more complex in omega than it is in epsilon; hence, an understanding of the Lorenz curve (the standard measure of inequality) is necessary.

The most common way to measure income inequality is by using the Lorenz curve. It is a box with two axes: the horizontal measuring accu-mulated population and the vertical accumulated total income, each axis going from 0 to 1. The vertical axis measures functional distribution, as fac-tor shares; the horizontal axis measures population shares of social groups, which are in order according to their relative mean incomes, from the poor-est to the richest. As a result, the Lorenz curve will have an increasing slope, where each slope indicates the mean income of the corresponding social group relative to the national average (given by the diagonal and equal to 1); hence, the slopes (measuring relative mean incomes) must be smaller and higher than the diagonal.

The Lorenz curve captures both functional and personal income inequal-ity at the same time, together with social group shares in the population. The diagonal of the box indicates perfect equality, and a curve that is further away from the diagonal indicates a higher degree of inequality. The Gini coefficient of inequality is just a measure of this distance and it can take values between zero, when the Lorenz curve coincides with the diagonal, and one, when the Lorenz curve coincides with the horizontal and vertical axes of the box (one person receives the total income).

Figure 4.2 depicts the Lorenz curve OBCO′ for omega society, which shows income inequality at the beginning of the growth process along the transition dynamics. The segment OB refers to self-employed workers in the subsistence sector; the segment BC to wage earners, and CO′ to capitalists. The slopes of the segments are shown to be increasing, which indicates the increasing relative incomes of the social groups, from the poorest to the richest groups.

How would the Lorenz curve change in the economic growth process? The answer is given in equations (4.12) and (4.21). In the transition dynam-ics, the output per worker in the capitalist sector grows at a higher rate than


that of the subsistence sector. Within the capitalist sector, the real wage rate grows at the same rate as the output per worker in the capitalist sec-tor, which implies that average income of capitalists also grow at the same rate. Therefore, relative incomes in the aggregate become more unequal: the poorest group becomes relatively poorer. At the same time, the labor share of the poorest group falls over time. Hence, inequality will increase, but not as much as compared to the case when labor shares had remained unchanged.

The change in income inequality in the transition dynamics in omega society is also shown in figure 4.2. The segment OB will be moved to OB′ because the subsistence sector has experienced a fall in relative income and a fall in labor share. The segment BC moves to B′C′ because the group of wage earners have experienced an increase in relative income and an expan-sion in labor share. Finally, because the small capitalist group experiences an increase in relative income and since the population share remains con-stant, the segment CO′ moves to C′O′. As a result, the Lorenz curve moves outward from OBCO′ to OB′C′O′, that is, income inequality increases in the growth process.

Along the growth frontier curve, where the subsistence sector no longer exists, the income distribution problem involves only the capitalist sector. Relative incomes will remain unchanged and so will population shares; thus, income inequality will remain unchanged. Therefore, changes in

O

B´

B

C´

C

O´

[ω]

Figure 4.2 Inequality changes in the growth process in omega society.


income inequality in the economic growth process can be summarized as follows: in the transition dynamics, the degree of income inequality tends to increase; but once the growth frontier is reached, the degree of inequality tends to stabilize.

What is the effect of changes in the exogenous variables upon the inequal-ity shown in figure 4.2?

An increase in e and E, and a fall in n, implies a higher level of q* and a higher level of the growth frontier curve. The transition dynamics curve of the capitalist sector will move from the initial value to the new frontier, at a higher growth rate. Therefore, the relative income of the capitalist sector (q/y) will increase, and so will w/y and p/y, which implies a fall in v/y. The labor share in the capitalist sector will be higher and that of the subsistence will be smaller. There will be another Lorenz curve in figure 4.2 showing a higher degree of income inequality.

An increase in variable g will imply a higher slope for growth frontier curve and thus a new curve. The transition dynamics of the capitalist sector will move from the initial value to the new curve at a higher growth rate. Therefore, the effect upon income inequality will be similar to the effects shown above for the case of e and E.

Another exogenous variable in the omega model is the asset distribu-tion between individuals of the omega society (δ). If asset distribution is more concentrated, total profits (P) will go to a smaller group of capital-ists; hence, p/y will increase, without changes in population shares. Hence, there will be another Lorenz curve in figure 4.2 showing a higher degree of inequality.

In sum, in the transition dynamics the degree of income inequality (D) increases endogenously in the process of economic growth. Changes in the exogenous variables of the omega model have a positive effect on inequality, except for the variable population growth (n), which has a negative effect. These results also refer to the transition dynamics of the model and can be written as

D (t) = G (n, e, E, g; δ; t), G1 < 0, Gi > 0, t ≤ t* (4.22)

The relevant analysis of the growth process in omega society is that of the transition dynamics. Once the national income per worker reaches the growth frontier, omega society will move along the growth frontier, that is, omega society will become epsilon society endogenously. The growth process in omega society implies not only a quantitative change but also a qualitative change: omega becomes epsilon.

CHAPTER 5

The Sigma Society: A Dynamic Model

As developed in chapter 6 (volume 1), sigma society is an overpopulated and socially heterogeneous capitalist society. People are endowed with unequal amounts of economic assets and also unequal entitle-

ments of political assets. Capitalists own the entire capital stock of society. Workers are endowed with unequal levels of human capital: high and low. Those who have low levels of education are also second-rate citizens; they are called Z-workers. The rest are called X-workers.

How does the economic growth process operate in such a society? What does happen to the initial income inequality in the growth process? Such are the questions that this chapter will seek to answer.

Economic Structure of Sigma Society

The dynamic model presented in this chapter will differ in one aspect from the static model constructed in chapter 6 (volume 1). This model will have just one labor market, that for X-workers. These workers are endowed with the human capital necessary to operate the modern technology utilized in the capitalist sector. In contrast, Z-workers are not endowed with human capital necessary to operate the modern technology in the capitalist sector; thus, they are forced to become self-employed in the Z-subsistence sector. Including another labor market for Z-workers (as we did in static model) will not alter the basic results of the dynamic model, but it would make it more complicated to operate.


As to the X-labor market, it operates like the omega model. Therefore, the dynamic sigma model will include the following assumptions: the analysis starts at effective full employment equilibrium situation, in which the excess labor supply will take the form of self-employment in the X-subsistence sec-tor; money supply will be neutral in the economic process; and the X-labor market will constitute the core of the general equilibrium in the capitalist sector.

The equations representing production functions in the three sectors of sigma society are:

Capitalist sector:

Q = Kα(ADhx)1–α, 0<α<1 (5.1a)

X-subsistence sector:

Vx = F (hx, Lx) = hxβ Lx

1–β, 0<β<1 (5.1b)

Z-subsistence sector:

Vz = F (hz, Lz) = hzγ Lz

1–γ, 0<γ<1 (5.1c)

Aggregate:

Y = Q + Vx + Vz (5.1d)Lx = Dhx + Lsx (5.1e)

The sigma economy is thus composed of the omega sector and the Z-subsistence sector. In this model, the Z-subsistence sector is not con-nected to the capitalist sector, whereas the X-subsistence sector is, via the labor market. As the capitalist sector expands, the X-subsistence sector will contract.

The initial labor productivity level of the Z-subsistence sector is lower than that of the X-subsistence sector because it is endowed with lower human capital level and, consequently, lower technological level. Actually, the Z-subsistence sector uses mostly traditional technology, together with some of the technology used in the capitalist sector. The labor productiv-ity level of the X-subsistence sector is in turn lower than that of the capi-talist sector because of its low endowment of physical capital. Hence, the Z-subsistence sector has the lowest labor productivity level among the three sectors.

The Sigma Society: A Dynamic Model l 59

The dynamic model will assume that the initial conditions correspond to the static equilibrium conditions, which include the following order for the average incomes:

p0 > q0 > wx0 > vx0 > vz0 (5.2)

In the capitalist sector average profit (p) is higher than average wage rate (w). Among X-workers, there is the constraint that the real wage rate must be higher than the marginal labor productivity of the X-subsistence sector, for this gap constitutes the effort extraction device. Although the average labor productivity is always higher than the marginal productivity, the model leads to the equilibrium condition that real wage rate must also be higher than the average labor productivity in the subsistence sector. This constraint is included in the sequence of inequalities.

Output Growth in Sigma Society

The omega dynamic model was presented in chapter 4, this volume; so we already know about the growth process of this component of the sigma soci-ety. In particular it is important to recall that the growth frontier equation of the capitalist sector will also be the growth frontier of sigma society as a whole. This frontier is rewritten here for easy reference, in which the values of the exogenous variables will take different values compared to those of omega society. Then

q*(t) = F (e, n, E, g, t), F2<0, Fi>0 (5.3) = F (q0*, g, t), Fi>0Δq*/q* = g = ΔA/A = Δh/h = ΔA0/A0 (5.4)

In the transition dynamics, the relation between the growth rates in the cap-italist sector and the X-subsistence sector were also established in chapter 4, which are also rewritten here as follows:

Δq/q = Δwx/wx > Δq*/q* = g > Δvx /vx (5.5)

Output per worker in the capitalist sector grows along the transition dynam-ics at a rate that is higher than the rate along the growth frontier and also higher than that of the output per worker of the X-subsistence sector.

The next task is to determine the growth rate of the Z-subsistence sector. From equation (5.1c), we get


Δvz/vz = ΔVz/Vz – ΔLz/Lz = γ (Δhz/hz – ΔLz/Lz ) (5.6) = γ (ΔAz/Az – ΔLz/Lz ) = γ (ΔA/A – ΔLz/Lz ) = γ (g – ΔLz/Lz ) < g.

Z-workers seek to learn the skills that will enable them to adopt the new technologies and thus increase their income levels. The process of learning skills and adopting new technologies follows the same process as in the case of the X-subsistence sector: people will find ways to learn the new tech-nologies, other than on the job training in firms. Then the growth rate of human capital will be equal to the growth rate of technology (g). However, this process is about the growth rate of learning skills and about the adop-tion rate of new technologies, not about equalizing levels of technology, as shown in equation (5.6). Z-workers are endowed with the lowest human capital level. Low human capital implies low level of modern technology (A0z); hence, in this process the initial gap (A/A0z) will remain unchanged over time.

According to equation (5.6), a positive growth of output per worker in the Z-subsistence sector requires that the growth rate of human capital (equal to g, the growth rate of technology frontier) should be higher than that of the Z-population. Therefore, in the last term, the difference in the parenthesis must be positive; if it were zero, productivity growth would also be zero, that is, no growth. This condition implies that the growth rate of output per worker in the Z-subsistence will be smaller than g. Moreover, assuming that Z- and X-populations grow at the same rate, it follows that output per worker in the Z-subsistence sector will tend to grow at a smaller rate than the average rate in the X-subsistence sector.

Including this result in equation (5.5), in the transition dynamics, the three sectors will grow at different rates, as follows:

Δq/q = Δwx /wx > Δq*/q* = g > Δvx /vx > Δvz/vz , t ≤ t* (5.7)

Output per worker will grow faster in the capitalist sector than in the X-subsistence sector, which in turn will grow faster than in the Z-subsistence sector. These relations hold true in the transition dynamics of the capitalist sector, which occurs before period t*, at which the X-subsistence sector will have disappeared.

Figure 5.1 displays the growth process in sigma society. The curve C*R* is the growth frontier of sigma society, which corresponds to the growth frontier of the capitalist sector, with intercept of q* and growth rate equal to that of technology (g). The initial output per worker in the capitalist sector


is lower than that corresponding to the intercept of the frontier (q0<q*) and the transition dynamics (with excess labor supply of X-workers) is given by the segment CJ, in which the rate of growth is higher than g. At point J the excess labor supply of X-workers has been eliminated. The X-subsistence sector grows at the average rate g′<g along the curve XX′. The Z-subsistence sector grows at a rate g″<g′<g along curve ZZ′. Therefore, poorer sectors grow at slower rates.

In the aggregate, the initial national income per worker (y0) is the weighted average of the output per worker in each of the three sectors, with the weights given by the labor shares. In the transition dynamics, the weights will change over time: the share of X-workers who are wage earners will rise, that of the X-self-employed will decline, and that of Z-workers will remain fixed. Thus, the growth rate of national income per worker will vary over time.

Another consequence is that the national income per worker will not reach the growth frontier curve. Let national income per worker grow along the curve SJ′. This trajectory does not reach the growth frontier because at period t*, when the X-subsistence sector has disappeared, the Z-subsistence sector continues functioning, that is, point J′ lies below point J, which is on the frontier. A third consequence is that the curve SJ′ will not neces-sarily grow faster than that of the capitalist sector CJ (as in omega society) because, even though it starts from a lower value, it will not reach the same

O

y

tt*

R*

J

(q*) C *

S´

X´

Z´

J´

J´´(v0z) Z

(v0X) X

(q0) C

(y0) S

Figure 5.1 Growth of output per worker in sigma society.


point in the frontier. Just for the sake of simplicity, assume that it grows at the same rate as does the capitalist sector.

Beyond period t*, the trajectory of national income per worker will move along curve J′S′. The growth rate of J′S′ will be a weighted average of the growth rate of the capitalist sector (along curve JR*) and the growth of the Z-subsistence sector (along J″Z′), where the weights are given by the constant population shares; then the growth rate of curve J′S′ will also be constant, and smaller than g. In sigma society, therefore, the growth process could not lead to the growth frontier curve. If the assumption were that the population growth rate of Z-population is higher than that of X-population (poorer groups show higher population growth rates), then the growth rate of curve J′S′ would decline over time away from the growth frontier curve. The conclusion is that the curve J′S′ will not reach the growth frontier curve.

In sum, according to this sigma dynamic model, in the process of eco-nomic growth the X-subsistence sector will be eliminated, which occurs at period t*, but the Z-subsistence sector will persist; therefore sigma society will not be able to endogenously become an epsilon society. The capitalist sec-tor will eventually coexist with the Z-subsistence sector. The reason is that in the economic growth process, Z-workers cannot endogenously become X-workers. Z-workers are initially endowed with the lowest quantities of human capital and also with the lowest degree of political assets (as sec-ond-class citizens) and, as shown in chapter 2, the education process is not human capital equalizing. In the process of economic growth, the initial conditions do matter. As second-class citizens, Z-workers have access to only second-class public goods because public goods are supplied as local, not universal. This is an equilibrium situation because no social actor has the power or will to change the situation.

Beta Propositions

The effect of changes in the exogenous variables upon the growth process will be analyzed for the transition dynamics, which is the relevant trajectory, that is, before period t*. Again, our knowledge of the growth process in the omega society will be of great help in this task.

Three groups of variables will determine the trajectory of national income per worker (y) in the transition dynamics. They are: the exoge-nous variables that determine the growth frontier of the capitalist sector; the initial conditions of average incomes of the three sectors; and the labor shares of the three sectors, which vary over time and are represented by τ(t). Then,


y (t) = F [e, n, E, g, q0, v0x, v0z ; τ(t)] < q*(t), t ≤ t* (5.8)F2<0, and Fi>0.

Given the exogenous variables and the initial conditions, the national income per worker in sigma society travels along a particular trajectory in the tran-sition dynamics, which will never reach the growth frontier.

Substituting the exogenous variables e, n, and E for the initial level of output per worker in the growth frontier, and the initial incomes of the sec-tors for the initial national income per worker, equation (5.8) becomes

y (t) = F (q0*, y0 , g, t) < q*(t), Fi>0, y0< q0*, t ≤ t* (5.9)

As to the growth rate of national income per worker, it is determined by the following factors:

Δy/y = F (q0*/y0, g) > g, Fi > 0, y0 < q0*, t ≤ t* (5.10)

National income per worker will grow at a rate that is higher than that of the growth frontier (g). Although the trajectory of national income per worker in the transition dynamics does not reach the frontier, it will move toward the frontier.

The individual effects of the exogenous variables and initial condi-tions upon the trajectory of national income per worker in the transition dynamics—as indicated by the partial derivatives in the two equations (5.9) and (5.10) above—can be easily justified with the help of figure 5.1, as follows:

1. Higher e will cause faster growth rate of y: The growth frontier curve of the capitalist sector will be shifted upward. From the same initial condition, output per worker in this sector will grow faster to reach the new frontier along a new trajectory of transition dynamics. The two subsistence sectors will remain along their trajectories, with the same growth rate. As a result of these effects, from the initial position, national income per worker will increase along the new transition dynamics and will approach to the new frontier curve that is further away growing at a higher rate.

2. Lower n will cause faster growth rate of y: The growth frontier curve of the capitalist sector will be shifted upward. This effect will just be the inverse of the effect of an increase in investment rate (e), which was shown earlier.


3. Higher E will cause faster growth rate of y: The growth frontier curve of the capitalist sector will be shifted upward. Education has level effect, not growth effect. However, the transition dynamics will imply a faster growth rate of q. The output per worker in the sub-sistence sectors will also be shifted upward, but their growth rates will remain unchanged. The initial national income per worker will thus increase. In the capitalist sector, transition dynamics will grow at a higher rate to reach the new frontier; then the trajectory of the national income per worker will also grow at a higher rate induced by the higher growth rate of the capitalist sector.

4. A lower initial value of q0 will cause faster growth rate of y: A lower value of the initial output per worker of the capitalist sector implies a higher gap with the frontier. Hence, transition dynamics will make the capitalist sector grow at a faster rate (convergence theorem). This behavior of the capitalist sector will lead to a faster growth rate of the aggregate output per worker. Poorer sigma societies will grow faster than richer sigma societies.

Hence, the signs of the partial derivatives of the two equations (5.9) and (5.10) are now justified. These constitute the beta propositions or the causal-ity relations of the sigma dynamic model of economic growth.

Income Distribution in the Economic Growth Process

Income distribution in sigma society, at the initial period of the growth pro-cess, is represented by the Lorenz curve OABCO′ in figure 5.2. The segment OA refers to the Z-subsistence sector, segment AB to the X-subsistence sec-tor, segment BC to wage earners, and segment CO′ to the capitalist group. The slopes increase across the segments indicating inequality by the rising relative incomes of the four social groups.

How would the Lorenz curve change in the growth process? As shown above, in the growth process of sigma, the relevant trajectory is that given by the transition dynamics. Along this trajectory, the average output per worker in the capitalist sector (q) increases at a higher growth rate com-pared to the subsistence sectors, as shown in equation (5.7); therefore, the relative income of the capitalist sector (q/y) will increase and those of the subsistence sectors will fall over time. We also know that distribution within the capitalist sector will not change, which means that average wage rate and average profit will increase at the same growth rate of q, and thus their relative incomes with respect to average incomes in the subsistence sector will increase.


Labor shares between sectors also change in the transition dynamics: Dh/L increases, Lx/L falls, whereas the shares Lz/L and L′/L (capitalist class) will remain fixed. Just for the sake of simplicity, assume that the population of capitalists, X-workers and Z-workers grow at the same rate; hence, what changes in the growth process is the allocation of X-workers between wage employment (increasing) and self-employment (decreasing).

Figure 5.2 depicts the change in income inequality in the transition dynamics in sigma society. The segment OA will move to OA′ because the Z-subsistence sector will experience a fall in relative income and con-stant labor share. The segment AB will be moved to A′B′ because the X-subsistence sector will experience a fall in relative income and a fall in labor share. The segment BC moves to B′C′ because the group of wage earners will experience an increase in relative income and an expansion in labor share. Finally, because the small capitalist group will experience an increase in relative income and keep population share constant, the segment CO′ moves to C′O′. As a result, the Lorenz curve moves outward from OABCO′ to OA′B′C′O′, that is, income inequality increases in the transi-tion dynamics.

As growth proceeds further, the X-subsistence sector will tend to dis-appear. This process implies that the segment A′B′ will be reduced contin-uously, until it becomes nil. At that period, there will be only three social

O

AA´

B´

B

C

C´

O´

[σ]

Figure 5.2 Inequality changes in the growth process in sigma society.


groups, but the Lorenz curve will have reached a level that is further away from the initial curve shown above and from then on income inequality will still tend to increase, but more moderately, as the growth rate of the capital-ist sector will decline.

What is the effect of changes in the exogenous variables upon the inequal-ity shown in Figure 5.2?

An increase in e and E, and a fall in n, implies a higher level of q* and a higher level of the growth frontier curve. The transition dynamics curve of the capitalist sector will move from the initial value to the new frontier, at a higher growth rate. Therefore, the relative income of the capitalist sector (q/y) will increase, and so will w/y and p/y, which implies a fall in v/y. The labor share in the capitalist sector will be higher and that of the subsistence will be smaller. There will be another Lorenz curve in figure 5.2 showing a higher degree of income inequality.

An increase in variable g will imply a higher slope for growth frontier curve and thus a new curve. The transition dynamics of the capitalist sector will move from the initial value to the new curve at a higher growth rate. Therefore, the effect upon income inequality will be similar to the effects show above for the case of e and E.

Another exogenous variable in the sigma omega model is the initial asset distribution among individuals (δ). If physical capital ownership is more concentrated, and total output remains unchanged, then total profits (P) will go to a smaller group of capitalists; hence, the relative income of capital-ist (p/y) will increase. In figure 5.2, the original segment CO′ will move out-ward to C′O′ and the other segments will move outward, keeping constant the labor shares. In sum, income inequality will be shifted outward and thus the degree of income inequality will increase to a higher level.

Now consider that human capital endowment is more concentrated. Suppose X-population has a higher human capital endowment: more years of schooling. Then human capital will initially be more concentrated in the X-population. As a result the average income of the X-population relative to that of the Z-subsistence sector will rise. In figure 5.2, the segment OA will move to another level, which has lower slope, and the segment AB will move outward and show a higher slope; hence, the new Lorenz curve will be shifted outward. The degree of income inequality will tend to increase.

Finally, suppose political assets are more equally distributed. Then peo-ple will be more equal before the law and in the access to other public goods, in quantity and quality. The education process will tend to equalize human capital among all workers. Differences in labor productivity levels between X-subsistence and Z-subsistence sector will tend to diminish, and thus the degree of income inequality will fall.


In sum, income inequality (D) increases endogenously in the process of economic growth, that is, it increases along the transition dynamics, which is to say income inequality increases over time. Changes in the exogenous variables of the sigma dynamic model have a positive effect on inequality, except for the variable population growth (n), which has a negative effect. These results also refer to the transition dynamics of the model and can be written as

D (t) = G (n, e, E, g, δ, t), G1<0, Gi >0, t ≤ t* (5.11)

Given the values of the exogenous variables, the degree of income inequal-ity increases as economic growth proceeds, that is, it increases over time. Therefore, the effect of increases in the values of the exogenous variables will be to shift upward the equilibrium trajectory of income inequality, except for the variable population growth, which will lead to a downward shift.

The Persistence of the Z-subsistence Sector

According to the dynamic model, sigma society does not become epsi-lon society in the economic growth process. The reason is that, unlike the X-subsistence sector, the Z-workers cannot be transformed from self-employed to wage earners in the growth process.

Why is it that the Z-subsistence sector cannot be ultimately eliminated in the growth process?

The model answers this question by simply assuming that Z-workers are totally excluded from the labor market. Now assume that they participate in the labor market, as we did in the static model (chapter 6, volume 1). There the assumption was that Z-workers were required in the production process of the capitalist firms in a fixed proportion of X-workers employed. With this assumption, the Z-subsistence sector would be eliminated, as demand for Z-labor will also grow faster than the supply of Z-workers. The stability condition of the model applies to X-workers, but now it will be extended to Z-workers as well.

However, the elimination of the Z-subsistence sector would require a par-ticular coincidence: the factor endowment ratio of X-workers to Z-workers should be equal to the technological proportion in which they are used in production. Assuming that the first ratio is lower is sufficient to have a per-sistent Z-subsistence sector. Assuming in addition that labor-saving techno-logical change makes Z-workers less essential to production over time, the growth rate of demand for Z-workers will be equal to or smaller than the growth rate of labor supply of Z-workers; hence, the Z-subsistence sector


will not be eliminated endogenously in the growth process. This is the same conclusion we have reached in the model developed in this chapter, in which Z-workers are totally excluded from the labor market; so this assumption was not as restrictive as it appeared.

The dynamic sigma model also implies that if the endowment of human capital of Z-workers were exogenously increased (overnight) to the level of that of X-workers, the excess supply of X-workers would increase, but the expansion of the capitalist sector would ultimately absorb total labor, given the stability condition that the derived demand for labor will grow faster than the labor supply, as seeing in the omega dynamic model. It would take longer, but the X-subsistence sector will be eliminated.

However, according to the theory of education presented in chapter 2 of this book, among workers, human capital associated with education is an endogenous variable. It depends upon the individual socioeconomic back-ground, that is, to the initial inequality variable. Z-workers follow a different path in the education system, for they attend public schools of low quality, which generate low-quality basic human capital as well. This is related to the fact that Z-workers are second-rate citizens. As long as this initial inequal-ity remains unchanged, the education system will not be human capital equalizing, nor income equalizing among workers. Moreover, Z-workers may have more real income in the growth process, but more money does not transform them into first-class citizens. Hence, the conclusion that the Z-subsistence sector will persist in the growth process still follows.

In sum, the Z-subsistence sector will persist in sigma society even in the growth process, in which society goes through many quantitative changes, but qualitatively this society will continue to be a sigma society. Sigma soci-ety cannot endogenously become omega society and thus cannot become epsilon society.

Do we have a unified theory of the capitalist system? Do these partial theories generate a theory of growth and distribution for the capitalist sys-tem, taken as a whole? Can they explain the persistence of differences in income levels and degrees of income inequality between the First World and the Third World, which correspond to Facts 6 and 7 listed in chapter 2 ( volume 1)? These questions are analyzed in the next chapter.

CHAPTER 6

Unified Theory of Capitalism: A Growth and Distribution

Model

The economic growth process has been explained for epsilon, omega, and sigma societies, taken separately. Three partial theories have been presented using particular dynamic models. The question now

is whether we have a unified theory that can explain growth and distribu-tion in the capitalist system, taken as a whole.

The partial models reveal that there are only two growth frontiers, one corresponding to epsilon and the other to sigma. The growth trajectory of omega is just a curve showing the transitional dynamics to the frontier of epsilon. In this sense, omega and epsilon are qualitatively the same type of society, with only initial quantitative differences. The differences in their factor endowments disappear in the long run and omega becomes epsilon. There is no path dependence, that is, the initial conditions, the history, do not matter in the growth process of omega and epsilon societies.

In contrast, epsilon and sigma societies are qualitatively different and remain so in the growth process. Sigma does not become epsilon endog-enously. Therefore, the study of the capitalist system as a whole must deal with the interactions and the general equilibrium of epsilon and sigma soci-eties put together. The growth frontier curve of output per worker in each epsilon and sigma societies is given by the dynamic equilibrium of the corre-sponding capitalist sector. The frontier curve is determined by the same set of exogenous variables. A unified dynamic model that integrates the partial models will now be developed.


On the Interactions between Types of Societies

The partial models were constructed under a set of common auxiliary assumptions, which were listed in chapter 1, this volume. Those auxiliary assumptions will be maintained in the construction of the unified dynamic model. Some further auxiliary assumptions on the aggregation of the three societies will be introduced now.

On investment-savings relations, the unified dynamic model will assume that aggregate investment is endogenously determined. In equilibrium, how-ever, aggregate investment must be equal to aggregate savings. Domestic sav-ings will depend upon total output in each type of society; therefore, aggregate savings will depend on aggregate output, with a global saving rate (s*). As a condition of aggregate equilibrium, savings must be equal to investment. The aggregate investment fund will then be allocated to each type of society. The equality between savings and investment need not hold true for each type of society; in the aggregate, however, it must. Net foreign savings must be equal to zero in the aggregate of societies. Moreover, in the aggregate, investment is determined by savings; hence, economic growth is savings driven. Changes in s* will modify the aggregate savings and thus the aggregate investment, which will then be allocated into the different types of capitalist societies.

The unified model thus assumes that the interactions between the dif-ferent types of capitalist societies are reduced to the allocation of the global investment. Foreign investment is assumed to have perfect mobility across societies. Contrary to the perfect mobility of capital, it is also assumed that there is no mobility of workers. Hence, societies compete with each other in attracting investment, particularly investment in physical capital. Under this particular stage set, in which social actors perform their roles, general equilibrium in the capitalist system will be pursued.

From the partial dynamic models, we can see that the basic endogenous variables of the unified dynamic model still include the growth rate of output per worker and the degree of income inequality in each type of society. The exogenous variables include the global savings rate (s*) and the global rate of technological progress (g). Among exogenous variables that are society-spe-cific (specific to society j), the model includes the rate of population growth (nj), the investment ratio (ej), the average years of schooling of workers (Ej), the initial factor endowments (k0j), and the degree of initial inequality (δj).

The Theory of Investment Behavior

The investment theory proposed here assumes that financial capital is per-fectly mobile across societies. It also assumes that the investor’s choice about

Unified Theory of Capitalism l 71

the allocation of investment among societies is taken from portfolios that offer different average rates of return and measurable risk. Under this con-text of economic choice, investors will have an appropriate rationality.

About portfolio choice, the theory will assume the following rationality:

α(C). (3) Theory of investment: The investor’s rationality to choose a port-folio is based on lexicographic preferences about mean rates of return and measurable risk. This implies a sequence of decisions. First, the individ-ual seeks to avoid portfolios where the risk of losses is unbearable; sec-ond, among the affordable portfolios, the investor will choose a portfolio according to his preference on mean rates of return and risk.

The first choice has to do with a class-survival strategy; the second refers to the maximization motivation; moreover, the first objective has priority over the second. The exogenous variables include resource endowment of the capitalist, the mean returns, and the risk (measurable risk in this case) of individual assets.

According to this rationality, capitalists seek to avoid playing economic games in which the risk of making losses under bad events could reduce their individual capital stock to a level that is zero or below the threshold value that is needed to continue as member of the capitalist class, even if large gains might result under good events. If this loss happened, it would mean an economic disaster because the individual would stop being a capi-talist. Therefore, capitalists set limits on the risk of losses to be taken; capi-talists will play only those games where outcomes exclude any possibility of economic disaster.

Under this rationality, firms are the means to obtain these objectives. Capitalists set up firms in particular regions to get profits, but have no inter-est in the firm itself or in the region per se. Thus, firms may go bankrupt, but capitalists do not necessarily disappear, for the investment was chosen with a bearable risk of losses. Personal bankruptcies constitute the excep-tions, not the rule, according to this theory.

A model of the investment theory will be developed now. Some consistent auxiliary assumptions will be added. First, in order to assure class position, capitalists will seek to have a level of wealth that is above a threshold value. Let this threshold value be K*. This is the minimum amount of capital that the individual must own in order to remain as a member of the capitalist class. This threshold value may represent the collateral that capitalists are required when asking for bank credit. Second, the portfolio choice refers to projects in capitalist societies in which the rate of return and the risk depend


upon the particular characteristics of each society. We can consider them to be investment projects referring to the production of the same good, but in different countries. The societies are two: epsilon and sigma. Third, risk is measured by the variance (V ) of the mean rate of return (m).

The typical investor’s behavior can be represented by the following struc-tural equations:

Given U = U [U1 (1/V ), U2 (m, V )] (6.1)Maximize U2 = U2 (m, V ), V ≤ V*, U21>0, U22<0Subject to m = f (V), f ′>0mj = g (kbj, hj), g1<0, g2>0, and j=ε, σVj = h (δj), h′>0, and j=ε, σI = Σj Xj

V* = F (K).

The first equation shows the lexicographic utility function of the investor, where m is the mean return and V is the variance of the portfolio of projects. The terms mj and Vj represent the mean return and variance of an invest-ment in epsilon or sigma society; therefore, m and V will show the mean and variance of the portfolio of projects, which is equal to the corresponding weighted averages of those values, where the weights are determined by the share of projects in the portfolio.

The second equation indicates that the capitalist seeks to maximize the second-order utility function, subject to the constraint that the first-order utility function is satisfied; here V* is the threshold of tolerable risk, a devi-ation from the mean in units of the standard deviation. Thus, the threshold of income losses that are bearable by the individual is given by (m – √V*) multiplied by the investment; beyond this threshold, the losses would imply economic disaster.

The third equation shows the feasible set of portfolios: the higher the variance of a portfolio, the higher its mean return should be, if the two soci-eties can compete in the portfolio of the investor. If investment in sigma has higher mean return than in epsilon, the risk must be higher in sigma than in epsilon; if risk were lower in sigma, then projects in epsilon could not compete and all the investment would go to sigma. More generally, portfolio choice requires that the society that presents the lower rate of return should be less risky.

The fourth and fifth equations show the assumptions about the deter-minants of the rate of return and risk in each society. The rate of return in


society j will depend negatively on the stock of physical capital per worker (kb), due to diminishing returns to the factor, and positively on the stock of human capital per worker (h), which increases the return of physical capital. The risk of investing in society j will depend negatively on the ini-tial inequality (δ). The assumption is that higher initial inequality implies higher income inequality, which in turn implies higher social disorder and much riskier society, as shown in chapter 7 (volume 1). It should be noted that the values of the rate of return and risk are unobservable, for they are expected values attributed by investors to the projects in each society. However, these relations indicate on what observable variables the expected values depend.

The two final equations in the system (6.1) indicate idiosyncratic restric-tions that the investor faces. The first says that the investor is endowed with a given amount of investment fund (I), which must be allocated to these two economies. The second says that the investor’s bearable losses (V*) depend positively upon his wealth (K ). Then big investors will be able to invest in large and very risky projects, in which small investors cannot. If the possible losses leave the capitalist with wealth equal or higher than the value of capi-tal needed to be a member of the capitalist class (K*), then we say that those losses are bearable and cannot generate an economic disaster.

Consider the following example. Let us consider a portfolio A with mean return of 10 percent and standard deviation of 20 percent and a portfolio B with values of 30 percent and 50 percent respectively. Let the value of K* be equal to 100 dollars and the capitalist’s wealth be 150 dollars, which is totally invested. Choosing portfolio A implies a possible loss of 30 dollars (20 percent of 150) and a possible reduction of wealth to 120, which is still higher than 100 dollars. Choosing portfolio B implies a possible loss of 75 dollars (50 percent of 150) and a possible reduction of wealth to 75, which is below the threshold of 100 dollars. Hence, the capitalist will choose port-folio A instead of portfolio B, even though B has a higher mean return and a larger gain if a favorable event occurs. Suppose another capitalist has a wealth of 300 dollars, then he could consider choosing portfolio B because the possible loss is 150 dollars, which would reduce his wealth to 150, above the threshold of 100; so this loss would be bearable and he would be able to earn 50 percent over his investment.

From this example, it is clear that the higher the capitalist’s wealth is, the higher the total losses he can bear, and the higher the mean return he can get from investments. The implication is that capital accumulation tends to increase wealth inequality within the capitalist class because the very wealthy, relative to the less wealthy, will be able to invest in risky portfolios but with the possibility of obtaining high mean returns, which will further


increase their wealth. This prediction seems to be consistent with the few large corporations that dominate the oil industry.

Capitalists also face the risk of destruction of their capital stock in every period. This risk loss can be avoided through the insurance market. The capitalist will purchase a certain amount of dollars of insurance and will pay a premium per unit of time. The physical capital insured will not be smaller than K*. In other words, the capitalist will not seek to play risky games, that is, games that might lead to a loss beyond the bearable level, even if large profits occur due to a favorable turn of events. The capitalist behavior is guided by the motivation of aversion to risky games in this precise sense. This assumption is different from risk aversion, which is the assumption made in standard economics—mean–variance theory. In this case, the capitalist will prefer a portfolio that offers a higher mean return at the same risk, or lower risk at the same mean return; but the capitalist will also prefer a higher risk portfolio if the mean return is sufficiently high to compensate for the high risk. There are no limits to risk under the assumption of risk aversion behav-ior. The capitalist does not care for economic disaster.

Risk aversion theory predicts that the portfolio will not change as wealth increases. An optimum portfolio remains optimum if the investor has more capital to invest. The aversion to risky games theory predicts that the port-folio will change as wealth increases. As the wealth of the investor increases, he can take those more risky portfolios that were not bearable before, but are now. In the real world, portfolios seem to vary across wealth levels of capital-ists. This fact clearly refutes the prediction of the risk aversion theory, but it does not the prediction of the aversion to risky games theory.

Across societies, the investor’s portfolio choice will depend on the differ-ences in the rate of return and the risk of projects between epsilon and sigma societies, which in turn depends upon differences in their factor endow-ments and initial inequality. On the rate of return, the difference depends upon factor endowments; on the standard deviation, the difference depends upon social order, that is, on the degree of initial inequality.

Factor endowments are such that capital per worker is higher in epsilon compared to sigma; but epsilon is also more endowed with human capi-tal per worker, as Robert Lucas (1990) pointed out. The first makes the mean rate of return lower (due to diminishing returns) in epsilon, while the second increases that return; hence, factor endowments do not gener-ate a clear difference in mean returns between these two types of societies. Thus, the critical factor will be risk. Investment projects in sigma will be riskier than in epsilon because sigma is a more unequal society, as shown in chapter 7 (volume 1). Therefore, investors will have incentives to allocate much of their investment portfolio to epsilon society rather than to sigma;


consequently, the investment ratio in physical investment will be higher in epsilon than in sigma.

Empirical studies are consistent with this prediction of the investment model. The bulk of foreign direct investment flows are within the First World countries (Markusen, 2002, Table 1.2, p. 9, and UNCTAD, 2006, Table 3.9, p. 108). Markusen concludes, “Not surprisingly, the developed countries are the main source of outward investment, but perhaps less known, they are the major recipients as well” (p. 8).

The investment ratio e has then been endogeneized. Hence, for society j

ej = Ij/Yj = rj I /Yj = rj (I/Y)/(Yj /Y) = rj s*/bj, j=ε, σ (6.2)rj = F (δj / δk), F ′<0ej = Φ (δj / δk, s*), Φ1<0, Φ2>0

The first equation of the system (6.2) just follows the definitions and introduces new terms: rj is the investment share of society j in total investment, I is global investment, Y is total output, bj is the share of society j in total output, and s* is the total savings ratio. The model assumes that investment is independent of domestic savings in each society; however, total investment must be equal to total savings in the aggregate. The second equation says that the investment share of a society depends upon its degree of inequality relative to the inequal-ity of the other societies. The third equation is just the reduced form, which implies that investment rate will be higher in epsilon than in sigma.

Output Growth in the Capitalist System

The investment rate has already been endogenized. The unified dynamic model will make additional assumptions for endogenizing other exogenous variables.

Regarding investment in formal education, the unified model will assume that the investment ratio in human capital is higher in richer and more equal societies, in which the supply of public goods (in quantity and quality) to satisfy the demands for human capital of their more homoge-neous citizens will be higher. This is the case of investment in education and health services. Therefore, the investment ratio in education will also be higher in epsilon than in sigma. On the growth rate of population (n), the model will assume that this rate is lower in rich and more equal socie-ties. Children are seen as assets in families, but more so in poor families and socially unprotected ones. Then population growth rate will be higher in sigma than in epsilon.


The reduced form equation of the growth frontier in the unified dynamic model can then be written as follows:

yj*(t) = f j ( ej , Ej , nj; g, t), j= σ, ε (6.3)= F j (δ j /δk; s*, g, t), F1<0 and Fi>0.

This equation implies a difference in the growth frontiers of epsilon and sigma due to the higher value of the initial inequality in sigma compared to epsilon. Then

[δε < δσ] → [yε*(t) > yσ*(t)] (6.4)

The growth rates of the growth frontiers are equal to the growth rate of tech-nology (g) in both societies. Hence,

Δyε*/yε* = Δyσ*/yσ* = g (6.5)

Equations (6.4) and (6.5) comprise the general equilibrium conditions of the growth process in the capitalist system. The gap between the growth frontiers of epsilon and sigma is due only to their differences in initial inequality. In explaining differences in income levels between epsilon and sigma, the reduced form of the dynamic model indicates that the initial inequality is the ultimate factor, whereas the exogenous variables e, u, and n are just proximate factors.

Figure 6.1 shows the unified dynamic model. The curve E*F* repre-sents the growth frontier in the epsilon society, whereas S*R* corresponds to that in sigma society. The growth rate along both frontiers is equal to g, the growth rate of technological change. The transition dynamics are also shown here. Any epsilon society with initial conditions of output per worker (determined by the initial physical capital per human capital) that is lower than the intercept of the frontier curve will move spontaneously toward the frontier curve E*F*, along the transition dynamics, which implies a growth rate that is faster than g. The segment EF′ shows this transition dynamics, which reaches the frontier at time t1*. Any omega society will also move toward the frontier curve E*F*. This is represented by the segment GF″, which is also transitional dynamics. At period t2*, omega has eliminated overpopulation and has endogenously become an epsilon society.

Any sigma society will also tend to approach spontaneously from any ini-tial condition toward the growth frontier curve S*R*, as indicated by the seg-ment RR′. This path implies that the capitalist sector of sigma moves along its own transition dynamics (segment CC′) and reaches the frontier S*R* at


period t3*, when the X-subsistence sector has been eliminated. The segment RR′ is the trajectory of the national income per worker, which grows at a rate that is near the growth rate of segment CC′. Beyond period t3*, the segment RR′ changes to R′R″, the growth rate of which is smaller and equal to the weighted average of the output per worker of the capitalist sector moving along the frontier S*R* and that of the Z-subsistence sector that moves along a path that is located at a lower level. As shown in the graph, the growth frontier curve will be approached endogenously, but it will never be reached. The existence of the Z-subsistence sector leads to this result.

Explaining Income-Level Differences in the Capitalist System

The growth frontier curves or trajectories are different between types of cap-italist societies: that of epsilon lie at a higher level compared to that of sigma. This gap will persist over time, as long as the exogenous variables remain fixed. The relevant exogenous variable is the initial inequality difference.

Savings rate is another exogenous variable, but it does not affect the dif-ference in income levels. The growth rate of technological change (g) is also

y

t

R´

y0 (ε)

O

y0 (ω)

y0 (σ)

C´ R´´

F´´

F´

E

G

C

Rq0

E*

F* [g]

R* [g]

S*

t *3t *2t *1

[s*, δ(σ), δ(ε)] y**

[s*, δ(ε), δ(σ)] y*

Figure 6.1 Growth of output per worker in the capitalist system.


exogenous, but it does not affect the gap between the curves. Changes in both variables will shift the growth frontier curves of each society, so the difference in the levels of the growth frontier curve will persist over time.

These predictions of the unified dynamic model refer to changes in the growth frontier curves, that is, on the structural differences in income levels between epsilon and sigma. But the growth frontier curves are unobservable. What is observable is the trajectory of the transition dynamics. Thus, the observed behavior of national income per worker will lie below their growth frontier curves. The transitions dynamics of national income per worker in each type of capitalist society can then be written as follows:

yj (t) = f j (q0j*, y0j, g, t), fi>0, y0 < q0*, t ≤ tj*, j=σ, ω, ε (6.6)

For each type of society q0* refers to the initial value of the growth frontier of the capitalist sector, which is also the frontier of the society. The term y0 indicates the initial output per worker, which in turn is determined by the initial factor endowments (physical capital per worker and human capital per worker, together with the technological level). The assumption is that factor endowments are higher in epsilon than in sigma, whereas omega falls in between. Finally, the term t* is the period at which the transition dynam-ics is completed.

From the system of equations (6.6), and from visualizing the curves shown in figure 6.1, it follows that in transition dynamics

yε (t) > yω (t) > yσ (t), t ≤ t* (6.7)

The unified dynamic model predicts that differences in income levels between epsilon, omega, and sigma follow this order among societies. On growth rates, the unified model has shown the following results:

Δy/yj = F j (q0j*/y0j, g) > g, Fi > 0, t ≤ t*, j=σ, ω, ε (6.8)

In the three societies, the growth rate is higher than that of the frontier (g). The growth rate in each society depends upon the gap between the initial value of the growth frontier curve and the initial condition and the value of g.

Does the model predict differences in growth rates across societies? Although epsilon and omega have the same growth frontier, omega will necessarily start from a lower initial value in output per worker because its factor endowment is lower; it is an overpopulated society. Thus, there are two effects: compared to epsilon, omega’s lower initial income implies


a higher growth rate, but its overpopulation implies a lower growth rate. Therefore, the difference in the growth rate between omega and epsilon is undetermined.

Sigma society has a transition dynamics trajectory that moves toward a lower-level frontier curve from a lower initial income compared to that of epsilon. Its capitalist sector will grow at a rate that is higher than that of its own growth frontier. Nevertheless, the growth frontier will never be reached. Therefore, the model cannot predict differences in growth rates between sigma and epsilon.

In sum, the equilibrium conditions of the unified dynamic model do not generate empirical predictions about differences in the growth rates across societies in the capitalist system. What the model predicts is a different fea-ture of the capitalist system: because the frontiers of destination for the tran-sition dynamics are different for sigma and epsilon, the income levels will not be equalized in the growth process, no matter how fast sigma grows compared to epsilon. Hence, differences in the growth frontier and income levels are endogenous; what is exogenous is the initial degree of inequality of countries, which determines the allocation of investment across countries.

Differences in average labor productivity or output per worker between epsilon and sigma societies imply differences in real wages, for real wages cannot be independent of labor productivity; therefore, real wages do not tend to equalize between epsilon and sigma societies in the process of eco-nomic growth. Even if free international trade of goods were allowed in the model, there will not be real wage rate equalization, unless trade equal-ized labor productivities. As shown earlier, countries compete with their degree of inequality in the international arena for private investment, which goes mostly to epsilon societies; so labor productivities cannot be equalized. How could then low-productivity countries be able to compete in the inter-national markets of goods? They can compete because their low produc-tivity is compensated with their low wage rate. Hence, international trade patterns are also explained by the initial degree of inequality of societies (Figueroa, 2014).

As to comparative dynamics, if the initial inequality (δ) in sigma society declines relative to that of epsilon, its frontier will be shifted upward. Hence the gap q0*/q0 will be higher and thus the growth rate will increase along the new transition dynamics within the capitalist sector. This change will have an effect upon the trajectory of the national income per worker, that is, the gap q0*/y0 will also be higher and thus it will grow faster along a new trajectory, as indicated in equation (6.8). Thus, a decrease in the degree of initial inequality in sigma society will increase both its income level and its growth rate and thus will reduce the income gap with epsilon society. The


other exogenous variables (s* and g) are general for the capitalist system and thus will affect both sigma and epsilon; however, income-level gaps between these two societies will tend to remain unchanged.

Explaining Income Inequality Differences in the Capitalist System

The task is now to determine the predictions of the dynamics models regard-ing changes in the level of income inequality differences between the three abstract societies. Income distribution is determined, as measured by the Lorenz curve or Gini index, by both functional distribution and personal distribution.

Figure 6.2 shows the level of income inequality in each of the three capitalist societies. First, consider the distribution of income in the sigma society, which is shown by the Lorenz curve OABCO′. Assume that the concentration in physical capital ownership is not too different across soci-eties; furthermore, assume that profit share is also similar. Then the seg-ment CO′ may also refer to profits in epsilon society; then the Lorenz Curve OCO′ will represent income distribution in epsilon society, in which the segment OC refers to wage earners. It is pretty clear from the graph that the degree of income inequality in sigma will be higher than that in epsilon.

OA

B

C

O´

ε

σ

ω

Figure 6.2 Levels of income inequality in the capitalist system.


As to level values, it can also be shown that the degree of income inequality in sigma is higher than that in omega. Suppose as a first approx-imation that segments BC (wage earners) and CO′ (capitalists) belong to sigma and to omega. Because human capital is homogeneous in omega, the remaining segment would be OB (single subsistence sector). Omega’s Lorenz curve will be OBCO′, which implies that inequality is smaller in omega than in sigma. There is human capital concentration in sigma, between X-workers (high skill) and Z-workers (low skill), which is respon-sible for separating the OB segment into two: OA (Z-workers) and AB (X-workers). The segment OB is the average relative income of the two subsistence sectors in sigma. However, workers in omega are homogeneous in skills; so income inequality among workers in omega will be lower than that in sigma. Then point B in omega could be located higher up, at point B′ (not shown), which would imply a Lorenz curve OB′CO′ (not drawn) in omega that shows a degree of inequality that is much smaller than that in sigma.

In sum, at the beginning of the growth process, the degree of income inequality (D) in the three societies can be ranked. The unified static model made the assumption about the degree of asset inequality in the three soci-eties as follows: higher initial inequality in sigma than in the other societies due to higher concentration of both human capital and degree of citizen-ship, as discussed in chapter 7 (volume 1). Then we know that the level of income inequality depends upon the initial asset distribution, as shown in the partial dynamic models, chapters 3–5 (this volume). Figure 6.2 just veri-fies this prediction, which can be written as follows:

[δ(σ) > δ(ω) ≥ δ(ε)] → [D(σ) > D(ω) ≥ D(ε)] (6.9)

The next question is to determine whether this order changes in the process of economic growth. As shown in the partial dynamic models, the degree of income inequality tends to increase in the growth process in omega and sigma, but tends to remain constant in epsilon. The unified model can-not predict differences in the speed of change between omega and sigma; hence, the model predicts that the initial order of income inequality will tend to persist in the growth process.

Figure 6.3 displays the predictions of the unified model upon the trajec-tory of income inequality in the growth process (along the transition dynam-ics). Line EE′ represents the trajectory of epsilon society, which tends to be constant over time. Line MM′ corresponds to omega society and it increases over time. Line SS′, which corresponds to sigma society, also increases over time.


What is the effect of the exogenous variables of the dynamic models upon the differences in income inequality between societies?

As shown in chapters 3–5 (this volume), any factor that shifts the growth frontier curve upward (e, n, E, g) will have the effect of increasing the level of income inequality in each society; moreover, the variable ini-tial inequality (δ) of each society has a positive direct effect upon its income inequality. In this chapter, it has been shown that those variables that affect the growth frontier, apart from variable g, can be reduced to the ratio of initial inequality of sigma to epsilon. Then it follows that the trajectory of income inequality will increase when variable g increases and when the ini-tial inequality increases relative to that of the other societies, for the relative inequality effect operates through changes in the growth frontier. Let δj/δ represent the degree of the initial inequalities of society j relative to those of the other societies or that of the capitalist system (δ).

According to the unified dynamic model, therefore, the causality rela-tions for the degree of income inequality (D) in each type of society can be written as follows:

D(ε) (t) = F (δε /δ, g), Fi > 0 (6.10)D(σ) (t) = G (δσ /δ, g, t), Gi > 0, t ≤ t* (6.11)D(ω) (t) = H (δω /δ, g, t), Hi > 0, t ≤ t* (6.12)

O

D

t

E

S

M

E´

M´

S´[δε, δω. δσ, g]

[δε, δω. δσ, g]

[δε, δω. δσ, g]

Figure 6.3 Income inequality changes in the growth process in the capitalist system.


Given the values of the exogenous variables, the growth process (along the transition dynamics) implies that the degree of income inequality is con-stant in epsilon, but it increases over time in omega and sigma. Changes in the values of the exogenous variables will modify these trajectories. Thus the level of income inequality increases in any society if the relative initial inequality increases in the same society, that is, if δj/δ increases in epsilon, investment will move to sigma, increasing the rate of investment and thus shifting upward the growth frontier of sigma, which will lead to a higher growth rate of the transition dynamics in the capitalist sector, which in turn leads to higher income inequality in sigma. Income inequality of each soci-ety will increase if the growth rate of technology (g) increases.

According to the unified dynamic model, the economic growth process (income growth and income inequality) is interdependent among the soci-eties of the capitalist system, for changes in the exogenous variables will affect all societies. The capitalist system operates as a general equilibrium model. Relative income inequality between societies changes only when the relative initial inequalities change; variable g affects the trajectory of income inequality of all societies, so the differences between societies may remain unchanged.

Beta Propositions

The empirical predictions of the unified dynamic model about the trajecto-ries of income levels and income inequality along the transition dynamics in the capitalist system can be summarized as follows:

(a) The initial income level gap between omega and epsilon will decline and will tend to disappear, for there will be convergence. The initial income level gap between epsilon and sigma societies will not tend to converge.

(b) The level of income inequality will remain constant in epsilon, but will increase in omega and sigma; so the initial differences between sigma and epsilon societies will rise.

(c) Overall income inequality in the capitalist system will tend to increase. This follows from (a) and (b): between-society inequality will rise and within-society inequality will become higher in poorest societies.

Predictions (a) and (b) refer to the trajectories of income and income inequal-ity, which constitute the equilibrium paths of growth and distribution in the each capitalist society. They will proceed over time as long as the exogenous variables remain unchanged. The exogenous variables include the factor


endowments and the initial inequality of each society, together with the aggregate rate of savings and the growth rate of technological change in the capitalist system. Changes in these exogenous variables will have the effect of shifting upward or downward the trajectories, as shown earlier.

Note that the initial inequality does not change endogenously in the growth process in any type of society. The partial dynamic models assume that there are mechanisms by which the initial inequality tends to be repro-duced. Thus, inheritance, access to credit and insurance markets, influence in public policies, and social networks tend to reproduce inequality in physi-cal and human capital. These models then predict that owners of large phys-ical capital are too big to fail, whereas owners of small physical capital are too small to grow. They also predict that education is neither human capital nor income equalizing. Therefore, the initial inequality can only change exoge-nously in any capitalist society.

Prediction (c) refers to the degree of income inequality in the capitalist system, taken as a whole, which is the result of within-society inequality and between-society (income levels) inequality. Changes in savings rates and in the growth rate of technological change will show their effect the same direction as the trajectories of income levels in the three types of soci-eties; hence, their gaps will tend to remain unchanged. Changes in both the income levels and their gaps between societies will depend upon the changes in the initial inequalities of societies alone.

Aggregating the equations (6.9) to (6.12), the reduced form of the overall degree of inequality in the capitalist system (D) can be written as follows:

D = F (δ, g, t ), Fi > 0, t ≤ t* (6.13)

The beta propositions are then the following: (1) Given the degree of initial inequality in the distribution of economic and political assets in the capi-talist system (δ) and the growth rate of technology (g), the overall income inequality will increase over time together with the economic growth pro-cess. (2) The initial distribution of economic and political assets among indi-viduals tends to remain unchanged through several mechanisms, including private property inheritance, human capital accumulation, and through lack of incentives to change citizenship inequality, that is, there is no mechanism that can endogenously alter the initial inequality. (3) The income inequal-ity trajectory will be shifted upward if, exogenously, the initial inequality increases or the growth rate of technology rises. The global savings rate (s*) has been neglected in this equation on the assumption that, in the long run, it also depends upon the global initial inequality.


According to the unified dynamic model, the growth frontiers of epsilon and sigma societies are separate and hierarchical. This is the major feature of the economic process in the capitalist system, which implies the exis-tence and persistence in income level gaps between epsilon and sigma soci-eties. The separate growth frontier curves reflect different initial conditions (history), which refer to differences in the initial inequality, which in turn reflects on the legacy of the European colonial system. The mechanism is that colonial systems leave colonial societies with the legacy of a highly unequal society, not only in terms of high concentration of physical cap-ital and human capital, but also in terms of political entitlements. Factor endowments, the other initial condition, are not essential, as overpopulation can be eliminated in the process of economic growth, as in the case of omega society. The existence and persistence of within-country inequality between epsilon and sigma also originate in the initial inequality in the distribution of economic and political assets in each society and in the capitalist system as a whole.

Empirical Evidence: The Capitalist World, 1950–2010

The dynamic model of the unified theory presented here intends to explain the basic empirical regularities of capitalist countries on growth and distri-bution. The abstract societies (epsilon, omega, and sigma) intend to explain the First World, the Third World with a weak colonial legacy, and the Third World with a strong colonial legacy, considered separately. We now examine their empirical predictions as unified theory.

Growth and Distribution in the Capitalist System

The predictions (a) and (b) of the unified dynamic model refer to transition dynamics. This is the relevant trajectory, assuming that initial inequality and growth rate of technological changes have remained unchanged in the past decades. These two predictions are indeed consistent with the empirical regularities 6 and 7 of the capitalist system presented in table 2.2 (chap-ter 2, volume 1). Income level differences between epsilon countries and sigma countries are large and have increased even more (from 4.0 to 6.4 times) in the three decades for which comparable information is available; on the other hand, the income level differences between epsilon countries and omega countries are not as large, and the gaps have declined from 2.5 to 2.0 times.

Regarding within-country inequality, table 2.2 (chapter 2, volume 1) showed that the average degree of income inequality in the period 1950–1970,


measured by the Gini index, has the lowest value in the epsilon countries and the highest in the sigma countries, with the omega countries falling in between. This order has been maintained in the growth process as indicated for the 1971–2008 period. This fact is consistent with the second prediction of the model.

The international literature dealing with the economic growth process tends to corroborate the consistency of the predictions of the model with new facts. A recent data set constructed by Professors Jones and Vollrath (2013, Appendix C) shows income levels relative to the US income level and growth rates by countries for a large sample of countries of the world for the period 1960–2008. Selecting only capitalist countries and classifying them into the three categories of the unified theory, a sample of 102 capitalist countries were obtained, 21 for epsilon, 11 for omega, and 70 for sigma.

Table 6.1 shows the results from this sample. The figures are consistent with the prediction (a) of the unified model: (1) income level differences taken as groups of countries follow the prediction of the model; (2) income levels of the epsilon and omega countries move toward the “growth fron-tier” given by the US income level, but sigma countries do not. Considering growth rates of output per worker, table 6.1 shows that omega countries grew faster than epsilon countries in the period 1960–2008, although the differences are not statistically significant. Sigma countries show the low-est growth rate. To recall, the unified dynamic model has no predictions about growth rates differences among types of societies, as can be seen in figure 6.1; what it predicts is different growth frontiers.

On the persistence of income-level gaps, the classic empirical study on convergence by Barro and Sala-i-Martin (2004) found that one pattern in the cross-country data is that the growth rate of real per capita GDP from 1960 to 2000 is positively correlated (although slightly) with the level of per capita GDP in 1960 in a sample of near 100 countries. If there were convergence toward a unique growth frontier, then there would be strong negative correlation: the poorer countries should grow at higher rates, which is not the case. However, this study includes in the sample capitalists and noncapitalist countries. The other pattern is more significant for our theory, for it found that convergence does exist within the OECD countries, which largely corresponds to our empirical definition of epsilon countries; hence, according to the unified model, we could say that all epsilon countries tend to converge to the common growth frontier, as the unified model predicts.

The unified model predicts that omega societies tend to catch up with epsilon societies. This prediction has been corroborated by empirical data presented in table 6.1 for a recent history. In the long run, according to eco-nomic historian Angus Maddison (1995), Japan is the only case of catching

Table 6.1 Income per worker and growth rates in the capitalist system, 1960–2008

Group N Average GDP per worker, relative to the US value

(US =1.00)

Average annual growth rate of

GDP per worker

1960US$:39015

2008US$:84771

(1960–2008)

A. First World: 21 0.6887 0.8549 0.0215Epsilon society (0.2256) (0.1869) (0.0061)

B. Third World with weak colonial legacy:

11 0.2648 0.5096 0.0268

Omega society (0.1459) (0.2901) (0.0152)C. Third World with strong colonial legacy:

70 0.1379 0.1368 0.0136

Sigma society (0.1308) (0.1465) (0.0143)

Test of means for the average GDP per worker, 1960 vs. 2008

Test of means for the average annual growth rate of GDP per worker, 1960–2008

Epsilon t-statistic –3.812 Epsilon vs. Omega

t-statistic –1.446p value 0.001 p value 0.174

Omega t-statistic –2.469 Omega vs. Sigma

t-statistic 3.025p value 0.033 p value 0.010

Sigma t-statistic 0.087 Sigma vs. Epsilon

t-statistic –3.641p value 0.931 p value 0.001

Notes: (1) The numbers in parenthesis indicate standard deviation. (2) The sample of epsilon countries includes 17 western European countries, Canada, United States, Australia, and New Zealand; the sample of omega countries includes Argentina, Costa Rica, Iran, Israel, Japan, Singapore, South Korea, Taiwan, Thailand, Turkey, and Uruguay. (3) Testing of mean differences was made using nonparametric statistics. At p=0.05, all differences are statistically significant, except in two cases: mean income differences within sigma countries and mean growth rate differences between epsilon and omega countries.

Source: Author’s calculation, based on the data set presented in Jones and Volltath (2013, Appendix C, pp. 278–282). Income per worker in the United States is measured in nominal dollars.


up in the modern times. A country that in 1820 was among the group of poor countries, Japan has become a full member of the club of the rich countries. Japan’s income level was only 0.36 of that of the United States in 1960, which jumped to 0.76 in 2008 (Jones and Vollrath, 2013, Appendix C). (This is the reason to include Japan in the group of omega countries in table 6.1.) The other countries to be included here in the near future are South Korea and Taiwan. In light of the unified model, these three Asian countries indeed started capitalist development as omega societies; there-fore, these countries’ growth performance cannot be seen as “miracles,” as they are usually seen, for the unified model predicts this behavior.

According to the unified dynamic model, differences in the initial out-put per worker of each type of society is determined by differences in factor endowments. Estimates of capital per worker show that indeed it is higher in the epsilon type countries than in the sigma type. According to the Penn Table data, the average value was 54,000 dollars per worker for the former and 9,000 for the latter in 1998, for a sample of eight and seven countries, whereas the value for South Korea was 27,000 (shown in Carbaugh, 2011, Table 3.2, p. 71). The average human capital is also consistent with the pre-dictions of the model: an average of 10.7 years of schooling in epsilon type of countries, 9.1 in omega type, and 6.1 in sigma type for 2008 (estimated by the author from Jones and Vollrath, 2013, Appendix C).

Thus, the unified theory predicts that First World countries and Third World countries with a strong colonial legacy have different growth fron-tiers; hence, in the process of economic growth they will converge to their respective growth frontiers. Catching up is thus the exception, not the norm. This prediction is consistent with Fact 6 (chapter 2, volume 1).

By comparison, the unified dynamic model and the models of the neoclas-sical growth theory (Barro and Sala-i-Martin, 2004) are similar in that they both predict conditional convergence. However, they differ in the exogenous variables: in the unified model, differences in the initial inequality consti-tute the ultimate factor that determines the difference in the growth frontier curve between the epsilon countries and the sigma countries. Therefore, the country-specific characteristics, such as investment ratio, population growth rate, government policies, and many others included in the standard neoclassical models constitute proximate factors only, not ultimate factors.

More recently, economist Odar Galor (2011) has proposed a unified the-ory of output growth, which intends to explain this process for the entire human society. The observed divergences in income levels across countries are explained by the differences in their time of take-off from stagnation to growth, which in turn reflect differences in specific geographical and his-torical factors, including colonial status, of countries. Because the transition


from stagnation to growth is inevitable, this neoclassical model predicts endogenous convergence of income levels in the long run for all countries of the world, not only capitalist countries; thus initial conditions, including the colonial history, do not matter; there is no path dependence. In contrast, the unified theory of capitalism presented in this chapter predicts conver-gence between epsilon and omega societies only, but not between epsilon and sigma societies. Again, this prediction is consistent with facts.

It should be pointed out that sigma theory differs from the theory devel-oped by Ernest Gellner (1983), according to which ethnically heterogeneous societies tend to operate with more social conflicts, which lead to lower growth rate. This idea has given rise to some empirical work to test the correlation between degree of ethnical diversity and economic performance across countries (Alesina et al., 2003, Patsiurko et al., 2013).

To be sure, sigma society refers to a society that is multiethnic but hier-archical, the origin of which lies in the European colonial legacy. Before the colonial period, there were native populations, which after the colo-nial period became Z-populations. This is the essential factor that explains the income level differences between the First World and the Third World. So the fact that some European countries of today show ethnic diversity is ignored in sigma theory; similarly, the fact that many African countries show ethnic diversity among Z-populations is also ignored. Sigma is not a theory about ethnicity; it is about the role of the European colonial legacy in the economic growth process of the capitalist system.

On the comparisons of income inequality, we need to recognize that in the Third World income inequality data are scarce, quantitatively and qualitatively. The quantitative limitations are clearly shown in the database of household surveys: the sample size of countries is reduced drastically when the number of observations per country is increased. Qualitatively, it is known that profits and top salaries are not well captured in the Third World household surveys. (This is another characteristic of a sigma soci-ety, in which economic elites simply are not accessible for participation in household surveys.) Income inequality from these surveys seems to measure mostly the distribution of labor incomes rather than national income (which includes profits and top salaries).

The consequences of these limitations regarding inequality data in the Third World for the predictions of the unified model would be twofold. As to differences in the level of inequality, the degree of income inequal-ity in the Third World countries would tend to be underestimated; there-fore, the real gap between the Gini index for the First World and the Third World shown in table 2.2 (chapter 2, volume 1) is underestimated. As to stability on inequality trends over time that some researchers have found


(Li, Squire, and Zou, 1998), the estimated empirical changes in national income inequality in the Third World are uncertain because the database refers mostly to changes in the labor income part only.

A study on functional income distribution (calculated through the method of national accounts of United Nations) utilized a sample of 12 countries from the Third World and also 12 countries from the First World and found that the average profit share in national income was 22 percent in the former and 24 percent in the latter, around 1990 (Gollin 2002, Table 2, p. 470). To be sure, in the data shown in table 2.2, chapter 2 (volume 1), profits are mostly included in the Gini index for the First World countries, but they are not for the Third World; hence, income inequality differences are underestimated. To make them comparable, the Gini coefficient for the Third World would have to be recalculated attributing income from profits, 22 percent of national income to, say, the 0.1 percent of households!

Growth and Changes in Assets Distribution

About the main exogenous variable of the unified dynamic model, what evi-dence do we have about differences in the inequality of assets distribution in the First World and the Third World?

Regarding differences across countries about the degree of asset inequality, empirical studies are even scarcer. A study on household wealth inequality presents estimates of Gini coefficients for a sample of 19 capital-ist countries (16 from the First World and 3 for the Third World) for the year 2000, in which the average Gini coefficients are very similar, around 0.67 (Davies et al., 2010, Table 7, p. 246). Another study shows higher wealth concentration for the case of the United States in 1995: The Gini coefficient for the distribution of household net worth was 0.83; for finan-cial assets (net worth excluding the value of owner-occupied houses), it was 0.91 (Wolf, 1998, Table 12, p. 149). In contrast, the Gini coefficient for income inequality in the First World is around 0.30 in the First World and around 0.50 in the Third World (table 2.2, chapter 2, volume 1). These calculations show another empirical regularity in the capitalist system: the concentration of the stock of wealth is higher than the concentration of the flow of income.

On agricultural land concentration, one of the few studies about inter-national comparisons, based on a sample of 103 countries of the world from the FAO database, for the period 1950–1990, showed estimates of Gini coefficients by regions. Considering only capitalist countries, the average Gini coefficients for the First World and the Third World were not much different, around 0.60 (Deininger and Squire 1998, Table 2, p. 266).


Differences in human capital concentration can be measured using the international data of schooling years for 1950–2010 constructed by Barro and Lee (2013, Table 3), based on the UNESCO database. Taking the 2010 data and the highest level of education, the category “completed tertiary level of education” (post-secondary) was found to comprise 14.5 percent of the adult population as the level of human capital in the First World, while in the the Third World this was found to be only 4.6 percent. According to the unified model, this striking gap reflects differences in the distribution of political entitlements between epsilon and sigma societies.

These estimates on inequality in the distribution of land, physical capi-tal, and human capital suggest that the overall inequality in economic assets is higher in the sigma countries compared to epsilon countries, in which dif-ferences in the high concentration of human capital seems to be the salient feature. There were found to be no significant differences in concentration of land resources and information on the concentration of physical capital was scarce.

Regarding changes in political entitlements, some evidences can be shown. Citizenship is a qualitative variable and thus much harder to measure. The concept of second-class citizenship applies to individuals who are entitled to equal rights within the formal norms of the democratic system, but their ability to exercise those rights are limited by informal norms. The unified model assumes that second-class citizenship exists in the Third World hav-ing a strong colonial legacy, where descendants of the subordinated popula-tions of the European colonial history, which are called Z-populations in the unified model, are indeed second-class citizens. Historians usually point out this legacy by indicating the nature of the colonial institutions: “Colonial societies were generally characterized by apartheid and segregation and often were based on notions of innate racial inequalities” (Wesseling, 2004, pp. 242–243).

The international literature supplies many qualitative studies describ-ing the different forms that second-class citizenship may take in the Third World and pointing out their importance in the economic and political pro-cesses (cf. Stewart, 2001, 2008). Inequality in the distribution of human capital and citizenship are the two major factors that seem to indicate that indeed the initial inequality is higher in the Third World countries with strong colonial legacy.

Have there being changes over time on the initial inequality? There are few studies on this question. Neiman and Karabarbounis (2013) have shown that the labor share has declined significantly in the period 1975–2010 in 37 countries of a sample of 46 countries of the First World, from 0.65 to 0.59, on average. This result seems to refute the unified theory, which predicts


constant income inequality given that the initial inequality remains fixed. However, the study by Thomas Piketty (2014) shows that the concentration of capital among the top 1 percent of owners increased in that same period in three countries of Western Europe (France, Sweden, and the United Kingdom) from 21 percent to 24 percent and in the United States from 28 percent to 34 percent (Appendix, Table S10.1). According to the unified theory, these increases in the initial inequality have led to the observed rising income inequality in the First World in the last decades. These differences in the level of wealth concentration can also explain the fact that the level of income inequality in the United States is higher than that of Western European countries, as predicted by the unified theory.

In sum, the unified model predicts that differences in the level of within-country inequalities among capitalist countries depend upon differences in their initial inequality. The empirical evidence indeed tends to corroborate this prediction: countries with strong colonial legacy have the highest ini-tial inequality; moreover, these countries also have the highest degree of income inequality among the capitalist countries of today, as was shown in table 2.2, chapter 2 (volume 1).

Conclusions

This chapter has presented a dynamic model of the unified theory of capital-ism. The model is able to explain the determinants of both income growth and income distribution in the capitalist system taken as a whole.

According to the unified dynamic model, sigma and epsilon societies travel along different paths in the economic growth process, for they have separate and hierarchical growth frontier curves. Therefore, the initial gaps in income and the initial gaps in the degree of inequality persist in the growth process; hence, sigma societies do not become epsilon endogenously. However, omega societies tend to become epsilon. These are equilibrium paths because there is no social actor that has both the power and the will to change the trajectories; hence, these trajectories will proceed over time as long as the exogenous variables remain unchanged. The exogenous variables include the initial inequality, the aggregate savings rate, and the growth rate of technological progress. The latter two have effects upon all societies and tend to maintain their differences; it is the variable initial inequality that determines the income and inequality gaps.

These predictions have been submitted to the falsification process. Because changes in the initial inequality in the distribution of economic and politi-cal assets (the power structure) across capitalist countries are not significant, the observed data would more likely reflect the economic growth process


alone. The available empirical data are indeed consistent with the empir-ical predictions of the unified dynamic model. In particular, the dynamic model of the unified theory predicts Fact 6 and Fact 7: the persistence in income level gaps and in the gaps of income inequality levels between the First World and the Third World. Both gaps are explained by differences in their initial condition (history), namely their initial inequality.

This leads us to conclude that the abstract societies constructed in the unified theory do resemble quite well the real world that the theory intends to explain. Hence, there is no reason to reject the unified dynamic model, and we may accept the unified theory at the present stage of our research, although only provisionally, until new empirical data or a superior economic theory appears.

According to the unified theory of capitalism, the global inequality in the capitalist system (which comprises between-country inequality and within-country inequality) will persist as long as the distribution of economic and political assets at the national and international levels remains unchanged. This is to say, as long as the initial power structure remains unchanged. According to the unified theory, therefore, there is path dependence in the process of capitalist economic growth, that is, history matters. The history that matters is the European colonial legacy. In order to change the initial inequality, there is the need to break with the past.

The idea of constructing a unified theory of capitalism confronts another challenge that has to do with the unity of knowledge in modern economics. In order to meet this new challenge, economics must study the interactions between changes in the biophysical environment and the growth process. The dynamic model of the unified theory of capitalism that has just been presented here assumes that there are no limits to economic growth, that is, economic growth can go on forever. The same can be said about economic growth in the noncapitalist societies of today. Explaining the relationships between growth, distribution, and the environment should be pursued by any economic theory of modern economics, for environmental degradation constitutes one of the fundamental problems of our time. This challenging question is pursued in Part II of this volume.

PART II

The Very Long Run: Economic Growth and

the Environment

CHAPTER 7

Economic Growth under Environmental Stress

In the economic growth process shown in previous chapters, dynamic equilibrium implied continuous output per worker increasing over time in each type of capitalist society. The economic process was seen

as a mechanical one, for economic growth could proceed forever. There were no limits to economic growth. For one thing, the dynamic models ignored the interactions between the economic process and the biophysical environment.

In this chapter, those interactions are taken into account. Economic growth will be seen as an evolutionary process, in which as quantitative changes take place in the process of economic growth (increasing output per worker), qualitative changes in the environment will also occur, which will affect the growth process. In the construction of an evolutionary model of economic growth, the chapter will follow the approach initiated by the late economist Nicholas Georgescu-Roegen (1971) according to whom the laws of thermodynamics (dealing with matter and energy relations) are included in the economic process.

The model of the unified theory will now assume the capitalist system taken as a whole. It will also assume that at this stage of capitalist history (and human history), the economic process takes place under environmental stress. So the interaction between the economic process and the environ-ment cannot be ignored; on the contrary, it is time to construct an evolu-tionary model of the unified theory in which this interaction is assumed to be essential to understand the economic process of today and to explain, at the same time, the empirical regularity that growth has been accompanied


by environmental degradation (Fact 8). In order to build such an evolution-ary model, several intermediate models will be constructed in this chapter to understand this complex process step by step.

Model A: Economic Process with Nonrenewable Natural Resources

An economic process refers to the process of production of goods and its dis-tribution among social groups in human societies. In order to construct an evolutionary economic process, some new assumptions will be introduced. Regarding input-output elements, there will be two types of elements cross-ing the boundaries of the process: those that go into the process and come out of the process, and those that either enter or come out. The first group is called fund factors and the second flow factors. Fund factors include stocks, such as machines and workers, while flow factors include both material inputs and material output.

In the production process, therefore, material input flows from the bio-physical environment into the production process, from which material out-put flows out with the help of fund factors, the agents of change that provide the services of machines and labor in the production process. The underly-ing mechanism of this transformation is technological knowledge and social institutions.

When natural resources are taken into account, the economic process now interacts with the environment. The idea is that the environment and the economic process constitute an integrated system. Two categories of nat-ural resources are now distinguished: renewable (biological) and nonrenew-able, which will be called mineral resources here. A theoretical model is now needed to establish those relationships more rigorously.

The economic growth process will now be seen as an evolutionary pro-cess, in which qualitative changes take place as the process is repeated and, therefore, time is conceptually historical time (with past, present, and future). Call it Time T. This is contrary to the view of economic growth as dynamic process, in which time t (as used in previous chapters) refers to mechanical time: economic growth moves in the same way irrespective of when the event occurs in historical time, just like a pendulum movement, which is invariable with respect to historical time.

The evolutionary model will also assume a single-world human soci-ety, in which capitalism is the dominant system. Only one good—called good B—will be produced in this society. So machines are made of good B. International trade will thus be ignored. This society is endowed with stocks of machines and workers, and a given level of technology.

Economic Growth under Environmental Stress l 99

It is also endowed with stocks of mineral resources, distributed across planet Earth. Mineral resources will be treated as a single and homo-geneous resource. Three models will be presented step by step, so as to construct a logically correct final model, that is, free of internal logical inconsistencies.

The algorithm applied in the construction of the proper evolutionary model starts with model A. The production process will be represented in the form of a production system, as follows:

Y*(T) = F (K(T), L(T)) (7.1)Y*(T) = G (N(T)) = (1/z) N(T), z>0 and ΣNj≤S0, j=1, 2, . . . , T (7.2)

The production system (7.1)–(7.2) assumes that the flow of gross output Y* is produced in period T with the use of quantities of two types of produc-tion factors: The fund of services contained in the stocks of capital K and labor L—equation (7.1)—and the flow of material inputs N coming from the stock of mineral resources (S0), which are used as both the material input to be transformed into material good B and as the source of energy used for this transformation, equation (7.2). Total quantity of workers L partici-pates in the production process as wage earners or as self-employed persons; hence, L refers to effective full employment situation in the world society. Renewable natural resources will be ignored for the time being.

The production system assumes limitational technology, that is, the first type and the second type of factors are not substitutable for each other. Mineral resources N cannot be substituted by capital or labor; however, K and L are substitutable factors, as indicated by equation (7.1). Mineral resources enter into the production process in a fixed proportion to gross output, which is represented by the coefficient z, and are technologically determined. Feasible output will then be determined by the minimum value of the two equations (7.1) and (7.2).

Material input N needs to be produced by transforming energy and matter in situ into usable input in the production process. For the sake of simplicity, the model will assume that production of good B and of N are consolidated into one single process. Hence, given the stocks of K and L, good B and the necessary quantities of N will be produced, but the stock of mineral resources will be decreased in every period.

Finally, the production system also assumes given values for the length of the working period, and the work intensity supplied by workers in the production units. For the analysis of the long run, which is the one that concerns us here, the unit of time would be a long period, say, a decade.


Some of these assumptions will be modified by constructing two more models later on. The laws of thermodynamics (dealing with matter and energy relations) will be introduced in model B; substitution between funds and flows will be discussed in model C. Model B will turned out to be the proper model.

In model A, consider for a moment that mineral resources are redundant factors; therefore, the relevant equation in the production system is equation (7.1). Net output is by definition equal to gross output minus the quantity of goods devoted to the reposition of the stock K. The term “reposition” in this case means the quantity of good B needed to maintain constant the stock K, which implies securing the same stocks and thus the same quantity of ser-vice funds, period after period.

Let the coefficient b measure the reposition of a unit of K, that is, b mul-tiplied by the quantity of K will give us the total quantity of good B needed to replace directly the wear and tear (depreciation) of machines and thus keep the stock of capital K constant period after period. The model assumes effective full employment of machines and men.

The reposition equation for any period T can then be written as

R(T) = b K = r Y*(T), 0< r <1 (7.3)

Therefore, R indicates total reposition of machines. For a given K/Y* ratio (a dynamic equilibrium condition in the growth process), the flow of repo-sition R can be represented as a fixed proportion of the flow of gross output, the coefficient r. Because we are dealing with a production process that is productive, the coefficient r must be less than 1.

The flow of net output Y can then be written as:

Y(T) = Y*(T) – R(T) = Y*(T) – r Y*(T) = (1 – r) Y*(T) (7.4) = f [K(T), L(T)]

This equation shows that the flow of net output Y is a fixed proportion of the flow of gross output Y*; so, given the value of r, net output is also a function of K and L. The use of reposition makes the stock K a renewable factor and net output can be repeated period after period, as long as the mineral resources are redundant. Therefore, the net output Y of any period can be allocated to capital accumulation (as physical or human capital) and to consumption.

Now consider that society is endowed with machines and men in quan-tities that make them redundant factors of production. Then the relevant equation in the production system is now equation (7.2). The initial stock of


mineral resources S0 will decrease continuously in the production process, even if the same quantity of gross output is produced period after period. Therefore, the quantity remaining of the stock of mineral resources at the end of the period T, the term S(T), can be written as

S (T ) = S0 – Σ Nj = S0 – Σ z Yj*, j=1, 2, . . . T (7.5) = S0 – z Y* T = S0 – [z / (1– r)] Y T = S0 – μY T, where μ = z/(1– r).

If the quantity of net output Y is given, the initial stock of mineral resources declines irrevocably over time at the rate of N=μY per unit of time. The new stock at period T becomes S(T) according to the number of periods that the production process was repeated.

The period at which the stock of mineral resources is eventually depleted can be found by setting equation (7.5) equal to zero, that is, S0=μYT; call it T=T′. From this equality it follows that, given the initial stock of mineral resources and given the technological coefficient μ, the quantity of total out-put to be ever produced (Y × T ) is fixed. Two properties of the production process then appear: (a) if the net output is fixed, there will be a finite period T=T′ at which the stock is depleted; (b) if the net output is doubled, the number of periods that can be repeated will be reduced to half or if the net output is reduced to half, the number of periods will double, and so on.

Dividing equation (7.5) by μ, the time path of the stock of mineral resources S(T) can be transformed into the time path of net output Y. Hence,

Y (T) = S0/μ – Y T, such that T≤T ' (7.6)

The first term on the right-hand side shows the net output that society could produce with the initial stock of mineral resources. Then net output Y is producible and it is repeated over time, the society’s capacity to produce Y declines over time. This output level cannot be repeated forever, but only for a finite number of periods, up to the critical period T ′, when mineral resources become depleted.

The two equations of the production system (7.1) and (7.2) have been developed independently, each representing the constraints of funds or flows. In order to determine the actual production possibilities of produc-tion both equations must be taken into account. Let K1 and L1 be the socie-ty’s factor endowments of machines and men, which can produce net output Y1. Then


Y1 = f (K1, L1) (7.7)

The path of net output Y1 that can be produced with the stock of mineral resources could be obtained by replacing in equation (7.6) the value Y=Y1. Hence,

Y (T) = S0/μ – Y1 T (7.8)

Equations (7.7) and (7.8) take into account the constraints of both funds and flows in the production of net output Y1.

Figure 7.1 displays the flow-fund production system. The horizontal axis measures historical time and the vertical axis net output. Given the stocks of K1 and L1, and also making explicit the given level of technol-ogy A1, the corresponding flow of net output is represented by the segment OY1. This is the constraint given by equation (7.7). Equation (7.8), showing the mineral resources constraint, is represented by the line MV. Then OM

1 2 3 4 5 6 7 8 9

Z

B

O

Y1

M

C

T

Y

P

V

T * T ´ T °

B´[K1, L1, A1]

Line MV: Y(T ) = (S0/µ) – Y1T

1/4Y1

Figure 7.1 Economic process with depletion of mineral resources.


units of net output could be produced initially with the given stock of min-eral resources; hence, the assumption is that mineral resources are initially redundant (OM>Y1).

Figure 7.1 also shows that as Y1 units of net output (produced using K1 and L1) are repeated period after period, the society’s capacity to sustain this output with its mineral resources declines; net output that can be pro-duced with mineral resources is still higher than Y1, but the gap is closing, until both quantities become equal, which occurs at period T*. Beyond this period, mineral resources become the constraint factor of production, and eventually net output will become equal to zero when mineral resources have been depleted.

By setting Y(T)=0, the period of depletion is determined, and has been called period T′, such that T′=(S0/μ)/Y1. This occurs at point V, that is, output Y1 can be repeated for six periods in figure 7.1. The period at which mineral resources stop being redundant and become scarce can also be determined by setting Y(T)=Y1. Call this period T*. It is clear that T*=T′–1. This is the basic nature of the flow-fund production process, as initially represented by the production system (7.1)–(7.2).

Another assumption will now be introduced into the model. Given that period T′ would imply the end of human species, human society will not let nature determine the end of its history and thus, confronted with the risk of extinction, it will take actions; in particular, assume society will decide at period T* (when mineral resources are no longer redundant) to extend the duration of the remaining stock of mineral resources for more than one period by setting the consumption at a lower level. The remaining stock of mineral resources can then be extended over several periods and used at the rate given by the new consumption level until these resources become depleted. This end period, socially determined, will be called T°, such that T*<T′<T°.

Let net output be allocated to consumption alone in figure 7.1. At period T* (period 5), when mineral resources are no longer redundant, society decides to intervene and extends the duration of the remaining mineral resources by reducing consumption to a fraction of the current consump-tion level. The mineral resources left unused in the final period can then last one more period or several periods until they are eventually depleted, which depends upon the social choice regarding the new level of consumption. If the choice is for maintaining the consumption level and thus extend for one additional period, then the choice is for point B′; if the fraction is one-half, the extension will be for two periods; if the fraction is one-third, the exten-sion will be for three periods, and so on, which is shown by the curve B′Z, which is an equilateral hyperbola.


The time path of the consumption possibilities may be called the intergenerational consumption frontier. In figure 7.1, it includes the seg-ment Y1B and the social choice of one, and only one, point on the curve B′Z (thus represented by a discontinuous line). The first segment is con-strained by the stocks of K1 and L1 and the segment B′Z by the stock of mineral resources S0. Let the social choice on the segment B′Z be point P. Beyond period T*, the consumption level is given by the segment CP (the level C is one-fourth of Y1) and will last for four additional periods, until mineral resources become depleted in period T °. Hence, the bro-ken line Y1BCP represents the intergenerational consumption frontier. More generally, this frontier can be represented as Y1B[B′Z], in which the bracket indicates the choice of one, and only one, point along curve B′Z.

To simplify, assume that in the segment CP the number of workers remains unchanged, even though only a fraction of total workers are needed in production. Some institutional changes will have to be introduced into society to accommodate this separation between production and distribu-tion: Although only a fraction of total labor force is needed in production, all workers will have to participate in the distribution of total output to make production socially viable.

The stock of machines will remain unchanged, for capitalists will pre-fer so. The distribution of consumption between generations can then be seen in the intergenerational consumption frontier, as shown in figure 7.1. The consumption level of the present generation (Y1) will be higher than the average consumption level of future generations. Consequently, there is consumption inequality between generations. The reason lies in the finite stock of mineral resources, which prevents consumption level Y1 from going on forever.

In conclusion, the first model A shows that when the stock of nonrenew-able natural resources is included in the economic process, society is faced with an intergenerational consumption frontier. Once society chooses the current level of total consumption, the periods of survival of the human species is determined endogenously. This consumption level cannot be repeated period after period forever, that is, the current consumption level is unsustainable. Furthermore, any current consumption level is unsustainable. This is just the result of the inevitable depletion of a given stock of exhaust-ible natural resources. Moreover, there will be a degree of inequality in the level of consumption between generations: The average consumption level of future generations will necessarily be smaller than that of the current generation.


Laws of Thermodynamics in the Economic Process

The production system (7.1)–(7.2) assumes that material goods are produced out of material inputs, which enter into the production process in the form of raw materials or energy sources. Hence, there is in the production process a relationship between matter and energy. The relationship between matter and energy is established in physics by the laws of thermodynamics. These are among the major empirical laws of physics, just like the law of gravity. The production system has so far ignored these relationships, which will now be introduced in model A.

The first law of thermodynamics is known as the Law of Conservation of Matter and Energy: Matter cannot be created or destroyed, only rear-ranged. The second is known as the Entropy Law. Since matter and energy are quantitatively unchanged, the only possible change that can occur in the physical environment would be of the qualitative nature. This is what the entropy law says: As rearrangement takes place, there will be qualitative changes, which include the continuous and irrevocable degradation of the physical environment.

These two laws of thermodynamics are of relevance in the economic pro-cess. Economist Nicholas Georgescu-Roegen introduced the second law of thermodynamics—the Entropy Law—into the economic process. The way he put it simply is worth quoting here:

Let us take the case of an old-fashioned railway engine in which heat of the burning coal flows into the boiler and, through the escaping steam, from the boiler into the atmosphere. One obvious result of this process is some mechanical work: the train has moved from one station to another. To wit, the coal has been transformed into ashes. Yet one thing is certain: the total quantity of matter and energy has not been altered. That is the dictate of the Law of the Conservation of Matter and Energy—which is the First Law of Thermodynamics . . . At the beginning the chemical energy of the coal is free, in the sense that it is available to us for pro-ducing some mechanical work. In the process, however, the free energy loses its quality, bit by bit. Ultimately, it always dissipates completely into the whole system where it becomes bound energy, that is, energy which we can no longer use for the same purpose. . . . In other words, high entropy means a structure in which most or all energy is bound and low entropy, a structure in which the opposite is true. . . . [This is] the Entropy Law, which is the Second Law of Thermodynamics. All it says is that the entropy of the universe (or of an isolated structure) increases constantly . . . and irrevocably. We may say that in the universe there is


a continuous and irrevocable qualitative degradation of free into bound energy. (Georgescu-Roegen, 1971, pp. 5–6)

The implication of the first law is that the outcome of the production pro-cess includes not only good B, but also waste (not another good), which is also an irrevocable outcome of the production process. In the production of a table, for example, a piece of wood is transformed into a table and waste (say, sawdust). The quantity of matter of material inputs must be equal to that of output and waste. Similarly, the implication of the first law is that the natural resource that enters into the economic process as energy source will come out as used energy that has produced mechanical work and as dis-sipated energy, which is also waste.

The first law has another implication in the production process. The production of material goods consists in the transformation of some materials into others (the f low elements of production) by some agents (the fund elements). There cannot be dematerialized production of phys-ical goods. Therefore, mineral resources are an indispensable production factor in the economic process (as raw material or energy) in the sense that N=0 implies Y*=Y1=0. This property was already introduced as assumption of the production system (7.1)–(7.2), in which technology is limitational.

According to the Second Law of Thermodynamics in order to gener-ate mechanical work in the production process, mineral resources will be burned, which will release both mechanical work and carbon dioxide (CO2); hence, once the free energy contained in mineral resources has been used, we are stuck with the CO2. This carbon dioxide is dumped into the atmo-sphere, which pollutes the biophysical atmosphere, and thus degrades it. There cannot be transformation of free energy into mechanical work with-out pollution.

According to the entropy law, in any closed system, in which matter or energy is not exchanged with the exterior world, entropy (disorder) always increases with time. The implication of this law for the economic process is that entropy increases with every action of transformation of inputs into output. In the example of the production of the table men-tioned above, the piece of wood is transformed into a table and sawdust, which implies a higher degree of disorder; and in the example of the production of mechanical work, the piece of carbon is transformed into mechanical work and pollution, which also implies a higher degree of disorder. Economic process—the repeated human action of production and distribution—implies higher entropy in the environment, such as pollution.


The entropy law also implies irreversibility. From the table and the saw-dust, we cannot go back to the piece of wood, neither can we go back from the CO2 to the piece of carbon because we cannot put back the energy we took out. The original inputs cannot be recovered from the output. The entropy law implies that the economic process goes in one direction only (irreversible) and is subject to continuous and irrevocable qualitative degradation of the environment, as in environmental pollution. According to the entropy law, time also goes in one direction only; this is the historical time T, which is to be distinguished from the mechanical time t, as was defined earlier.

Both laws of thermodynamics are interrelated. According to physicist Kyle Forinash (2010), while the first law says that energy cannot be created or destroyed but can only be changed from one form to another, the second law says that converting energy from one form to another, energy always degrades in the sense that it becomes less available to do useful work each time is converted. The implication is that this law limits the efficiency of any process that involves the conversion of heat energy (burning fuel) into mechanical energy. The energy not converted into useful work is considered as waste and it is generally given off to the environment as heat. Hence, any time energy is converted from one form to another, some energy is lost into a nonuseful form.

Economist Kenneth Boulding also interpreted the interrelation as follows:

In a closed system, the first law says that all that can happen is rearrange-ment; the second law says that if rearrangement happens, it is because there is some kind of potential for rearrangement and, as rearrangement goes on, potential is gradually reduced to zero and we get to the point where nothing further can happen. (Boulding, 1976, p. 5)

We humans live under a natural greenhouse effect, which is responsible for the comfortable temperatures that make our existence as species viable on Earth. The waste energy or bound energy from burning fossil fuel is carbon dioxide (CO2), which is a greenhouse gas. When dumped into the atmosphere, it leads to an increase in the temperature of the Earth, if noth-ing else happens, but there are other changes that take place. Clouds, the other factor that regulates temperature, will also change endogenously; thus, the net effect of greenhouse gas emissions will be smaller (Muller, 2008, Chapters 20–21). Clouds also change exogenously, due to variations in the solar cycles. Therefore, it is difficult to separate empirically the effect of greenhouse gas emissions upon climate change from the other effects and hence these will be ignored in this chapter.


The economic process is therefore dependent upon the biophysical envi-ronment in two ways: (a) as a source of mineral resources and (b) as a sink for waste. The finite size of Earth imposes limits to both components: it implies a given stock of mineral resources and also a finite capacity to absorb waste. More specifically, the human ecosystem has a limited capacity to absorb waste if it is going to be able to continue supporting human life, as we know it. Catastrophes can then arise from small changes in the human ecosystem. The given stock of mineral resources would not cause a problem in the eco-nomic process if everything could be recycled, but the entropy law prevents complete recycling, for it requires energy; waste would not be a problem if the absorptive capacity of the ecosystem was large, which is not the case. The first refers to the depletion problem, whereas the second to the pollu-tion problem.

We can then say that the production process only rearranges matter and energy, but in so doing, the production capacity is qualitatively degraded. Therefore, as the production is repeated period after period, the potential of the production system is continuously and irrevocably degraded. The eco-nomic process is not mechanical, but entropic.

Model B: An Entropic Economic Process

How would the introduction of the laws of thermodynamics into the eco-nomic process affect the intergenerational consumption frontier? Model B will assume that the economic process is entropic. This assumption will be done in two steps. First, the model will assume that the energy used in the economic process comes from mineral resources, which in turn increases the degree of degradation of the environment. Second, the model will also assume that a feedback effect exists and operates from pollution and deple-tion to the economic process.

The production process indicated by the system of equations (7.7) and (7.8) will have to be modified. For given stocks of K1 and L1, and technolog-ical level A1, a flow of gross output Y1* will be produced, provided mineral resources flow into the production process in the required quantity. The depletion effect of production is already included in equation (7.8).

The pollution effect is new. Its concentration in the atmosphere at period T, represented by Π (T ), can be written as

Π (T ) = βΣNj = β z ΣYj*, j= 1, 2, . . . , T (7.9) = β z Y1* T, which using equation (7.5) becomes = β μ Y1 T


The coefficient β indicates the pollution rate into the atmosphere from using mineral resources in the production process. The stock of pollution accumulated in the atmosphere is thus equal to the rate β multiplied by the total N utilized up to period T. In its reduced form, it is a linear function of T.

Figure 7.2 presents the first step in the construction of an entropic pro-duction model. Panel (a) shows the depletion effect, which was already explained earlier in figure 7.1. The pollution effect is represented in panel (b) by the line O′F. Then, as net output is repeated, period after period,

Y1

O

O´

F

G

B´

V´

M

T

TV

Π*F´

(b)

(a)

Tp* Td*

S0 /µ – Y1T

P

Π

Π = βµ(1/4)Y1TΠ = βµY1T

= βN1T

C(1/4)Y1

[K1, L1, A1]

Y

B

Figure 7.2 Economic process with linear depletion and pollution.


mineral resources are depleted and pollution concentration in the atmo-sphere increases. Both effects are continuous and irrevocable. At period Td* mineral resources become scarce. Given that point P is the choice of society, the rate of depletion shifts to BV′ and the rate of increase in the concentra-tions of pollution falls, as indicated by the smaller slope of the line FG. It is clear from panel (a), that the net output cannot be repeated forever, as min-eral resources set a limit.

Can pollution increase forever? Human life can exist only under special ecological conditions and any change in them can disrupt the living condi-tions. Hence, the model will assume that there exists a threshold of pollution tolerance beyond which human life, as we know it, cannot continue. Some physiological adaptations would need to take place; for example, low avail-ability of oxygen in the air could imply a more anaerobic human life. Call this threshold Π*. Assume further that it appears at time Tp*, which occurs earlier than Td*, as shown in panel (b). Thus, it is pollution, not depletion, which puts the limit to the production of net output and to the survival of human species.

Consider now the second step, in which the feedback effects going from the biophysical environment to the economic process are included. Production comes together with waste, which implies pollution of the environment (including water, air, and soil), to which we may include climate change (in the form of natural disasters). Thus, pollution implies higher costs of pro-duction due to its higher risk damages to machines, soil, and human health. Depletion in turn also implies higher costs of production as the exploitation of natural resources are subject to Ricardian diminishing returns.

What would be the feedback effect of these environmental changes upon the production process? Human health may suffer and, consequently, labor productivity may fall, or else cost of labor service maintenance would increase. Damage and reposition of machines would also increase. In addi-tion, mineral deposits of lower quality will have to be exploited instead of those that are of high quality (high in mineral content and easy access). In order to get the same net output, gross output will have to be higher, which implies more quantity of mineral resources as inputs per unit of net output.

For the sake of simplicity, consider only the case of feedback effect of pollution upon machine reposition. Introducing the coefficient r′ as the unit cost of reposition from pollution, the path of reposition costs R(T) can then be written as follows:

R (T) = r Y1* + r′ Π(T ) (7.10) = r Y1* + r′ β z Y1* T


= (r + r′ β zT ) Y1* = λ(T) Y1*, where λ = (r + r′ β zT ), 0< λ<1, λ′(T )>0

Now the reposition rate λ is not only higher than the initial coefficient r, but it increases with time due to the cumulative nature of pollution.

The depletion path and the path of net output Y1 as given by the mineral resource constraint now become

S (T) = S0 – z Y1*T (7.11) = S0 – z/(1 – λ(T ))Y1T = S0 – ε(T )Y1T where ε=z/(1– λ), 0<(1– λ)<1, and ε′(T )>0Y (T) = S0/ ε(T ) – Y1T (7.12)

Coefficient ε measures the quantity of mineral resources that is required per unit of net output. It is higher than the initial coefficient μ (due to the higher reposition rate) and increases with time. As net output Y1 is repeated for the second period, pollution will increase, the rate of reposition will also increase, and the coefficient ε will increase; when repeated for the third period, this coefficient will again increase, and so on. Hence, the rate of depletion will increase with time, and the frontier of net output determined by mineral resources constraint will not be linear, as in the first case, but it will be nonlinear (convex). Period Td* will be reached sooner.

The path of pollution will also be different. Replacing in equation (7.9), the reposition coefficient μ for the new reposition coefficient ε, we get

Π (T ) = β z Y1* T= β (z/[1–λ(T )]) Y1 T= β ε(T ) Y1 T (7.13)

The path is now nonlinear. As the net output is repeated for a second period, the coefficient ε increases, which implies a higher quantity of mineral resources utilized, which in turn implies an increase in the concentration of pollution at a higher rate; when repeated for a third period, an even higher amount of mineral resources will be utilized, which implies an increasing concentration of pollution at an even higher rate, and so on. Hence, the pol-lution path will be nonlinear, a curve rising over time at an increasing rate.

Figure 7.3 displays the nonlinear entropic process, which is contained in equations (7.12) and (7.13). Panel (a) shows that the depletion rate will increase over time, as indicated by the frontier MW (determined by the


constraint of mineral resources), which is non-linear. The corresponding intergenerational consumption frontier is given by the path Y1E[E′X]. By comparison, the case in which the feedback is ignored is represented by the frontier MV, which is linear. Panel (b) in turn shows that the concentration

Y1

O

Pollution

O´

F

G

B

X

W

E

M

Net output

T

TV

Π*

E´´

F´

(b)

(a)

E´[K1, L1, A1]

Tp* Td*

Curve MW: Y (T )= [S0/ε(T )] – Y1T

Curve O'F: Π(T ) = βε(T )Y1T

Figure 7.3 Economic process with nonlinear depletion and pollution.


of pollution will proceed at an increasing rate, as shown by the curve O′F. The threshold of human tolerance to pollution is given by the value Π* at period Tp*. Consequently, both critical periods Td* and Tp* will occur sooner compared to the nonfeedback effect.

Just for the sake of completeness on the trajectory of panel (b) consider the following case: If from the set E′X, consumption level E′ is chosen, then the curve O′F will continue to increase up to point G, as shown in the graph; if a smaller consumption level were chosen, then the curve O′F would still grow, but at a lower rate (not shown in the graph).

The feedback effect originates in the pollution effect, as shown earlier. We already know that pollution is the result of the entropy law. The qualita-tive change that accompanies to the economic process could not maintain a linear production system, even if finite. Therefore, the entropy law implies a nonlinear production system and a finite one.

Depletion and pollution resulting from the economic process will impose different threshold periods for the existence of human species, depending on which of the two periods comes first. Which one will come first? This will be determined by the incentive system under which the capitalist system operates. Depletion could be postponed because, as mineral resources become scarce, market incentives would increase prices, which would induce technological progress that is mineral resource saving.

In contrast, there are no incentives to take care of the increasing fragility of the ecological system because it involves solving the problem of a public good or a public “bad.” Pollution can be seen as an instance of the problem of the commons, for the services provided by the ecosystem are free goods (Stavins 2011). Markets cannot solve this problem. There is no mechanism by which supply can meet the increasing demand for services. Governments have no incentives to deal with this problem either, for they act motivated by attracting voters for the next elections, which implies shortsighted and myopic views on the problem of the commons.

Model B thus assumes that the pollution threshold (Tp*) will come sooner than that of depletion (Td*), as shown in figure 7.3. The relevant constraint of the environment is, in this case, the capacity of the ecological system to support human society, not the depletion of mineral resources. This eco-logical capacity is the ultimate element of scarcity in the economic process. Everything can be produced except ecological resources. The model says that we humans cannot supply ourselves with another ecological system. Therefore, the model predicts that intergenerational consumption frontier shown in figure 7.3, panel (a), will not attain the entire time path, but only up to segment Y1E″.


The economic process is analogous to the gravitational force, dragging the Earth down to the no human life state. The critical periods represent thresholds at which regime switching will take place. These are bifurca-tion points of unpredictable change. However, the theory constructed here makes assumptions about the adaptive behavior of humans when already confronted against the critical periods.

Model B indeed assumes that the human society will take actions when confronted with the risk of its extinction. In this case, human society would have to move to another age via technological and institutional innovations. The case shown in figure 7.3 says that the age of mineral resources will be abandoned before the mineral resources have been exhausted. In the history of human society, the Stone Age was abandoned not because stones became scarce.

In sum, compared to the first model A, model B now shows two mech-anisms leading to the intergeneration consumption frontier: depletion of nonrenewable natural resources and pollution. As can be seen in figure 7.3, distribution conflict among generations holds even if the level of total cur-rent consumption remains fixed, that is, even if we have a zero-growth soci-ety, in which both population size and capital stock remain unchanged. The current total consumption level cannot be repeated forever, that is, it is unsustainable. The usual idea that the economic process can be seen as a steady state process—as a mechanical process—is a mirage. Certainly, the social conflict will be more acute if society embarks on a process of eco-nomic growth, even with technological progress, as will be shown next.

Model C: Mineral Resources Substitutability and Renewable Resources

The Question of Substitution of Mineral Resources

Standard economics has another set of assumptions about the production process. They are summarized in the arch familiar concept of production function, which says that the quantity of output produced depends upon the stocks of machines, workers, and natural resources, so that these factors of production are all substitutable (Solow 1974, p. 34). The production func-tion is usually written as

Y = F (K, L, N) (7.14)

This apparently innocent equation says that the standard production theory assumes implicitly that the three factors are substitutable in the production


process; hence, net output could even be produced with machines and work-ers alone. Mineral resources are not an indispensable factor of production. Note the difference with the flow-fund theory, which was represented as a production system, in which mineral resources are an indispensable factor of production—equations (7.1)–(7.2), that is, N=0 implies Y=0.

A consequence of the standard economics assumption about the produc-tion process is that the production of a given net output can go on forever. Therefore, output growth can also go on forever. There are no limits to the production of goods. This view can be summarized as follows:

It is now generally accepted that the limited supply of non-renewable resources does not necessarily imply a limit to growth. In particular, the neoclassical theory gives rise to three main possibilities: (i) substitu-tion of the resource by other inputs, such as capital; (ii) improvement of the resource efficiency; and (iii) development of backstop technologies. However, without any technical change, none of these outcomes will balance the resource exhaustion and continue to sustain some positive growth in the long run. (Lafforgue, 2008, p. 541)

According to view (i), a way to introduce substitution between machines and mineral resources would be by assuming that the technological coefficient of mineral resources per unit of net output can fall as the stocks of machines increase. This substitution would be induced by changes in the relative prices of minerals, that is, as mineral resources become more expensive.

Even accepting the possibility of substitution, the question is, where would the additional quantity of machines come from? It would have to be produced and then more mineral resources will be used in its production. Then the net effect of substitution on the saving of mineral resources would be smaller than what the pure substitution effect implies. (Windmills can substitute oil in generating energy, but the posts of windmills produced in factories would need minerals and other inputs.) In addition, the net output is a material good, which cannot be totally dematerialized, for that would go against the first law of thermodynamics, which also sets limits to the substitution possibilities.

If a quantity of capital can substitute mineral resources, then the line MV of figure 7.3 would be shifted outward, to another line (say to line M″V″, not drawn). However, producing that quantity of capital would require mineral resources and would also imply reposition costs in terms of mineral resources. So the net effect of substituting minerals would be smaller than the initial effect (a change from line MV to, say, line M′V′, which would lie below line M″V″). Assume that the net effect is positive.


Then the intergenerational consumption frontier would be shifted outward. Consequently, period T* would be expanded, but it would still be finite. More substitution could proceed over time, but a substitution limit would be reached sooner or later. Let the line MV represent this limit in substitu-tion possibilities and model B will have captured the full substitution effect. (As to technological change effects, the final Lafforgue’s argument, they will be analyzed in the next section.)

In sum, in the entropic production process, substitution between fund and flow factors is possible, but only to a certain extent. This is due to the assumption that mineral resources are an indispensable factor of produc-tion, which is consistent with the laws of thermodynamics. However, these substitution effects will not eliminate the existence of the intergenerational consumption frontier, for substitution possibilities have limits. Once these limits are reached, the intergenerational consumption frontier will become a fixed curve. Therefore, model B is consistent with the laws of thermody-namics and thus constitutes the appropriate model to study the interactions between the economic process and the biophysical environment.

Introducing Renewable Natural Resources

Renewable natural resources in the economic process have been ignored in the entropic model B. The implicit assumption has been that renew-able resources were redundant, that is, the constraint given by renewable resources in the production of good was placed above point M as a hori-zontal line in figure 7.1. This assumption will now be revised. For this pur-pose, two sources of energy must now be distinguished in the production process: (1) the finite stocks of mineral resources in the Earth’s crust, which is exhaustible; (2) the sun’s stock of energy, from which the flow of solar radiation comes to Earth and is the source of energy for the existence of renewable natural resources.

The Earth is a closed thermodynamic system in the sense that it does not exchange matter with outer space, but only energy from the sun (Baumgärtner, 2004, p. 320). Therefore the scarcity of renewable natural resources comes from the Earth’s limited size as a net to catch solar energy. This is the case with forestry and fisheries. It also includes agricultural soil, which is of limited size; in addition, soil is also subject to degradation due to erosion by wind and rainfall, and soil formation takes a longer time to offset natural erosion; hence, agricultural soil belongs to the category of nonrenewable resources.

Mineral resources are needed not only as an energy source in the produc-tion process, but also as material base for the production of material goods


(first law of thermodynamics). Renewable resources can substitute mineral resources as energy source (biofuel and food for human energy) and mate-rial base (wood), but only partially. Some material goods are based on the processing of minerals. In general, production of material goods will need both types of natural resources.

Fisheries, forestry, and other biological renewable resources may however be subject to depletion if the rate of biological reposition is smaller than the rate of exploitation by humans. When renewable natural resources are not renewed, they will be subject to depletion, just as in the case of mineral resources. Deforestation is one well-documented case. The other, less docu-mented, is topsoil in land resources, which will be analyzed in the following chapter. Whenever this is the case, the renewable natural resources may be treated as nonrenewable and they are already included in the coefficients that determine the intergenerational consumption frontier in model B. These renewable natural resources that are in fact renewed will be considered as redundant factors in model B and may thus be ignored in the analysis.

Under these assumptions, therefore, model B is more general than it was initially thought. Therefore, the intergenerational consumption frontier that it was shown in its most elementary form in figure 7.1 is also a more general representation of model B, as it can now be interpreted as deter-mined not only by the constraints of nonrenewable resources, but also by the constraints given by those renewable resources that the human activity has transformed into nonrenewable ones.

Market System and Entropic Economic Process

The nature of equilibrium in the entropic model B needs to be clearly under-stood. As we have seen, even for a constant consumption level, the economic process goes through quantitative and qualitative changes and it cannot go on forever. As the economic process is repeated, environment is degraded continuously and irrevocably: mineral resources tend to become depleted, the atmosphere becomes polluted, and the environment degraded. The capacity of the environment to support human life, as we know it, is limited. Model B assumes that human society would take actions and would tend to adapt, and some institutional changes to the economic process would have to be made. The entropic economic process can then be seen as an evolution-ary process, in which both quantitative and qualitative changes take place in the economic process.

The entropic economic process cannot be seen as a static process. The standard definition of static equilibrium says: the value of the endogenous variable will be repeated period after period forever, as long as the values of


the exogenous variables remain fixed. In the entropic model, the endoge-nous variables include the quantity of net output and the degree of degrada-tion of the environment; the exogenous variables include the endowments of machines, workers, and mineral resources in the crust of the Earth, together with the level of technology. In the entropic economic process, static equi-librium is therefore unviable because as net output is repeated period after period, the stock of machines and workers can remain unchanged, but the stock of mineral resources cannot. Depletion or pollution will put an end to the economic process, as shown by the intergenerational consumption frontier.

Can the entropic economic process be seen as a dynamic process? In a dynamic process, there exist intertemporal relations among the endogenous variables, as part of the structural relations. Then the standard definition of dynamic equilibrium says: the value of the endogenous variable will move along a particular trajectory over time forever, as long as the exogenous vari-ables remain fixed. Only quantitative changes will thus take place over time and the movement along the path can thus last forever. In the entropic eco-nomic process, the intergenerational consumption frontier shows a dynamic path of net output, but only temporarily. The evolutionary process includes a dynamic process but only for a finite number of periods, until a threshold is reached, beyond which the process goes through regimen switching.

Another fundamental question is still pending: How does the market system operate in the entropic economic process? Suppose net output Y1 in figure 7.3 is the solution of the market system. This level of net output has been produced with the stocks of K1 and L1 of capital and labor and the flow inputs N1 of mineral resources. There are three markets: goods, labor, and mineral inputs. Firms producing goods make maximum profits after pay-ing wages to workers and prices that cover the cost of extraction of minerals (and also costs of maintaining intact renewable resources). Given that the flow N enters into production of Y1 in fixed proportion, real wage is equal to the net marginal productivity of labor, that is, net of the cost of utilizing mineral inputs.

Net output will be allocated to consumption. So the market system can repeat this general equilibrium solution period after period. Nevertheless, this “static process” is a mirage, as can be seen in figure 7.3. Thus the market system cannot take into account the environmental degradation (depletion and pollution) that is involved in the entropic economic process. Markets for depletion and pollution do not exist and can hardly exist. Mother Nature has no cashier. Hence, with a market system perfectly working, and even with zero-growth of net output, society will inevitably reach its reproduc-tion limit, which implies the end of the human species. Because the capitalist


system tends to operate with positive growth of net output (chapter 6, this volume), the limit will be reached sooner, as will be shown next.

Changes in the Intergenerational Consumption Frontier

It is time to analyze the effect of changes in the exogenous variables upon the endogenous variables, along the intergenerational consumption fron-tier. The endogenous variable of interest is output and its intergenerational distribution.

Figure 7.4 shows the effect of higher amounts of machines, men, and a higher level of technological knowledge. The level of net output will be higher, which implies depletion of mineral resources at a higher rate and also increases in the concentration of greenhouse gases at higher rates. If the values of K, L, and A are higher, then the level of the net output will shift upward, which implies an inward shift of the depletion curve MV and an upward shift of the pollution curve from O′F to O′H. Thus the critical periods T′ and T* will occur sooner.

Another consequence is that the degree of intergenerational inequality will be higher: the net output level of the present generation will be higher, but the average net output level of the future generations will be lower. In other words, exogenous economic growth implies an increase in the inter-generational inequality. The higher net output level and consumption level enjoyed by the current generation will imply more mineral resources allo-cated to the current generation and, consequently, less amount of mineral resources will be left for future generations, which in turn implies a lower total consumption level for them.

Figure 7.5 presents the model in its linear form and displays the effect of an exogenous technological change that generates a decrease in the coefficient of mineral resources per unit of net output, a reduction of the coefficient ε. A reduction in the value of this technological requirement is equivalent to an increase in the initial stock of mineral resources. This is a mineral resource-saving technological change. This change will cause an outward shift of the depletion curve MW to M′W′ and, consequently, the pollution curve O′F will also be shifted outward to O′H. As a result, the critical periods T′ and T* will occur later.

It is still true that the current net output level cannot be repeated period after period forever; consequently, technological progress cannot elimi-nate the existence of the intergenerational production frontier; it can only move the frontier curve to another level. Moreover, this new frontier will reduce the degree of inequality between generations. These effects assume that technological change is cost-free. Taking into account the use of mineral

Y1

O

O´

F

B´

X

V

B

MY

T

T(½)V

Π*

C´

(a)

(b)

[K2, L2, A2]

[K1, L1, A1]

C2Y1 = Y2

T1Tp** Tp* Td*Td**

Z

H

H´

F´

Figure 7.4 Output growth effect upon depletion and pollution under linear relations.


resources in the activity of research and development (R&D), the net effect would be smaller.

Could technological change be so strong in saving mineral resources that a given level of net output might be maintained forever? Could technological change eliminate the constraints imposed by the laws of thermodynamics?

Y1

O

O´

B

M´

T

T

Π*

Π

Y

E´B´

Z U

M

F´ H´

H

F

W W´

E

Tp* T *d Tp** Td**

(b)

(a)

Figure 7.5 Effect of mineral resource-saving technological change on depletion and pollution under linear relations.


According to model B, the technological coefficient ε increases endoge-nously over time. Now suppose there is exogenous technological change that reduces this coefficient over time. Would the latter offset the former effect? The model cannot tell. Technological change might not offset the former effect. This is the case shown above. Suppose technological change just off-sets it; then ε will be constant over time. Then both the depletion curve and the pollution curve will become linear. If the effect of technological change more than offsets the former effects, then the value of ε will fall over time and, consequently, the depletion curve will shift outward continuously.

Consider now the nonlinear intergenerational consumption frontier in figure 7.3. Could the mineral resource frontier become a horizontal line starting around point M in panel (a)? If mineral resources were depleted by half in the first period of production, then it is possible to imagine that tech-nological change would take place and reduce the technological coefficient ε also by half in the next period, which is equivalent to increasing mineral resources by double. The consequence would be that the stock of mineral resources in units of net output could remain constant over time, that is, around point M. Mineral resources would have now become renewable nat-ural resource due to technological change. Then the net output level Y1 could be repeated forever in figure 7.3. Along this horizontal line, machines, workers, and minerals would all become renewable resources thanks to tech-nological change.

However, the panel (b) of figure 7.3 needs to be taken into consider-ation. The pollution effect will continue irrevocably. Mineral resources would be used to produce Y1 in the first period; although the stock of min-eral resources is economically recovered through technological change, the amount of mineral resources used up would have generated pollution. In the next period, net output will be repeated and mineral resources would be used; and, although the stock of mineral resources is economically recov-ered, the pollution effect of the used up mineral would have taken place and would have been accumulated in the atmosphere for two periods, and so on. Curve O′F would thus become linear and the limiting factor.

What the model B says is that even if mineral resources were infinitely abundant, such that depletion were an impossibility, the economic process would still produce pollution from using mineral resources. Then pollu-tion, not depletion, would be the limiting factor of the economic process. Technological change would now have to eliminate the concentrations of pollution in the atmosphere in order to avoid an entropic production process.

Technological change would have to solve two problems: depletion and pollution. Under the most favorable scenario, it is unlikely that technological


change can eliminate the laws of thermodynamics. It is even unlikely that mineral resources can be transformed into renewable natural resources by the action of mineral-saving technological change. Thus, the entropic model will assume that mineral resources are effectively nonrenewable resources, even in the presence of technological change.

Consider now the effect of reducing renewable resources over time, which have become nonrenewable due to human activity in the production process. Anthropogenic deforestation would be a typical example. This can be seen as an exogenous change in the production process. As shown above, the effect of deforestation will be to increase pollution for a given amount of net output; hence, the coefficient ε will tend to increase more rapidly over time.

So far, the output level has remained constant. Introducing an exogenous increase in the output level, the quantity of mineral resources utilized will increase and so will pollution. The rate of depletion of mineral resources will also increase. Taking into account technological change in model B (represented in figure 7.3), the net effect of output increase will be similar to that shown in figure 7.4, namely, the reduction of the threshold periods T′ and T*.

In sum, separate effects of the exogenous variables of the model B predict that the effect of mineral-saving technology will reduce the effect of total output growth upon the environment degradation, but it will not eliminate it. Basically, the ecosystem in which humans make their living, as we know it, is hardly producible and substitutable. If human society chooses eco-nomic growth, then its survival, as we know it, would be shorter, even with technological change. Technological change cannot eliminate the empirical laws of thermodynamics. The economic process causes a continuous and irrevocable degradation of the environment; what technological change can do is only to reduce the rate of degradation.

Economic Growth as Evolutionary Process

How does economic growth proceed under the entropic economic process? It is time to introduce the growth theory that was presented in chapter 6 (this volume) into model B. Consider the growth frontier equations only, just to simplify the analysis.

Along the growth frontier, output per worker (meaning net output per worker from now on) grows at the rate of technological change, which are labor augmenting. Let machines grow at 5 percent per year, population at 2 percent, and technology at 3 percent; then total output will grow at the rate of 5 percent, for technology is subject to constant returns to scale.


Output per worker will then grow at 3 percent. This is dynamic equilibrium and as such will go on forever. However, dynamic equilibrium is unviable in the entropic process because depletion and pollution will increase also endogenously and put limits to the process of economic growth.

The basic growth effect was actually shown in the previous section. Nevertheless, the comparison there was only between two levels of total output.

The economic growth process implies a continuous increase in the out-put level, which now can be introduced into the entropic production sys-tem, as represented in figure 7.3. Suppose Y1 corresponds to the output level in period 1, which implies a certain amount of depletion of mineral resources and of pollution concentration. Accumulation of capital (physical and human) and new technological level that is labor-saving and mineral resource-saving will take place in the same period, so that Y2 will be pro-duced in period 2, which implies depletion of mineral resources and pollu-tion, both in higher amounts than in the previous period, and so on.

As can be visualized in figure 7.3, the process of economic growth implies not only a continuous increase in total output, but also a continuous inward shift of the depletion curve MW and a continuous upward shift of the pol-lution curve O′G′. Model B assumes that, in spite of the mineral resource-saving technological change, coefficient ε increases endogenously over time, so that mineral resources are indeed nonrenewable, as argued before. Therefore, while the total output that can be produced with fund factors increases over time, the total output that can be produced with flow factors will diminish over time. At some point, both amounts will be equalized. At this period, mineral resources become scarce; thus the period corresponds to the concept of Td*. Similarly, the pollution curve will cross the threshold tolerance level at period Tp*, such that Tp*<Td*. The limit to the growth of total output is given by pollution, not by depletion.

Although depletion and pollution are both related to the level or scale of total output, the same results can be extended to the endogenous variable output per worker. The reason is that to each value of total output there will be a corresponding value of output per worker, for both variables grow over time, even if at different rates. Therefore, in the process of economic growth, while the output per worker that can be produced with fund factors increases over time, the output per worker that can be produced with flow factors (minerals) decreases over time. The stock of minerals that are ini-tially redundant will sooner or later become scarce.

Figure 7.6 shows the economic growth process of an entropic production system. Let curve DR represent the growth frontier path of output per worker in the aggregate capitalist system, which is the result of capital accumulation


(physical and human). The exogenous variables that determine this curve include the aggregate savings rate (s*), the world initial inequality (δ) and the growth rate of the world technological progress that is labor-augmenting (g). The aggregate growth frontier DR is just the weighted average of the growth frontier of epsilon and sigma society, where the weights are the labor shares, which are assumed to be constant, as was shown in figure 6.1, chap-ter 6 (this volume); moreover, these exogenous variables are derived from the same graph. (Savings rate will be made endogenous and depends upon the initial inequality below.)

Figure 7.6 also indicates that economic growth can be seen as an evo-lutionary process. Along curve DR, the quantitative increase in output per worker implies a qualitative change in the process: a continuous and irrevocable degradation of the biophysical environment. Hence, curve BN represents the depletion curve associated with the growth path of DR. As the latter curve rises, the former declines. The exogenous variables that

y

T

D

E

N [τ, δ0, g]

B

H

J

Td*Tp*

S

O

R [ δ0, g]

C [δ0, g, τ]

Figure 7.6 Economic growth as an evolutionary process.


determine curve BN include the grow rate of technological progress that is mineral resource-saving (τ), together with the exogenous variables of the DR curve. (The stock of mineral resources is an initial condition that can-not be changed.) Both curves cross each other at point E, in which mineral resources become scarce. This point corresponds to period Td*. Beyond this period, output per worker will change the trajectory from DE to EN, which implies declining output per worker because mineral resources constitute the binding factor, until it is depleted.

Let OH represent the threshold value of output per worker that makes human life, as we know it, still viable under pollution concentration in the atmosphere. Just for the sake of simplicity, suppose that OH is fixed, that is, the total output that corresponds to OH is the one that generates the threshold of human tolerance to pollution (Π*) and this threshold value depends upon total output only, not upon population size. (If the atmo-sphere is intolerable to 10 million people, it will be so to 100 million.) This constraint implies that growth of output per worker will end at point S on the DR curve. This point corresponds to the period Tp*. Beyond this period, output per worker will just tend to fall along segment SC.

Ricardian diminishing returns on investment are assumed in model B and it will play a significant role. Ultimately, the industry of extraction of minerals will find it uneconomical to exploit some of the lowest-quality deposits. Under this assumption, mineral resource scarcity would reach point E in figure 7.6.

The incentives of capitalists and governments will be to prioritize strat-egies that avoid the depletion of minerals, namely technological change to reduce the effect of Ricardian diminishing returns in the exploitation of lower-quality deposits and to substitute minerals with other sources of energy. However, incentives to fight pollution are not as strong. For one thing, it is a public good (actually a problem of the commons). Therefore, the model predicts that it is pollution that will set the limit to economic growth, as indicated in figure 7.6.

In sum, and as illustrated in figure 7.6, economic growth cannot go on forever. It has limits. Actually, the limits are given by two mechanisms that become the basic constraints: depletion of mineral resources and pollution, whichever comes first. The model B assumes that the limit is given by pollu-tion: the feasible economic growth trajectory is given by curve DSC, whereas the segment SR is unfeasible. According to model B, the neoclassical steady state growth—income per workers moving along the entire curve DR for-ever—is unfeasible; what the model predicts is temporary growth (segment DS) followed by de-growth (segment SC). This conclusion is analytically consistent with Georgescu-Roegen’s proposition: “We must not doubt that


our destiny is bound to our existence as biological species on this planet. For in the ultimate analysis, this is what we are: a biological species” (cited in Bonaiuti, 2011, p. 104).

Beta Propositions

The entropic model of the economic growth in the capitalist system is sum-marized by the trajectory DSC in figure 7.6, where at the threshold period T* the dynamic equilibrium moving along the segment DS suffers a regime switching and changes to segment SC. The exogenous variables in the tem-poral dynamic equilibrium include the initial inequality (δ), the growth rate of labor-saving technological change (g), and the growth rate of the mineral resources-saving technological change (τ). The endogenous variables of the entropic model include the path of output per worker (y), the path of income inequality (D), and the path of environmental degradation (E). A significant endogenous variable is also the value of the threshold period T*.

For the case of the output per worker variable, as shown in figure 7.6, the time path is given by the broken curve DSC. (Curve BEN is redundant.) Changes in the exogenous variables will change the shape of this curve. Hence, in this evolutionary model, T*=Tp*, is endogenous. Changes in the exogenous variables of the evolutionary growth model will cause changes on the critical threshold periods. These effects can be visualized with the help of figure 7.6.

Suppose an increase in the world inequality in the distribution of eco-nomic and political assets (δ) leads to social choices in favor of a higher investment rate and thus a higher level of the growth frontier. This result assumes that the aggregate savings rate (s*) is endogenous, as it will depend upon the initial inequality. This assumption will be introduced into the model from now on. Then the level effect of a higher-world initial inequality implies an upward shift of the DR curve, which will be accompanied by an inward shift of the depletion curve BN and a downward shift of the pollu-tion curve HS. Then the critical period (T*) will occur sooner.

A higher growth rate of technological progress that is labor-augmenting (g) will lead to a higher slope of curve DR; then, the curve BN will be shifted inward and curve HS downward. The critical periods will be shorter. On the other hand, the higher the technological progress that is mineral- saving (τ), the lower the rate of depletion of mineral resources, and the curve BN will be shifted outward and HS upward. The critical periods will be extended, but will remain finite.

Up to now, the evolutionary model has dealt with the behavior of the capitalist system only. Nevertheless, the degradation of the environment is


a world problem. We can introduce the economic growth process of the noncapitalist societies in the form of an exogenous variable, for the model does not explain the behavior of these societies. Call it variable ρ. Now sup-pose curve DR includes the growth frontier of noncapitalist societies as well. Then figure 7.6 now refers to the world interaction between growth and environment. An exogenous increase in the growth frontier of noncapitalist societies—an increase in the exogenous variable ρ, such as the rapid growth of Chinese economy in the last decades—will shift the DR curve upward, the curve BN inward, and point H downward, which will together reduce the value of T*. Therefore, ρ will capture the “China effect.”

The critical threshold period is determined by the values of the exoge-nous variables, as follows:

T* = f (δ, g, τ, ρ), f3 > 0, fi < 0 (7.15)

The increase in the values of all exogenous variables, except in that of the growth rate of the mineral-saving technological change, will increase the rate of degradation of the environment and thus reduce the critical threshold period at which an environmental crisis will occur.

Along the segment DS, there exists a certain distribution of the world net output. Income inequality in the capitalist system increases along the DR curve, for both within-society and between-society inequality tends to increase in the economic growth process, as shown in chapter 6 (this vol-ume). Now income of the capitalist class will include profits and economic rents for the exploitation of natural resources.

Empirical Corroboration: The Capitalist World, 1800–2010

The evolutionary model constructed in this chapter assumes that the eco-nomic process of today proceeds under environmental stress. This was not the case two centuries ago, but it is the case now, as human species are getting closer to environmental crisis. Although the model predicts the existence of a period of collapse, it has not happened yet; it is not part of history, but part of the future. Falsification applies only to observed data. Therefore, this pre-diction is non-alsifiable, that is, equation (7.15) is not a beta proposition.

However, the temporal dynamic equilibrium of the evolutionary model shows trajectories over time, which are observable and can then be subject to fal-sification. The beta propositions that can be derived from figure 7.6 include:

(a) Output growth is accompanied by continuous and increasing rate of degradation of the environment (depletion and pollution).


(b) The higher the growth rate of total output per worker, which implies a higher growth rate of total output, the higher the rate of degrada-tion of the environment.

These predictions are consistent with Fact 8 shown in figure 2.1 (chapter 2, volume 1), for the long-run period 1500–2000. World output growth was indeed accompanied by increasing pollution; moreover, the period in which world total output increased faster also was the period with pollution concen-tration increasing faster, as shown in figure 2.1 (volume 1) by the behavior observed in the period 1950–2000. The mechanism established by the entro-pic model is that output growth leads to pollution, but ultimately both are endogenous variables in the economic growth process. Around year 2000, as indicated earlier, capitalist countries produced 83 percent of the world output (at PPP prices) and concentrated 71 percent of the world population (World Bank, 2001, Table 1, pp. 274–275); hence, figure 2.1 (volume 1) reflects mostly the capitalist behavior output in this very long-run period.

About the prediction of the entropic model that economic growth will collapse at a finite time period in the future, it is nonfalsifiable, as mentioned earlier. If the collapse is not observed, one could save the theory saying that the critical period has not been reached yet; if it is observed, then the time has just arrived. This type of proposition about the future will never fail. It cannot be utilized to test the theory. The bottom line is that future events cannot be utilized to falsify a theory; only historical data can. However, evo-lutionary models can be refuted if the predicted trajectories do not fit the facts. Empirical data, as presented in figure 2.1 (chapter 2, volume 1) show that the time path of the endogenous variables (total output, pollution, and global temperature) follow the trajectory predicted by the entropic model of economic growth. This fact is therefore consistent with the prediction of collapse at a finite period in the future.

On the depletion of mineral resources, the studies by Chris Clugston (2012, 2013) show consistency with the prediction of the entropic model. Taking into account demand and supply, the most likely trajectories for 89 minerals, several mineral resources will be economically exhausted by year 2030; some will remain but at an increasing cost/price due to the Ricardian diminishing returns principle; and few are still in the rising segment of the depletion cycle. No mineral resource-saving technologies are significant, as measured by the ratio of quantity of minerals per unit of output in 1800 and 2005 in the US economy. Scarcity is reflected in the rising relative prices: for the case of the 15 minerals of significance, average relative market prices in the period 2000–2012 (which include the world recession of 2008–2009) are higher compared to the average prices of 1960–1999.


Clugston’s conclusion is that mineral resources are available in finite stocks and are increasingly of lower quality. Economically viable mineral resources are a small fraction of what exists in the crust of the Earth. Mineral resources will be the main scarcity factor in the economic process. All the same, on the forecasts of depletion years, we just have to wait.

Upon the limiting factor of economic growth coming from mineral sup-plies, physicist Kyle Forinash tells us the following: “Even if supplies of fossil fuels were limitless, their associated risks are too high. Rising energy use has meant a parallel increase in pollution. The fact that the atmosphere has 35 percent more carbon dioxide, 150 percent more methane, and 40 percent more nitrous oxide than at any time in the past 850,000 years is cause for alarm” (Forinash, 2010, pp. 386–387). This is consistent with the predic-tion of the model about the relevant limiting factor, which is pollution.

Conclusions

The process of economic growth has been seen as an evolutionary process in this chapter. The evolutionary or entropic model constructed here assumes that the quantitative increase in the flow of output is followed by a qual-itative change in the degradation of the environment, degradation that is continuous and irrevocable. The mechanism operates through the first two laws of thermodynamics.

The entropic model predicts that the process of economic growth cannot go on forever. Output can be repeated but for a finite number of periods only. The entropic model predicts that pollution, not depletion, will set the limits to economic growth and to the existence of human society, as we know it. The incentive system under capitalism explains this outcome, for pollution is a public good problem. The model also predicts that output growth in the world economy will be accompanied by increasing concentra-tions of pollution in the atmosphere. This prediction is consistent with Fact 8 that was established in chapter 2 (volume 1). These trajectories would lead to an end period of economic growth, which is the other prediction of the model.

In sum, the evolutionary model is not refuted by the available facts and thus the evolutionary theory of economic growth may be accepted at this stage of our research, although only provisionally, until new data or new theory appears. Therefore, the theory that economic growth process is evo-lutionary, not mechanical, may be accepted.

The implications of the evolutionary theory are several. According to this theory economic growth cannot go on forever; hence, there cannot be such a thing as sustainable economic growth or steady state economic growth.


The theory brings up the intergenerational consumption frontier as a new concept and a new analytical tool to understand the social choice dilemmas for the survival of human species. The risk of human society collapse would occur before mineral resources have been exhausted. This is similar to that period in the history of human society when the Stone Age was abandoned before stones were exhausted. In our time, the oil-age could be abandoned before oil stocks are depleted. Another age in human society would have to appear.

In contrast, the mechanical production process, or the circular flow equilibrium, presented in standard economics assumes the physical laws of mechanics, that is, it makes an abstraction of the laws of thermodynam-ics. Natural resources are taken into account in the production process, but mostly as renewable natural resources. Standard economics assumes static or dynamic processes. It views the economic process as a mechanical pro-cess, in which qualitative changes are ignored; hence, according to this view, which constitutes today’s paradigm, economic growth can go on forever, that is, economic growth is sustainable because natural resources are (or can be made) all renewable.

According to the entropic model, the regime switching in human history will come from two limiting factors, depletion of mineral resources or pol-lution. There are theoretical reasons to expect that land resources (through food supply) may also constitute another limiting factor in the economic growth process. This question will be analyzed in the next chapter.

CHAPTER 8

Land Resources and Food Supply

Could the limit to economic growth come from food supply? In light of the evolutionary theory of economic growth presented in the last chapter, the answer depends upon whether land resources that are

required to produce food are renewable or nonrenewable. This chapter will address this question through an entropic theoretical model and submit its empirical predictions to the falsification process.

The Food Market: A Walrasian Model

A simple theoretical model of the capitalist system will be constructed to ana-lyze the role of the food market in the process of economic growth. The mar-ket system will consist of the food market among other markets. The theory is that the competitive market system is able to solve for the prices and quantities of all markets; thus, there exists a general equilibrium solution. The interac-tions between the food market and the rest, the aggregate, include the following effects: changes in the aggregate affect the food market, which then affects the aggregate, which in turn affects the food market, and so on. However, the model will take into account only the first effect, and the rest of feedback effects will be ignored for the sake of simplicity. This will be a partial equilibrium model. There will be only one labor market, such that the allocation of total labor to food and nonfood production will also be solved by the market system.

The food market will be Walrasian. Initially, a static model will be pre-sented. Once the equilibrium is determined, the price and the quantity of equilibrium will be repeated period after period as long as the exogenous variables remain constant. Changes in the exogenous variables will cause changes in prices and quantities of equilibrium in the food market.


Food Production

The static model will assume the following production function for food production:

Q = F (K, R, L, A), Fi > 0, Fjj < 0, j=K, R, L (8.1)

Food output (Q) depends upon the stock of capital (K ) in the food industry, the stock of land resources (R), the quantity of workers (L), and the level of technology (A). The stock of seeds is maintained constant, as circulating capital, which is replaced by deducting from total output; hence, Q mea-sures net output, net of seeds replacement.

The effect of each production factor is positive. The additional assump-tion is that there is generalized diminishing return to factors.

Food Consumption

The static model will assume the following consumption function of food:

C = G (p, y, N, D), G1<0, G4<0, Gi>0 (8.2)

Total food consumption (C) depends upon the relative price of food (p), real income per person (y), total population (N ), and the degree of inequality in the distribution of total income (D). Relative price of food is with respect to the price of nonfood and real income is nominal income divided by nominal nonfood price; hence, p and y will be independent exogenous variables. Changes in y will imply constant relative price p; similarly, changes in p will imply changes in the nominal price of food and thus constant y.

The effect of relative price of food upon total consumption is negative. The effect of real income per person will be positive. An increase in the degree of inequality in the distribution of income will reduce total food consumption, for the model will assume the Engel Law: The marginal propensity to consume food is lower in rich people compared to the poor. Given relative prices, real income per person, and income distribution, an increase in population will increase food consumption proportionately; hence, consumption per person will remain constant. This population effect refers to the replication of households with the same real income per person of the current household distribution of society. The mean value of real income and its distribution are thus maintained fixed as population increases.

Land Resources and Food Supply l 135

Food Market Equilibrium

The food market model proposed here will assume that the short-run mar-ket solution of price and quantity will be as follows: quantity is exoge-nously determined, whereas price is endogenous and is demand determined. The food market is Walrasian: market price clears the market. Then Q=C implies

F (K, R, L, A) = G (p, y, N, D) (8.3)p0 = Φ (K, R, L, A, y, N, D) (8.4)Φ5>0, Φ6>0, and Φj<0 otherwise

The first equation indicates the market equilibrium condition. The second is the reduced form equation, which indicates the equilibrium relative price as a function of all exogenous variables of the model.

The food market model assumes that in the short run, when the quantity supplied is given, the equilibrium price is demand determined. In the long run, price and quantity are both endogenously determined by demand and supply factors.

Market equilibrium condition in the short run is clearly stable. Comparative statics can then be applied to establish causality relations. Exogenous increase in quantity produced (due to increase in factors K, R, A, L) will lower relative food price of equilibrium. Increase in real income per person will increase demand for food and thus will increase the food price of equilibrium. A higher degree of inequality will reduce demand and thus the relative food price of equilibrium will fall. An increase in population leads to an increase in demand and thus to a relative price increase.

Population Effect

Population size effect has been included in the demand function above, where food supply is exogenously determined. However, it is also implicitly included in the supply function, through variable L. The model will now assume explicitly that population affects demand and supply of food at the same time. Then

L = λ N (8.5)Q = F (K, R, A, λ, N), Fi>0, Fjj<0, j=K, R, N (8.6)

Here λ is the proportion of the population that constitutes the labor force allocated to agriculture, and will be treated as a parameter in the model.


An increase in population has two effects upon food price. It will imply higher size of agricultural workers and thus more food supply; it will also imply an increase in demand for food. The first effect leads to lower food price, while the latter to higher prices. Which effect will domi-nate? An increase in population by 10 percent will imply, first, a 10 percent increase in agricultural labor, which will increase total food supply by less than 10 percent, say 6 percent, due to diminishing returns; second, it will imply an increase in the quantity of households with the same income level, which implies an increase in the quantity of food demanded by 10 percent. Therefore, the net effect will be an excess demand for food, which will push the food price up.

The conclusion of this simple static model can thus be stated as follows: The pure effect of population increase operates via demand and supply of food, such that the net effect will be to generate excess demand and thus a higher food price.

For analytical purposes, it will be useful to present this conclusion using “per person” magnitudes for production and consumption. Consider the following equations:

Q/N ≡ (Q/L)(L/N) ≡ q = f (K, R, A, λ, N), f4<0, f5<0, fi>0 (8.7)C/N ≡ c = g (p, y, D), g1<0, g2>0, g3<0 (8.8)p0 = φ (K, R, A, λ, y, D; N), φ5>0, φ7>0, φi<0 (8.9)

The first structural equation refers to output per person, which is pro-portional to the labor productivity (Q/L) in food production, whenever λ remains constant. Therefore, let q represent the average labor productivity in food production, food output per person. In the second structural equation, population size has been excluded among the determinants of consumption per person, for function (8.2) is homogeneous of degree one in population size: double population will imply double consumption, leaving consump-tion per person constant.

Being the food market Walrasian, equilibrium implies q=c. The endoge-nous variable is the relative price of food. The reduced form equation (8.9) shows that the exogenous variables and their effects are the same as those determined for total quantities in equation (8.4). The difference is that in this case, the population effect operates through the average labor produc-tivity in food production alone. The population effect upon food price is positive, as shown before, and the reason is the same: Double population increases consumption by double, but it increases supply by less than double due to diminishing returns; then the net effect is to generate excess demand and thus food price increases.


Figure 8.1 shows food market equilibrium. The vertical axis measures quantity of food per person and the horizontal axis population size. Average labor productivity in the production of food is represented by curve V, which shows diminishing returns: Average labor productivity falls with higher pop-ulation size, for it implies a proportionate increase in agricultural labor. The horizontal line v is the constant quantity of consumption per person, which maintains the initial level c0 for any population size. Both curves cross each other at point E, indicating the market equilibrium situation, with initial population size N0, equilibrium consumption per person c0, and p0 as the equilibrium food price.

An increase of population by double will decrease food production per person. Double population will imply double workers, which will produce less than double output due to diminishing returns; so output per person will fall, along curve V; but double population will lead to double the quan-tity of food demanded, shown at point J in figure 8.1. Therefore, there will be excess demand for food at p0. Higher population size would imply a fall

q

N

Ec°

O

V´ [K´, A´, R´ ]

J

N0 2N0

v

E´V [K, A, R ]

Figure 8.1 Food market: Population effect upon food scarcity.


in the equilibrium food consumption level, from c0 to point E′, and higher price. Hence, as population increases, food scarcity will also increase and equilibrium food price will go up over time (p'>p0). Diminishing returns is underlying this result; if it were not for diminishing returns, double popu-lation would produce double quantity of food, average labor productivity would be constant; hence, consumption per person would remain constant. Food market equilibrium will lie along the horizontal line v.

Consider the joint effect of an exogenous increase in population and in real income (y). The initial equilibrium is at point E in figure 8.1. If popula-tion size increases by double, the new equilibrium is at point E′, with higher food price (p′>p0), as shown above. Now assume the income level (y) also increases. The demand for food will rise and thus the desired consumption level would be above point E′, that is, there will be excess demand for food. The real income effect will lead to a further increase in food price (p′>>p0) to clear the food market and adjust the consumption level to the level E′. Hence, in the economic process in which both population and income level increase over time, food will become scarcer and, consequently, food prices will rise more rapidly.

Carrying Capacity of Land Resources

Taking into account changes in the other exogenous variables that appear in equation (8.7), do land resources have a limited carrying capacity? Could more people be able to consume the initial quantity of food per person c0?

An increase in physical capital will have the effect of shifting the curve of the average labor productivity outward. Then point J in Figure 8.1 could be reached, provided sufficient capital is increased, and the food market equi-librium will maintain the same consumption per person (c0) and the same food price (p0). Equilibrium could move along curve v. Due to diminishing returns, capital will have to be added in higher and higher quantities for each increase in the population size by double. Eventually, there will exist a limit to maintain the food consumption level constant.

An introduction of new technology will also have the effect of shifting the curve of the average labor productivity outward; hence, point J could be attained, provided the technological innovation is sufficiently strong. In this case, the quantity of food consumed per person (c0) will remain constant and move along the horizontal line v, as food price will also remain unchanged (p0). Thus, land resources have the carrying capacity, the capacity to feed people of any population size with the same initial consumption level.

Income level has remained constant so far. If it increases, there will be excess demand and food price will have to increase. Therefore, in the


economic process in which population, income level, and technology increase exogenously over time, the consumption level can remain constant, along curve v, but at increasing food price. This is the market rationing mechanism when there is excess demand for food. The only way consump-tion level can increase is by shifting the labor productivity curve in food production above curve V′, which implies reaching a point J″ that is above point J. This principle applies to changes in capital and in land resources, which are analyzed now.

Land resources (R) will be decomposed into three components. First, assume that land resources that are currently cultivated in the production of food constitute a fraction b of total cultivable land (R0) on Earth, which is the land resource with which humanity is endowed. Then R=b R0. The rest of land may be used for nonagricultural purposes, such as urbanization, or it may remain idle. The urbanization effect implies that coefficient b decreases as population increases.

Second, land resources may be allocated to nonfood production, such as for growing coffee, tea, or for the supply of biofuels, which are very impor-tant as substitutes to fossil fuels. In the last decades, some agricultural goods (corn, soybean, beet, sugarcane, and wheat) have started to be utilized as biomass inputs for the production of biofuels (ethanol, biodiesel, and bio-gas). The production of bioenergy has thus increased significantly in the world. Increasing energy prices and the pollution problem from burning fossil fuels have induced this innovation.

The consequence is that now agricultural commodities have alternative uses as food and biofuels. Human energy and mechanical energy are thus in conflict. Part of the agricultural output will now go to the biofuel industry and part to the food market. Let the proportion of agricultural land devoted to food supply—or the proportion of agricultural output allocated to food supply—be given by fraction m; then R=mR0.

The higher the values of m or b, the higher will be R and the higher will be the quantity supplied of food, given the values of the other exogenous variables in equation (8.7). The curve of average labor productivity will then be shifted outward. When point J is reached in figure 8.1, it implies that the initial consumption level will remain constant. However, this effect can remain only for limited time, until the coefficients m and b reach the value of 1. Once the limit R=R0 is reached, more population will imply food scar-city, as shown by point E′ in figure 8.1.

Land resources include soil and water availability. The entropic model will assume that these factors are nonsubstitutable; hence, one of them will be the limitative factor and the other the redundant factor. The implication is that the analysis can be done for each factor separately, assuming that the


other is redundant. The model that follows will assume that soil erosion is the limitative factor. This is sufficient to understand the nature of the prob-lem, that is, the conclusions would remain if water resources were taken as the limitative factor.

Soil Erosion Effect

The agricultural production process depends upon land resources in two ways. First, land enters into the production function as land space, as a receptacle for sunlight, which is the energy used in the photosynthesis of plants. Second, land enters the process also in the form of topsoil, which contains the organic richness of the land, and thus constitutes the crucial production factor. Let the top soil (S) be a fraction r of the land space R; then S=rR. Water is another factor of production, which will initially be consid-ered as redundant.

Soil is the organic layer of land that is essential for food production. Fertile soil is what makes land resources a production factor. Soil is lost due to erosion. Top soil is subject to two kinds of erosion: natural erosion due to wind and rainfall and anthropogenic erosion due to cultivation practices and deforestation. The former is exogenous to the production process and it is continuous and irrevocable. The latter is endogenous; it is man-made. As man repeats the food production process, the erosion rate increases. Therefore, even if the total food output were maintained constant, endog-enous erosion would increase continuously. Some practices may decrease the erosion rate, such as terrace construction. However, at the same time, technological modernization, such as the use of more mechanization, will increase the erosion rate. The process of natural soil formation occurs at a negligible rate on the human time scale; hence, this effect is ignored. In sum, the model will assume that the process of food production has a negative effect upon soil erosion.

The model, showing the endogenous rate of erosion (e) over time (T ), for a given quantity of food supplied (Q), can be represented as follows:

S0 = r R (8.10)S1 = (1 – e) S0 = (1 – e) r R = r1 RS2 = (1 – e) S1 = (1 – e)2 r R = r2 R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ST = (1 – e)T r R = rT R

Therefore,


eT = f (Q, T), fi>0 (8.11)ST/R = rT = (1 – e )T r = h (Q, T ), hj <0 (8.12)

This assumption implies that soil content of land (S/R) will decline over time, for a given total output of food. If total output increases, then the declining curve over time will be shifted downward. If the natural erosion is included, the curve will be shifted even further down.

Another assumption will be introduced now: there exists a threshold of soil content in land space (r*) beyond which land is productive. The degree of land fertility falls with soil erosion, until it reaches the limit. Smaller con-tent of soil in a hectare of land will imply that this land is not fertile, or it is only marginally fertile, in which plants cannot have their roots and grow, or if they can it is not economically profitable.

The analysis of land resources (R) just completed can now be introduced into equation (8.7), in which it is substituted by its components:

q = f (K, A; m, b, r; λ, N), f6<0, f7<0, fi>0 (8.13)

The effect of changes in land resource components upon food market equi-librium was already discussed earlier. These effects refer to finite number of shifts in labor productivity. Continuous shifts in the labor productivity curve can only come from change in technology and soil erosion. Now it is time to include these factors into the analysis.

Changes in labor productivity in the agricultural sector are the result of two processes going on in opposite directions. One is the process of tech-nological innovations, which is land saving and labor productivity aug-menting. The other is the degradation of the topsoil, in which the rate of erosion increases over time thus reduces labor productivity. These processes affect labor productivity in opposite directions and the net effect needs to be determined.

This model will assume that degradation of top soil is continuous and irrevocable, taking into account both exogenous and endogenous erosion. It will also assume that there is a threshold of soil content in a land space to make it productive, otherwise output will be zero. Furthermore, the model will assume that initially the rate of technological change dominates soil erosion rate for some time, after which the latter will dominate. Labor pro-ductivity will increase in the first stage and then will decrease in the second stage and ultimately production will become nil. Soil erosion, the critical natural factor of agricultural production, will ultimately put an end to food production.


Figure 8.2 illustrates the model. The vertical axis measures labor pro-ductivity (q) and the horizontal axis time (T ). The initial value of labor productivity (q0=Q0/N0) corresponds to the initial equilibrium situation. The initial value of labor productivity falls over time due to the soil erosion effect, along segment q0x.

At period T1 a technological innovation is adopted, which shifts labor productivity upward to a level beyond the original value; from this higher level, the labor productivity curve declines due to soil erosion. A new tech-nological innovation is adopted at period T2, which shifts the value of labor productivity upward, and reaches value q′. From this new productivity peak, the effect of soil erosion makes the productivity curve to fall. So far, techno-logical change has dominated the erosion effect; thus, on average, the value of labor productivity has increased over time. Because erosion rate increases over time, the slope of the productive curve q′x′ is greater than that of the curve q0x.

q

T0 T0

q0

T4T3T2

x

x´q´´

q´

T5 T *

q*

Figure 8.2 Combined effects of technological change and soil erosion upon labor productivity in food production.


At period T3 another technological innovation is adopted, which shifts the value of labor productivity upward, but to a lower level than q′. In the next periods, new technological innovations are adopted, which shift the value of productivity to a higher level, but reach values that are below the previous peaks. Now the soil erosion effect dominates. Sooner or later, the value of r* will be reached and thus no technological inno-vation will be productive. The last technological innovation is adopted in period T5 and will lift the value of productivity to the level q″. From this peak erosion continues and reduces the soil content of land resources until it reaches the value of r*, and productivity reaches the value of q* at period T*. Beyond this period, agricultural output is unviable, and no output can be produced.

The model predicts an envelope curve (the curve q0 q′q*, the dashed line) that has the shape of an inverted U curve. In the upward stage, the technological change effect dominates the soil erosion effect, and pro-ductivity grows over time. However, eventually the latter dominates the former; thus, productivity falls over time. The soil erosion effect operates as a gravitational force, which ultimately dominates in the movement of productivity.

Higher mechanization in agriculture will shift the labor productivity curve upward, but the soil erosion effect will also be higher. As a result, the value of any particular productivity level chosen will decline faster. As a result, the envelope curve will make the U-turn sooner. The soil content of land space declines over time at a rate r(K, T ), which is a function that depends positively upon the degree of mechanization and time.

At what rate would the productivity of food production grow? Assume that technological change in agriculture proceeds at the same rate as techno-logical change in the economy, which was called g in chapter 6 (this volume). Call the ascending segment of the envelope curve as stage I and the descend-ing one as stage II. Then

Stage I: Δq/q = [g – r (K, T )] > 0 (8.14)Stage II: Δq/q = [g – r (K, T )] ≤ 0 (8.15)

Remembering that income per person also grows at the rate g, the model predicts the following relations on food scarcity in the process of economic growth:

Stage I: β Δy/y = β g < = > Δq/q = [g – r (T)] > 0 (8.16)Stage II: β Δy/y = β g > Δq/q = [g – r (T)] ≤ 0, 0 < β < 1| (8.17)


In stage I, the model predicts that in the process of economic growth, food scarcity is undetermined. In stage II, the model predicts economic growth with food scarcity and thus higher relative prices of food.

Figure 8.3 shows the food market equilibrium in which those results are taken into account. The vertical axis measures average labor productivity in the production of food and the horizontal axis, population size. Consider the initial equilibrium at point E. Population doubles, which is accompanied by a change in technology that shifts the productivity curve to curve U′, which is set back to V′ due to the effect of soil erosion, and the new market equilib-rium is at point E′. The level of food consumption remains constant. In the next period, population again increases, together with technological change that shifts the productivity curve V′ to U″, which is set back to curve V″ due to soil erosion. Now the market equilibrium takes place at point E″. The ero-sion effect has become dominant now, there is excess demand, equilibrium relative price goes up, and the level of food consumption falls.

Q/N

N

c°

0

[K´, A´, r´]

[K, A, r]

v[p°, y, D]E´ E´´

V´ V

[K´´, A´´, r´´]

3N0N0 2N0

U´ V´´ U´´

N*

E

Figure 8.3 Food market: Limits to food supply in the very long run.


In the following periods, the soil erosion effect will dominate, and the market solution will be with increasingly lower levels of food consump-tion. The threshold value r* will eventually be reached and food supply will become nil. This trajectory is shown by the segment E″N*. The implication of this result is that human species faces the end of its existence due to the lack of food.

Introducing Land Resources into the Unified Theory

An evolutionary model will now be developed to analyze food production in the context of economic growth, in which quantitative and qualitative changes will take place. Figure 7.1 (chapter 7, this volume), can represent the food production process that was developed in the previous section. Let the initial total consumption of food be determined by capital and labor, whereas the line MV represents the topsoil constraint. Topsoil is a nonre-newable natural resource. Hence, the intergenerational food consumption frontier is the one represented in that figure.

Land resources include soil and water availability. Water resources are renewable as surface and groundwater flow on the bases of the natu-ral hydrological cycle. However, water resources of the planet are mostly in glaciers and in the polar ice caps. According to some scientists, water supply tends to diminish over time due to global warming, which reduces the glaciers and changes the hydrological cycle; hence, water resources have become nonrenewable natural resources owing to human actions. Its effect upon the supply of food is thus similar to that of soil (also nonrenewable). Line MW could also represent water constraint, instead of soil constraint, that is, either water scarcity or soil scarcity, whichever comes first, will be the limiting factor of food production. The model has assumed that water is the redundant factor, but its conclusions will also follow if water is the limiting factor.

According to the model, land resources constitute the limiting factor of food supply. It may seem that there exist many easy ways to escape this limitation. Nevertheless, this is not the case as the following discussion will show.

The quantity of idle arable land is not significant. Therefore, investment in irrigations could be a way to increase the quantity of land space. However, this would only have a level effect on arable land availability, not a growth effect. The land space of the planet is given. Moreover, it is known that con-struction of reservoirs leads to destruction of local ecosystems and to salini-zation of land; so arable land can increase initially, but the net effect will be much smaller in the long run.


The human activity of food production adds the endogenous part, the anthropogenic part, of land resources degradation (soil and water). This increase depends upon land-cultivation practices, mechanization, and adop-tion of new technologies; hence, land equipment, monoculture, and the use of pesticides all contribute to increase soil erosion. So the higher the food output, the higher will be the value of the land degradation coefficient.

Technological progress will be exogenous and will take place at a given growth rate. As a response to the scarcity of land, technological change will tend to be land saving, such as the use of fertilizers, pesticides, and high-yielding varieties. Consistent with the incentive of profit maximization, technological change will be labor saving (machinery using). This will have a negative side effect upon labor productivity in the food-producing sector because soil erosion increases.

In addition, the new technologies of farming will tend to be fossil energy-intensive. Hence, as food production expands, environmental degradation will take place as in any other nonfood sector.

These conclusions just reinforce the inverted U-curve of yields shown in figure 8.2. The difference now is that there are more factors that lead to the downturn prediction with greater force. This result implies that both the downturn of the curve and the critical period T* would occur sooner than what was predicted before. Therefore, in the process of food produc-tion over time, there are two effects on the production curve: technological change will shift it upward and at erosion will shift it downward. The model will assume that initially technological change defeats erosion and the pro-duction curve shifts upward, but ultimately erosion defeats technological change and the production curve will ultimately shift downward. In any event, soil erosion increases over time and thus the critical value of erosion will be reached sooner or later, and that will be the end of the food produc-tion process and of human history. Call this period T*.

Figure 8.4 summarizes the evolutionary economic growth process pre-sented before in which food production is included. The first part just reproduces figure 7.6 (chapter 7, this volume). Historical time T is mea-sured along the horizontal axis and national income per worker along the vertical axis. Line DR represents the trajectory of income per worker (the growth frontier curve) that is generated by the process of capital accumula-tion and technological change. The line BN shows the trajectory of income per worker that is feasible with the initial stock of mineral resources and its continuous depletion. Line H indicates the limit of human health tolerance to pollution. The effective limit to growth of income per worker may come from either depletion or pollution, whichever comes first. In the figure, pol-lution comes first.


Now the food production process will be introduced into the graph. It is included in national income per worker, but will now be analyzed sepa-rately. Food market equilibrium is represented by curve c, which grows at a rate smaller than curve DR. In equilibrium, food consumption will increase at the same rate of food supply, given the rate of technological change in food production, which is represented by τf. As income per worker increases, food consumption per worker will rise too, but not proportionally (Engel Law). Topsoil erosion declines continuously but agricultural technology also improves continuously along curve c. Food production also generates pollu-tion, which is included in the total pollution associated to total output.

As long as technological change defeats soil erosion, the curve c will slope upward; but sooner or later the soil erosion effect will dominate, food scarcity will appear (excess demand), the relative price of food will tend to increase, and equilibrium will imply lower levels of food consumption. The equilibrium trajectory will imply that curve c moves further away from curve DR. Ultimately, at point X′, food scarcity will change the trajectory of

y

T

D

E

X

H

J

T *p T *e T *d

S

O

R [δ0, τ1]

c [τf]

F

X´

N

B

C

Figure 8.4 Land resources as a limiting factor of economic growth.


curve c, from rising to falling, until land resources cannot produce food at all, which occurs at time Te*.

Land resources will thus put limits to the growth of income per worker that is feasible through capital accumulation (the segment DE), which can-not go beyond segment DX due to food scarcity. Because food generates human energy, point X will not be reached, and the limit will then occur earlier. The basic reason for this outcome is that land resources are nonre-newable; in particular, topsoil is nonrenewable. The amount of soil is lost in each period, which is a kind of depreciation of land, but in which there is no reposition mechanism that can avoid it. In this sense, soil is just like mineral resources. As production is repeated, even if at the same level, soil gets depleted and ultimately becomes economically exhausted.

The limit to the economic growth process now comes from three sources: depletion, pollution, and food scarcity, whichever comes first. In figure 8.4, the limit still comes from pollution, given by the curve DSC. In this case, the end of human species would leave a planet with sufficient fossil energy for mechanical work and sufficient land resources (topsoil) to produce food for human energy. If food scarcity came first, then the end of human spe-cies would leave a planet in which fossil energy is not scarce and pollution is still tolerable. The economic and political elites would most likely pay more attention to depletion and food supply problems, which are private goods, compared to pollution problems, which lie in the domain of public goods problem. Hence, the model still predicts that pollution will be the limiting factor, as indicated in the graph.

Beta Propositions and Empirical Corroboration: The Capitalist World

The food market model predicts that the equilibrium level of food consump-tion will tend to fall in the very long run. This is due to the effect of continu-ous degradation in land resources (as soil erosion) in the production process. Food will then become scarcer in the very long run. Thus, the other predic-tion of the model is that relative food prices will tend to increase in the very long run. The third prediction is that most exogenous factors will only lead to a finite number of shifts in labor productivity in food production, whereas technological innovations and soil erosion will lead to continuous shifts.

On soil erosion and ecological disruption, the available data are consis-tent with the predictions of the entropic model. According to the model, agricultural land resources are naturally lost to erosion, due in part to winds and rainfall, which are related to the solar energy influence, and in part to human activity of land cultivation.


The thin layer of topsoil that covers the planet’s land surface is the foun-dation of civilization. This soil, typically 15cm or so deep, was formed over long stretches of geological time. Initially, new soil formation exceeded the natural rate of erosion. Topsoil was a renewable natural resource. However, sometime within the last century, as human and livestock populations expanded, soil erosion began to exceed new soil formation over large areas; thus, soil has become a nonrenewable natural resource. Soil erosion and for-mation take time. The effect of soil erosion upon agricultural land fertility is to lower it because of losses of water, organic matter, and soil nutrients.

A study by professor David Pimentel (2006) of Cornell University pres-ents a survey of the international literature on soil erosion and food supply. The main conclusions of this study are as follows:

(1) Humans obtain more than 99.7 percent of their food (calories) from the land and less than 0.3 percent from the oceans and other aquatic ecosystems.

(2) During the last 40 years, 30 percent of the world’s arable land has become unproductive, much of what has been abandoned for agri-cultural use (p. 123).

(3) The rate of natural soil formation is around 0.5 to 1.0 t/ha-year, but the erosion rates on cropland are 10t/ha-year in the United States and Europe and around 30–40 t/ha-year in Asia, Africa, and South America (pp. 123–124). According to these calculations, agricultural land is losing soil at a faster rate than its sustainable replacement rate would indicate.

(4) To recover the lost nutrients of soil with the application of fertilizers is subject to diminishing returns because of the reduction in the size of the topsoil due to soil erosion.

The facts presented in this survey study tend to be consistent with the pre-dictions of the food market model. In particular, conclusions (3) and (4) indicate the significance of soil erosion in the process of food production.

Available empirical information tells us that agricultural food per cap-ita has increased over time. Moreover, 90 percent of this increase is due to increase in yields and only 10 percent to the increase in total land resources, that is, arable land per capita declined from 0.45 ha in 1960 to 0.30 in 1990 (FAO, 2009). Increases in yields are thus the result of technological change. So rises in food consumption per capita in the process of economic growth has basically been supported by technological change, which has even offset the negative effect of soil erosion. However, as the model predicts, the effect of technology is reaching its limits. Indeed, the same FAO study reported


that globally the rate of growth of yields of the major cereal crops has been steadily declining since the Green Revolution years: From 3.2 percent per year in 1960 it fell to 1.5 percent in 2000 (pp. 2, 19).

On ecological disruption, calculations have been made about the eco-logical footprint. This concept refers to the use of natural resources com-pared to the planet’s ecological capacity to regenerate. It is the land and sea area required to supply the necessary natural resources a given human population consumes and to assimilate the associated waste. According to Global Footprint Network (GFN), an international thinktank advancing the measurements of ecological footprint, since the 1970s, humanity has been in ecological overshoot with annual demand on resources (the foot-print) exceeding what Earth can regenerate each year (biocapacity). It takes the Earth one year and six months to regenerate what humans use in one year; it is as if we already consumed the biocapacity of 1.5 planet Earths (GFN, 2013).

The measures of ecological footprint have implications for the amount of natural resources needed to equalize the income level of Third World countries to that of the First World, and conclude that it is unviable. Edward Wilson, a Harvard biologist, stated this problem as follows: “To raise the whole world to the US [present living standard] level with existing technol-ogy would require two more planet Earth” (Wilson, 1998, p. 282).

Some empirical work has been done on the relations between food mar-kets and energy markets. Thus, Ciaian and Kancs (2011) found that prices of crude energy and food are statistically associated, taking nine agricultural commodities and the price of oil for the period 1994–2008. This study also showed that the share of bioenergy in total energy consumption is still small, and that the share of agricultural commodities utilized as biomass inputs in the energy industry is also still small. However, it is expected that these shares will tend to increase over time. Available empirical data also show that the prices of food, biofuel, and oil tended to move along similar paths in the period 2003–2011, with peaks in 2007–2008, which was called the food crisis period (Kristoufek, Janda, and Zilberman, 2012, Figure 2, p. 1385).

These facts suggest that both food and energy prices tend to move together, which would indicate that they are complementary goods. This would be the result of competing for the same land resources (food and biofuel) and that fossil energy is an important input in the production of food. These price relations will become closer as the share of agricultural commodities utilized as biomass inputs in the energy industry increases.

On the land resources as limiting factor for economic growth, there are several pieces of empirical evidence that are consistent with the predictions of the evolutionary model. First, as more land is utilized to produce food,


deforestation will increase. In fact, tropical rainforest and woodlands have been lost at an increasing rate since 1750, leading to an accumulated value of 35 percent lost by the year 2000 (Emmott, 2013, pp. 56–57). Second, as more land is utilized more water is consumed, which puts stress on this resource. FAO data indicate that 70 percent of the fresh water of the planet is allocated to agriculture. Other indicators that water is becoming scarce include the fact that aquifers tend to be depleted as they cannot replenish water at the rate of consumption; water use is growing at a rate that is double the rate of population growth (Emmott, 2013, p. 71).

Other factors affecting food supply are presented in the literature. For example, it is argued that food scarcity does not lie on the supply side, but on the inequality in its distribution and in the waste in production and con-sumption. It should be clear that these effects only refer to level effects (a once and for all change), not to growth effects that change the equilibrium situation continuously. In the long run, according to the theoretical model developed in this chapter, land resource degradation constitutes the essential factor that sets the limit to food scarcity.

In sum, the empirical predictions of the food supply model presented in this chapter seem to be consistent with the available facts. Therefore, there is no reason to reject the model and the food market theory proposed here may be accepted, although provisionally, until new facts or superior theories become available.

Up to now, the book has shown that economic growth leads to higher consumption levels in society. At the same time, economic growth cannot go on forever, that is, there is no such thing as sustainable growth. Moreover, economic growth viewed in light of the unified theory has two important side effects: (a) the high degrees of income inequality are not reduced and even tend to increase, which lead to social disorder, and (b) the rate of degra-dation of the environment is increased. Does economic growth lead to social progress? If yes, then the limits of economic growth constitute a human tragedy; if not, then human society may operate without growth. This ques-tion will be analyzed in the next chapter.

CHAPTER 9

Economic Growth and Quality of Society

The unified theory of capitalism has so far shown that output per capita over time is not the only outcome of the economic growth process. The other endogenous variables include output distribu-

tion among social groups in society and the degree of degradation of the biophysical environment. Hence, in the economic growth process, the same exogenous variables of the theory determine the values of these three endog-enous variables.

In this chapter, the unified theory will include in the economic process another endogenous variable: quality of society in which people live. What would make a given society a better one?

We need a criterion to measure social progress. The criterion utilized in standard economics is Pareto efficiency, which is logically derived from neoclassical economic theory. A neoclassical general equilibrium implies a particular allocation of scarce resources, which is another outcome of the economic process. This allocation is defined Pareto optimum if there is no way to make some social group better off without making other social group worse off. Thus, income transfers from the rich to the poor cannot be con-sidered a social improvement in society. However, neoclassical theory does not explain capitalism, as shown in this book; thus, the criterion of Pareto efficiency loses its relevance.

An alternative criterion can be derived from the unified theory, which is the objective of this chapter. The main analytical question is, therefore, whether the quality of society is improved in the economic growth process. Unity of knowledge possibly faces its biggest challenge in this endeavor.


Scientific knowledge in economics thus becomes the most important thing for the quality of human society in the current and future generations.

Quality of Society in the Unified Theory

Economics deals with the social problem of production and distribution of goods. In the unified theory, this is represented as an economic process; hence, process analysis is the basic analytical tool of the unified theory. Process analysis allows us to distinguish between endogenous and exoge-nous variables, which are established by the assumptions of the theory. The unified theory of growth and distribution assumes an entropic economic process.

The same idea of net output is a different concept under entropic eco-nomic process: a given level of net output cannot be repeated period after period forever, for it implies depletion of the nonrenewable natural resources, pollution of the atmosphere, and ecological disruption in the biophysical environment. “Net output” is net of costs of reproducing renewable natu-ral resources (biological resources) and man-made machines only; however, the cost of reproducing nonrenewable natural resources (mineral resources, which include topsoil and water) and ecological disruption is not taken into account, for they cannot be.

From the concept of the intergenerational consumption frontier, the social opportunity cost of economic growth is equal to the reduction in the consumption possibilities of future generations. Another social cost refers to the damage caused to present and future generations by pollution generated by economic growth. Yet, another social cost is the finite duration of the human species. In the entropic process, there is no such thing as “sustainable economic growth”; it is an economic myth. Economic growth is an evolu-tionary process, not a mechanical one.

Standard economics, in contrast, assumes that the economic process is mechanical. It can be repeated forever. Hence, GDP (Gross Domestic Product) is the measure of gross output, which only includes the cost of reposition of physical capital (depreciation). This net output (net of depre-ciation) can be repeated period after period forever if we wanted to. GDP is also taken as a measure of social progress: It measures the bundle of goods with which human needs can be satisfied.

In light of the entropic economic process, the outcome of the economic process in the capitalist system includes not only goods but also environ-mental deterioration and high degrees of income inequality, which implies social disorder. Then GDP can be considered as the measure of total output for the short run only, when both population size and the stock of physical

Economic Growth and Quality of Society l 155

capital are maintained fixed, and the rest of social costs involved in the production of goods (environmental deterioration and inequality) are con-sidered constant. It makes no sense to compare GDP over decades, for these social costs will become increasingly significant. This was shown in fig-ure 7.1 (chapter 7, this volume), where the current total consumption level will necessarily fall in the very long run.

In sum, GDP cannot measure social progress, for it ignores the social costs that accompany the entropic economic process. The limitations of GDP to measure social progress have been recognized even within standard economics (cf. Fleurbaey, 2009; Stiglitz, Sen, and Fitoussi, 2010). For exam-ple, GDP increases when things like rising crime, pollution, catastrophes, health hazards, and wars trigger defensive or repair expenditures.

What is the effect of the economic growth process upon social progress? Social progress is seen as quality of life in society. In order to achieve unity of knowledge, the concept of quality of life must be consistent with the eco-nomic process, as defined in the unified theory.

The unified theory assumes that in the context of the capitalist system individuals act motivated by self-interest and facts support this assumption, as shown in this book. Capitalist society is composed of selfish individuals, who prefer larger to smaller quantities of private goods, who seek to avoid unbearable risk, and who prefer free-riding behavior in the production of public goods. An implication of these assumptions is that people prefer to live a longer and a low-risk life than a high-risk one—either measurable risk or nonmeasurable risk, also called uncertainty. Another implication of this preference system is that people prefer to live healthy. These set of individual preferences are referred to as individual quality of life.

Does economic growth imply better individual quality of life? By defi-nition, goods do no harm to individuals; hence, more production of goods would in principle lead to better individual quality of life. However, this would only be true if society produced goods that are strictly private in con-sumption. In the aggregate, however, we must take into account the fallacy of composition problem: what is true for an individual is not for the aggre-gate of individuals. Given the interaction among individuals in a human society, consumption and production of goods generate negative externali-ties, unintended damage to others; moreover, individuals do not care about harming others with the negative externalities they generate because they act only in self-interest.

Public goods are also necessities in human societies. However, individu-als have no incentives to pay the cost of their production and expect others to do that. The reason for this is that once public goods have been produced, all people will be able to consume them, independent of the contribution to


their production. The collective action needed to produce public goods will tend to fail because individuals act only out of self-interest. This is known as the Olsonian problem or the free-ride behavior problem.

Therefore, the real question is whether production of more goods that economic growth brings about will imply a better quality of life in a collec-tive sense, which may be called the common good welfare criterion or prin-ciple. This is the relevant question from the social sciences point of view. Public goods consumption will lead to the common good, by definition. To ensure that private goods consumption does not lead to harming others, the common good principle will have to include regulations upon this type of consumption. Thus, a meaningful “quality of life” concept can only be social, not individual. The term quality of society is thus a more appropri-ate term to indicate the quality of life of the human population. There are bound to be high-quality and low-quality societies.

Life expectancy is usually taken as a measure of social progress. However, it does not take into account the quality of the number of years of life; hence, correcting life expectancy for periods of sickness, we can have a healthy life expectancy. This is a better measure of social progress in accordance with the common good principle.

Consider the following empirical definition of quality of society:

Quality of society is higher when people live a longer and healthier life.

We can measure quality of society by two observable variables contained in the concept of healthy life expectancy: aggregate death rates and morbid-ity rates. The consumption of goods, privately and communally, and the stress and worries about hunger, disease, unemployment, children future, and other risks people face in a capitalist society, will ultimately be reflected in the long run in those two variables. Although this definition is not based on a strictly biological view of human life, it reduces all the complexity of human life to two variables. Mortality and morbidity rates would incor-porate the unintended results from the workings of the market system and the democratic system, the basic institutions of capitalism. A good-quality society is one in which these rates are lower compared to those in other societies.

What is the mechanism by which the quality of society is an outcome of the economic process? It will be derived from the models of the uni-fied theory presented in the previous chapters (6–8, this volume). In those models, the exogenous variables included the global initial inequality (δ) and the rates of technological change (g and τ), whereas the endogenous variables included the trajectories of output per capita (y), degree of income


distribution (D), and degree of environmental degradation (E), trajectories that have only temporal existence, until threshold values are reached (T<T*). Now introduce the quality of society (QoS) as a new endogenous variable and assume that it is determined once the three endogenous variables are known. In this new model, the trajectory of quality of society will be endog-enous as well, and will ultimately depend upon the same exogenous variables of the old model, including time T.

Social order, clean environment (air, soil, and water), and human survival are public goods that play a significant role in the functioning of capitalist society. Call them basic public goods. The new model will predict the follow-ing relations, which are derived from the same models cited earlier:

1. The effect of output growth (y) on QoS is positive. Higher income levels imply higher consumption of goods, which will translate into higher nutrition and higher life expectancy of the population and lower morbidity rates. However, the relation will be nonlinear: higher income per worker will have a less than proportional effect. This kind of diminishing returns of higher income levels originates in the genetic limits of the human organism makeup and in some side effects of modernization (stress, processed food, sedentary life) that increase mortality and morbidity rates and thus reduce the aggregate rates.

2. The effect of income inequality (D) on QoS is negative. The higher the degree of income inequality, the higher the risk in daily life, and higher the mortality and morbidity rates. This is due to the higher degree of social disorder and stronger social conflicts that are gener-ated by higher income inequality. General equilibrium with excess labor supply is included in the general equilibrium with excess income inequality and social disorder.

3. The effect of environmental degradation (E) on QoS is negative. Pollution increases imply living with higher risk of health hazards and diseases, which leads to higher mortality and morbidity rates.

Figure 9.1 shows the empirical prediction of the entropic/evolutionary model of the unified theory upon quality of society. The horizontal axis measures income levels and the vertical axis number of years of healthy life expectancy, which is the definition of QoS. Curve MN shows the life expec-tancy curve as a function of income levels alone. This is the standard measure of social progress and also the standard hypothesis. In contrast, curve ABH depicts healthy life expectancy as a function of income levels and also as a function of the corresponding increasing values of income inequality and


environment degradation (pollution) that accompany the growth of income levels. Compared to point A, point B indicates the net effect of higher income level (positive), net of the higher income inequality effect (negative), and the higher pollution effect (negative), which is overall positive. As growth con-tinues, the negative effects of income inequality and pollution will become dominant and the net effect of growth will be negative, as shown by the seg-ment BH, where H indicates the end of the growth process.

As economic growth proceeds period after period, the positive income growth effect will be dominant in the first periods of the growth process, although the effect will tend to level off. Then at some point in time, the negative effects will become more significant, especially due to pollution, and eventually these effects will become dominant. Therefore, in the process of economic growth, quality of society will first increase, then will level off, and ultimately will fall, that is, there will be an inverted-U curve—curve ABH in figure 9.1, where the turn of the curve occurs at income level y*.

The Limits of Technological Change

According to the evolutionary model, one of the exogenous variables in the economic growth process is technological change. It is usually argued that

Output per worker

Degree of quality of life

O y *

A

B

H

N

M

Figure 9.1 Economic growth and quality of life.


environmental degradation, food scarcity, and health problems would all disappear through appropriate technological innovation. Technological change is expected to solve most of the social problems. However, the fact is that technological change has taken place continuously for most of the his-tory of capitalism and yet the two side effects of economic growth remain significant. The expectation about technology as the problem solver is there-fore not justified. This section aims at explaining the limits of technological progress to solve inequality and environmental degradation, the two factors that have negative effects upon the quality of society.

What are the incentives underlying technological innovations? The the-ory proposed here is the following. On the demand side, firms act motivated by profit maximization and thus prefer new technologies that increase the rate of return of capital and also reduce the risk. On the supply side, the incentive system for producers of new technologies is also profit maximi-zation. Hence, the industry of new technologies is governed by the profit-maximization motivation of the social actors. Wealthy capitalists are able to bear high risks, as shown earlier (chapter 6, this volume); therefore, new technologies that lead to high rates of return of capital even if it implies high risk will be part of the technology market equilibrium. The more con-centrated the physical capital is, the riskier are the new technologies that are adopted. The consequence is that the process of technological change does not seek a low-risk society, which is a requirement for a high-quality society.

Technological Change Is Labor Saving

Do capitalists prefer labor saving or capital saving technological change? Labor saving technological change is defined a la Hicks as follows: Given the same relative factor prices, new technology saves both capital and labor, but labor is saved more, which implies production with a higher capital-labor ratio. In the case of labor saving new technology, suppose double the quantity of output can be produced with half of the labor and 50 percent more of capital. Given the real wage rate, total wage bill will decrease; hence, labor share in the value of total output (which has doubled) will be smaller and, consequently, profit share will be higher. Labor saving technology is thus in the interest of capitalists. They will promote and adopt new technol-ogies that are labor saving.

This prediction of the theory of technological change seems to be con-sistent with facts. By and large, we observe that new technologies tend to reduce labor. Mechanization displaces labor continuously and irrevocably (a kind of economic law).


In the dynamic growth models presented in chapters 3–5, this volume, labor augmenting technological progress or Harrod-neutral was assumed. Because production maintains the same capital/output ratio, average pro-ductivity of capital is constant; hence, the marginal productivity of capital is also constant, and so is the rate of profit. However, real wage rate rises in the process of economic growth do not translate into a higher labor share because capital per worker increases. The result is that factor shares remain constant. This is also consistent with facts.

At the firm level, there exists labor saving technological change; but in the aggregate, there is no change in factor shares. Is this logically possible? Yes, it is. If factor prices remain constant, then capital per worker increases; hence, factor shares will increase in favor of profits. However, in the eco-nomic growth process, factor prices do not remain constant, real wage rates increase, and marginal productivity of capital remains fixed, which increases capital per worker even further; therefore, the increase in capital per worker tends to compensate for the relative increase of real wage and the final out-come is with constant factor shares.

The algebra is simple. Factor shares can be written as

P/W = (r/w) (K/L) (9.1)

Hicksian labor-saving technological change is defined as higher capi-tal per worker maintaining factor prices constant, which together imply a rise in the profit share. In the growth model, dynamic equilibrium implies a fall in factor prices and an additional increase in capital per worker, which together imply that the latter change tends to compensate for the former change, so that factor shares do not change. Therefore, it is logically consistent to have Hicksian labor-saving technologi-cal change at the firm level and constant factor share in the aggregate growth process.

In the dynamic equilibrium of the epsilon model, employment grows at the rate of population growth. Unemployment rate will remain unchanged in the process of economic growth. In the dynamic equilibrium of sigma society, employment in the capitalist sector grows at a rate that is higher than the population growth because workers in the self-employment sector are also absorbed; however, in this process, underemployment of X-workers will exist, even if decreasing over time, while the exclusion of Z-workers will continue. Hence, technological change per se is unable to solve the risk of unemployment and underemployment that workers face in the capitalist system, that is, the observed high degrees of income inequality will persist under this type of technological change.


New Technologies Are Hardly Fossil Energy Saving

The exploitation of mineral resources is subject to Ricardian diminishing returns. Therefore, more quantity of minerals will enter into the market, but at increasing prices. The introduction of new technologies will reduce costs and the supply will expand; hence, at the same price, more quantities will enter into the market.

However, there will be side effects upon risk. These may not be internal to the industry, but external. In the latter case, the side effect will take the form of an externality. For example, water contamination may increase due to the use of chemicals in the new technology. Risk of failure in the tech-nology may imply spillovers and thus more pollution to the area of exploita-tion (ocean, rivers, lakes). The motivation of short-run profits would explain this ecological disaster that some firms generate with new technologies. The opportunity of high market prices creates incentives to not only generate new technologies, but also to reduce the testing and checking for risk, which would take more time. The incentive is to leave risk as residual, especially if firms adopting the new technologies are big (can bear high risk), if there is no internal cost of the possible damage, or if it is insured.

Even if the ecological damage is internalized in the firm, the real cost of damage is not easy to calculate and would tend to be underestimated. If the real cost of ecological damage were internalized, firms would have no incen-tives to go into the business of exploiting mineral resources. They would have to replenish the stock of mineral resources to its initial amount!

Technological change aiming at saving fossil energy faces several predica-ments. First, one way to save energy is to reduce the consumption of exoso-matic gadgets, but humans are addicted to these goods, which are material goods produced out of material goods. This addiction is reflected in the observed obsession with economic growth. However, it implies degradation of the biophysical environment. Second, it is not easy to reduce the required amount of matter or energy per unit of output. An entropic viable technol-ogy would be the one that is able to maintain human species, as we know it. Other living organisms constitute cases of viable technology because they depend upon endosomatic elements (feet, wings). Birds maintain their spe-cies using endosomatic elements, for example wings, and not planes, but humans use technology that is unable to maintain the human species (man-made machines and gadgets for consumption and leisure).

Any viable technology must satisfy the Hawkins-Simon conditions, which means that it must turn out positive net output. Producing one gal-lon of oil fuel should not require as input more than one gallon of fuel in total, directly and indirectly. Nevertheless, this is the physical condition


only. The entropic condition would require constant environment factors, which makes most technologies unviable because the stock of oil reserves is depleted and the atmosphere is polluted continuously and irrevocably, as the laws of thermodynamics explain.

Given the finite nature of fossil fuels and the pollution they generate, we are in search of alternative energy sources. The evaluation of a physicist on these sources is worth taking into account:

At this point, there appears to be no single source that can fully replace fossil fuels . . . There is enough energy in the world to replace fossil fuels, but the economic and logistical aspects of this transformation are daunting . . . However, it should be kept in mind that alternative ener-gies are not necessarily environmentally benign. All energy sources cause pollution in their initial manufacture, their daily use, or disposal of the apparatus after its normal lifetime. (Forinash, 2010, pp. 387–388)

Among the alternative sources of energy, attention is now on biofuel energy and solar energy. As we have already shown in chapter 8, biofuel is con-strained by the needs of human energy. Viable technology for maintaining a given population size would imply that this population can be fed by organic agriculture alone, that is, it is consistent with the natural carrying capacity of the Earth. However, even in the old times of organic agriculture, man had to share his farming with his beasts of burden; so both food and fodder had to be produced from the same land resources. This difficult dilemma was sum-marized in the saying “the horse eats people.” Nowadays, when agricultural technology is mechanical, and biofuel is needed for the food supply, and for the production in other sectors, we may say “machines eat people.”

Solar energy is another favored source. However, as Georgescu-Roegen pointed out, we do have only the feasible recipes for the direct harnessing of solar energy—solar cells and solar collectors. The viable technology is not here yet. The harnessed solar energy cannot reproduce even the energy utilized in the production of its collectors (through collectors, net output of energy is not positive) because of the low intensity with which solar energy reaches the Earth (Bonaiuti, 2011, p. 156).

Food Supplies with New Technologies Are Mostly Entropic and Unhealthy

Profit maximization induces firms to generate and adopt new technologies in the food industry. The results are not always for the common good, such as supplying healthy food. Consider the following examples:


Adulteration is one side effect. Firms make profits by deliberately adding adulterants in food stuff.

Additives in food processing can cause harm. Not enough is known about their side effects, but producers use even before scientific research find-ings have proven them to be unsafe.

Toxins are used during the growing and processing of food. The human body has a limited tolerance to absorb these toxins.

There is a large preference among people for junk food—high on empty calories and bad for health—and this is directly linked to the explosion of noncommunicable diseases in the world.

New technology in food production tends to be land saving. This includes the use of fertilizers and farm equipment, increase in water use, monocul-ture crops, and pesticides. For example, 4,000 gallons of water and a third of a gallon of oil are needed to produce a bushel of corn with modern technol-ogy (fertilizers and farm equipment). This is an energy-intensive technology. As a result, 30 percent of CO2 emissions in the United States come from agriculture and livestock (Forinash, 2010, pp. 14–15).

People expect another Green Revolution to solve the food problem. However, it is clear that this revolution that happened earlier was a myth. As another scientist pointed out: “The Green Revolution was not a story about clever people who worked out how to get more food from our fields. The truth is that the Green Revolution was a story about clever people thinking it was a good idea to buy every extra unit of food through energy and chemicals . . . We do need a food revolution. But it’s a revolution that require a radically new kind of science” (Emmott, 2013, pp. 164–165).

The human diet imposed by modern lifestyle is also energy-intensive. “The World can feed about 10 billion people if they all were vegetarian. However, a world with US diet can support only 2.5 billion people using current technology because of the diversion of cereal and grain crops to pro-duce beef, poultry, and other livestock” (Forinash, 2010, p. 15).

New agricultural technology has become more energy intensive in a world in which energy sources are becoming more limited. In addition, this technology has also damaged the land by increasing salinity and decreasing the natural fertility and topsoil depth, that is, by generating more soil ero-sion. The use of reservoirs to acquire water destroys local ecosystems, which contributes to ecological disruption.

Given the nature of technological progress in the capitalist system, which is governed by the profit motive, as was presented earlier, the inverted U-shaped curve of quality of society as an outcome of the economic process


is reinforced. Therefore, as long as the rates of growth of technology (g and τ) remain fixed, the inverted-U curve will also remain unchanged.

A Final Model of the Unified Theory

In the generation of new technologies, social actors act motivated by self-interest, which refers basically to the self-interest of the economic and polit-ical elites, who have the power to set the agenda and finance the process of research and development (R&D), that is, the growth rate of technological change is not exogenous, but endogenous. Technological change depends upon the initial inequality (δ). Therefore, as long as the initial inequality—the power structure of society—remains unchanged, technological change will grow at the same rates (g and τ) and maintain the type of technological change that is more profitable to the elites, as indicated before.

Moreover, the growth rates of technological progress are hardly observ-able; hence, it would be more appropriate to include them as nonobservable elements in the mechanisms of the economic process, and thus maintained fixed. Technological change will then be part of the structural equations, in which it varies with changes in the initial inequality, not of the reduced form equations. This implies that in the dynamic models (chapters 3–6), the value of the variable g would remain unchanged; similarly, in the entro-pic models (chapters 7–8), the values of the variables g and τ would remain unchanged. This explains why in those models, the effects of changes in the rate of technological change upon the transitional dynamics were not analyzed.

In sum, according to the entropic unified model, the ultimate factor, the exogenous variable of the economic growth process, now includes the initial inequality only. The other exogenous variables are ignored for they refer to initial physical conditions: factor endowments (capital and labor that determine the initial income level) and the stock of nonrenewable nat-ural resources. The endogenous variables consist of trajectories of output per worker, income inequality, degree of environmental degradation, and qual-ity of society. The mechanisms by which the exogenous variable gives rise to the endogenous variables now include the institutional mechanism (markets and democracy) and the technological innovation mechanism. The entropic growth process will be repeated for a finite number of periods only.

The trajectory of the inverted-U curve shown in figure 9.1 will thus remain unchanged as long as the initial inequality (power structure) remains unchanged, which also maintains fixed the rates of technologi-cal change and the bias of new technologies. The model predicts that a decrease in the initial inequality will lead to another technology research


agenda, which will have a different bias: responding more to the interests of the people and less to those of the current economic and political elites. As a result, the inverted-U curve will be shifted upward and to the right, which will imply that the downturn point of the curve will occur at a higher income level.

Comparisons with the Literature

Constituents and Determinants

Individual quality of life, not quality of society, is the usual category dis-cussed in the literature. Within this, two categories are in turn distin-guished: the constituents and the determinants (Dasgupta and Weale, 1992, p. 119). “Health status” belongs to the former, “health care system” to the latter. Certainly, income belongs to the latter.

The usual indicators of quality of life in the international literature mix both types of categories. These indicators are:

(1) life expectancy at birth (C)(2) child survival rate (C)(3) adult literacy (C)(4) income per capita (D)(5) political rights (D)(6) civil rights (D).

Indicators 1–3 are constituents (C) and the rest are determinants (D). Indicator 4 appears in the ranking of countries in the World Bank’s World Development Report; indicators 1–4 appear in the UNDP’s Human Development Report. Indicators 5 and 6 were proposed by Dasgupta and Weale (1992).

Subjective Wellbeing

Quality of life is intended to be seen as subjective wellbeing by some authors, as reviewed in Deaton (2013). The degree of happiness of people is taken as the constituent. This approach goes back to utility theory. The unified the-ory assumes that people act based on self-interest, which implies that they seek to maximize their individual wellbeing.

The novelty lies in the intent to measure utility directly in humans. The existence of a hedonimeter would be needed, just like measuring blood pres-sure. Even if such a hedonimeter existed—which is doubtful—interpersonal


comparisons of utility or happiness will still face the old problem of Pareto. On the other hand, the common practice of measuring happiness by what people say in responding to surveys has no epistemological justification. Indeed, scientific knowledge can be constructed on what people do, on the behavior of people (observable), not on what people say they feel or say they do.

Human Development Approach

Philosopher and economist Amartya Sen has proposed a different approach to quality of life, which he prefers to call human development. “Development is the progress of human freedom and capability to lead the kind of lives that people have reason to value” (Drèze and Sen, 2013, p. 43). Education and health play a central role in the formation of human capabilities and in expanding people’s real freedom. Real incomes also play a significant role, but the success of society cannot be judged just in terms of GDP. Real income is only a mean to get ends, and ends are defined in this approach as the freedom and capabilities that people enjoy. Economic growth does not imply social progress in terms of freedom and capabilities if in that process the real income, education, and health of the poor fail to increase significantly.

The popular human development index (HDI) is meant to reflect empirically the human development approach. It includes three indicators, namely

basic education,●l

longevity, and●l

per capita income.●l

Longevity is included because of “the fact that people tend, by and large, to value living longer . . . and the fact that we value life at least partly because of the things we can do, if alive” (Sen, 2006, pp. 258–259). Education is included because “education enhances the ability of people to do what they value doing” (p. 258). Finally, real income is included as an indica-tor of “the command over resources to enjoy a decent standard of living” (p. 259). The limitations of the HDI are also spelled out: “The wellbe-ing and freedom that we enjoy have much internal diversity and they are influenced by a great variety of factors—political, economic, social, legal, epidemiological and others . . . HDI cannot do justice to the variety of pur-poses that can be served by the human development approach in general” (p. 259).


Theory of Human Need

Doyal and Gough (1991) proposed to distinguish between needs (uni-versal) to wants (culturally determined) and then defined basic needs as those universal preconditions that enable people to have social participa-tion. Physical health and autonomy are considered the basic needs that are universal. Physical health is undoubtedly essential to participate in social life. Autonomy refers to the capacity to make informed choices. Informed choices would be dependent upon education levels. Thus, individuals seek to live a social life, which will be hampered if physical health and autonomy are absent. Autonomy includes mental health, which can be added to physi-cal health and to the general category of health. Quality of life is social life.

The constituents of social life can thus include health and education. The determinants include a set of categories that is called intermediate needs (food, housing, schooling, etc.).

In general, the concept of quality of life is not uniform in the litera-ture. (Standard economics view of quality of life has already been discussed before and is included in the following conclusions of this brief literature review.) Quality of life is equated with the aggregate production of goods (GDP); it is individual and subjective; it is individual and objective (educa-tion, real income, longevity, and health). In contrast, the concept of quality of society adopted in this study, which is based on a scientific theory that explains capitalism (the unified theory), is social and objective, measured by healthy life expectancy. Thus, the literature reviewed tends to ignore the side effects of output growth upon the quality of society and the inverted-U curve therefore hardly exists.

Empirical Evidence: The World Society

The final entropic model of the unified theory predicts that quality of soci-ety shows an inverted-U shape curve in the economic growth process. One of the basic reasons for this prediction is that the economic growth process has positive effects upon social progress, but subject to diminishing returns; it also has side effects that are negative. This is a falsifiable proposition and will be confronted against the available empirical facts.

According to UNDP estimates, in the period 1970–2004, life expec-tancy jumped from 72 to 78 years in the First World and from 56 to 65 years in the Third World; infant mortality rates fell from 22 to 5 per thousand in the First World and from 108 to 61 in the Third World in the same period (UNDP, 2004, Table 9, p.171). After three decades of economic growth, life expectancy differences diminished from 16 to 13 years, while infant


mortality did from 86 points to 56 points. There is catching up; but at this rate, it would take more than a hundred years of economic growth to have equalization in these indicators.

As to the prediction that life expectancy increases with economic growth, but at a decreasing rate, the empirical evidence tends to corroborate it. The World Bank has made calculations for the worldwide social progress in terms of infant and child mortality rates over the period 1968–2010 (World Development Indicators, 2010, Web Page). Given that average income increases over time in the capitalist system, and in the world society, this is another way to relate the effects of output growth upon quality of society. Infant mortality rates fell by 65 points in this period of 42 years (from 102.63 to 38.00 per thousand live births), but 64 percent of the gain occurred in the first half of 21 years, and the rest 36 percent in the second half. Child mortality (under-5) rates fell by 100 points (from 152.97 to 53.30 per thou-sand live births), but 65 percent of the gain occurred in the first half and the rest 35 percent in the second half. It is clear that this indicator shows social progress, but subject to diminishing marginal gains over time, as predicted by the model.

As to life expectancy, the calculations made by the World Bank refer to the period 1970–2010. In these 40 years of output growth, the world gained 10 years of longer life (from 59.33 to 69.64 years of life expectancy), but 59 percent occurred in the first 20 years and 41 percent in the last 20 years. Again, this indicator shows social progress, but subject to diminishing mar-ginal gains over time, as also predicted by the model.

The book by Angus Deaton (2013, Figure 1, p. 30) shows a more analyt-ical result: the estimated income elasticity of life expectancy in the world is positive, but less than 1. This is the result of a cross-section analysis based on a large sample of countries of the world for year 2010. Among the poorest countries, increases in GDP per capita are strongly associated with increases in life expectancy, but as the income level rises, the relationship flattens out, and is weaker or even absent among the richest countries. This evidence cor-roborates the empirical prediction of the model: the income effect upon life expectancy is positive, but subject to diminishing marginal gains.

Regarding the prediction about healthy life expectancy, which should show an inverted-U curve in the growth process or over time, the available empirical evidence tends to corroborate this prediction in the sense that pro-gress tends to face limits, as the following study on the world health status indicates. The Global Burden of Disease Study 2010 (IHME, 2012) has made calculations on healthy life expectancy for a large sample of countries of the world in the years 1990 and 2010. Over 450 scientists and experts participated in this study. The results were published in December 2012 in


a special issue of the leading British medical journal The Lancet. The basic conclusions indicate that overall life expectancy has increased in that period; however, when it is corrected for disease episodes, healthy life expectancy has also increased, but more slowly, that is, people are living longer, but sicker. The study makes the following remark, “In analyses that use life expectancy as a key component in tracking overall social progress, a focus on healthy life expectancy could lead us to reassess progress” (Salomon et al., 2012, p. 2158).

The other result from the Global Burden of Disease Study 2010 is that pollution ranks among the top ten killers in the world. The air pollution effect operates through the exposure of population to ambient concentra-tion of particles, which generate lower respiratory infections trachea, bron-chus, and lung cancers, heart disease, cerebrovascular disease, and chronic obstructive pulmonary disease. Because exposure to air pollution increases the risk of cardiovascular disease (high blood pressure is the first killer), and other leading causes of disease and death worldwide, the global burden of disease due to air pollution is substantial. The air pollution effect leading to death is also reflected in the fact that the death risk due to this factor is much higher in regions of the world in which air pollution levels are the highest, as in Asia (IHME, 2012, Table 3, and pp. 2240–2245).

Local studies have also corroborated that air pollution has a nega-tive effect upon human health. Thus, a study shows negative relations between air pollution and mortality rates in the 88 largest US cities for the period 1987–1994 (Dominici et al., 2002). Another found that com-bustion emissions cause a large number of premature deaths per year in the United Kingdom (Yim and Barret, 2012). Other studies report the effect of air pollution increasing incidences of asthma in California (Mc Connell et al 2010), negatively affecting student health and academic per-formance in Michigan (Mohai et al., 2011), increasing respiratory allergies in children (Parker, Akinbami and Woodruff, 2009) and infants in the United States (Sheffield et al. 2011), infants in the Czech Republic (Hertz-Picciotto et al., 2007), and among the elderly in India (Mukhopadhyaya and Forssell, 2005).

The case of Northern China is a quasi-experiment. China’s Huai River Policy provided free winter heating via the provision of coal for boilers in cit-ies north of the Huai River but not to the cities in the south. A recent study found that ambient concentrations of total suspended particulates (TSP) are about 55 percent higher in the north; further, the results indicate that life expectancies are about 5.5 years lower in the north owing to an increased incidence of cardiorespiratory mortality. Air quality in China is known to be poor. The study thus concludes: “These results may help explain why


China’s explosive economic growth has led to relatively anemic growth in life expectancy” (Chen et al., 2013, p. 12941).

Recent empirical studies show that health at birth is sensitive to environ-mental factors, including maternal exposure to pollution. In particular, the negative effect of maternal exposure to particulates during the entire term of pregnancy upon the birth weight of the infant has been reported for a sam-ple of around three million singleton term births in nine countries; this is explained by the mother’s stress to dis-intoxicate from pollution (Dadvand et al., 2013). Another study found that poor mothers and low-educated mothers tend to live in neighborhoods where air pollution is high compared to wealthy mothers (Currie, 2011). If this empirical result were added to the previous one, then health at birth would depend upon the socioeconomic state of families. Path dependence would then appear in health inequality, in which pollution is a major factor.

The number of people leading lives with financial insecurities also shows an increase along the economic growth process, as the model predicts. Chapter 7 (volume 1) showed that higher income inequality leads to a higher degree of social disorder; hence, social disorder should be on the increase in the economic growth process because income inequality increases. Empirical studies on changes in the trend in criminality and political instability by countries are unavailable, but it is clear that cities are increasingly plagued with violence, congestion, and pollution.

Pollution has additional indirect effects on quality of life. These include:

Oceans become more acidic.●l

The ozone hole increases in dimension.●l

About half of the carbon dioxide released into the atmosphere dissolves into the surface water of the oceans, and that makes the oceans more acidic. Changing the chemistry of the oceans is a way of degrading them. The ozone layer, an absorber of ultraviolet radiation from the sun, is degraded by pollution. Ultraviolet light is the component of sunlight that does the most damage to human skin causing sunburn and possibly cancer (Muller, 2008, Chapter 20).

Whether climate change is endogenous to the economic process is still under scientific debate. The factors affecting climate change can be seen in three steps. First, human fossil-fuel burning causes pollution, such as rise in concentrations of CO2 in the air, which has accelerated since the industrial revolution period, as shown in figure 2.1 (chapter 2, volume 1); second, CO2 is a greenhouse gas; third, the greenhouse effect in turn increases average


global temperature and climate change. The first two effects are accepted by scientists (and have been included in the entropic model in chapter 7, this volume), but the third is under debate.

According to some natural scientists, emission of greenhouse gases causes climate change; that is, production of goods implies waste and pollution, which results in climate change (Aeschbach-Hertig, 2007). Climate change is thus endogenous to the economic process. Others feel climate change is exogenous to the economic process; it is mainly caused by the natural varia-tions in solar activity (Chilingar, Sorokhtin, and Khilyuk, 2008, p. 1572). Yet for the United Nations IPCC, although it is a complex problem and it is hard to separate empirically the relative quantitative significance of each effect with certainty, the conclusion is that part of the observed cli-mate change is undoubtedly endogenous, that is, it is very likely (90 percent chance) that humans are responsible for some of the climate change (IPCC, 2007), which was revised to 95 percent (almost certainty) in the last report (IPCC, 2013). In fact, a positive correlation between atmospheric CO2 and global average temperature for the period 1880–2010 is shown graphically in Stavins (2011).

In the entropic model, the pollution effect alone is necessary and suffi-cient to predict that growth is bad for the environment and for the quality of society, that is, this effect is independent of whether pollution causes global warming, or whether the observed climate change is endogenous or exogenous. If it is endogenous, as the IPCC reports indicate, then the nega-tive side effects of economic growth upon the quality of society will tend to be much more important. Including the climate change effect, the entropic model predicts more forcefully the inverse U-shaped curve of quality of soci-ety that was shown in figure 9.1. Hence, in what follows, we may consider that climate change is endogenous in the entropic model.

Advances in the information technology of satellites that orbit the Earth allow us to know with higher precision changes in the climate and other impacts on the environment, such as deforestation, reduction of glaciers, and natural disasters. Munich RE’s natural catastrophe database, which contains more than 31,000 entries, is the most comprehensive source of nat-ural catastrophe data in the world. According to this source, in the period 1980–2012, weather-related catastrophes (storms, floods, and climatologi-cal events such as heat waves, cold waves, droughts, and wildfires) increased worldwide from 300 to 800 events (Munich RE, 2013). The impact of climate change on food supply is another example. The 2008 Australian drought, the 2010 Russian drought, and the 2012 drought in the United States led to losses of between 20 and 40 percent of the entire grain and corn harvest (Emmott, 2013, p.67). With this information technology, the


relationship between economic growth and rapid environment degradation is becoming hard data.

In sum, the empirical prediction of the model is that economic growth has both positive and negative effects on the quality of society. The avail-able empirical evidence corroborates this prediction. On the first prediction of quality of society, life expectancy has indeed increased in the growth process, but at a decreasing rate; infant mortality rates and child mortality rates have declined over time, but also at a decreasing rate. Therefore, there are limits to the gain in quality of life, as measured by these indicators. On the other prediction, people live longer but are sicker; moreover, healthy life expectancy is much smaller than life expectancy, and increasingly less so. Therefore, economic growth does not bring social progress in a continuous manner, just as the entropic model predicts.

Conclusions

The final entropic model of the unified theory predicts that the economic growth process supplies society with increasing quantities of goods per per-son, which has a positive effect on quality of society, but it is subject to decreasing marginal gains. Economic growth has side effects as well, of which the most important ones are: an increase in income inequality and an increase in the degree of degradation of the biophysical environment. This chapter has shown that these side effects in turn have negative effects on the quality of society, causing increasing social disorder and social conflicts and natural hazards. The model thus predicts a trajectory of an inverted-U shaped curve upon the quality of society in the economic growth process. The chapter has also shown that the rates of technological change may be considered endogenous; hence, the only exogenous variable of the economic growth process is the initial inequality (power structure).

The available facts tend to corroborate the predictions of the entropic model. The income effect of output growth is found to be positive, but at decreasing rates. The side effects of output growth are indeed negative and tend to become increasingly dominant over time. Facts show that people live longer, but are sicker. This seems to indicate that we are entering into the downward sloping segment of the curve or maybe we are already there.

In sum, facts do not refute the predictions of the final entropic model of the unified theory. Therefore, there is no reason to reject the model, and we may accept the unified theory at this stage of our research, although only provisionally until new facts or theories become available. The unity of knowledge in the economics of capitalism has thus been attained: first, the unified theory has been able to explain production and distribution in the


capitalist system taken by parts (the First World and the Third World) and taken as a whole, and from the short run relations to the long run; second, it has been able to explain the capitalist system as a whole in the very long run, including here the side effects of economic growth: persistent inequality and social disorder, environmental degradation, and ambiguous progress in the quality of society. The unified theory has constructed a single logic system to understand a single world.

If economic growth is unable to guarantee a better quality of society, then the natural question is why human societies (capitalists and noncapital-ists) continue applying economic growth policies. Growth policies as soci-ety’s priority would be understandable in the beginning of capitalism, two hundred years ago, when economic growth improved unambiguously the quality of society, when the negative side effects of economic growth were weak and were not anticipated. However, today’s pro-growth public policies are paradoxical and certainly need an explanation. What would be the alter-native public policies that can be derived from the unified theory? These are the issues that will be analyzed in the next and final chapter of the book.

PART III

The Political Economy of the Unified Theory

CHAPTER 10

Science-Based Public Policies

Public policies need positive and normative sciences. Positive science is what this study has presented so far. It is another name for factual sciences. Normative science is a formal science and studies the logical

system underlying ethics, values, and norms. In short, while positive science seeks to answer the question of how the world is, normative science seeks to answer how the world ought to be.

Science-based policies are derived from scientific knowledge, but not from this alone. Alternatives also emerge from the policy implications of sci-entific knowledge, the choice of which would then require normative propo-sitions to choose from. In this case, both positive and normative economics are needed to discuss science-based public policies in economics. Only in the especial case of a theory with one endogenous variable and one exogenous variable, public policy would be logically derived from scientific theory, for there would be just one objective to seek (about the endogenous variable) and just one instrument to use (the exogenous variable). In general, there is no logical route from the proposition how the world is to the proposition how the world ought to be. Normative propositions are needed in between. The principle of public policies applied to the unified theory will be seen in action in this chapter.

Summary of the Unified Theory

As shown in this book, under the rules of Popperian epistemology, some of the basic facts of the capitalist system refute the predictions of standard economic theories. The need for a new theory thus emerges. The unified theory of capitalism that has been presented in this book intends to fill that


scientific need. Indeed, the predictions of the unified theory are not refuted by any of the set of eight empirical regularities of capitalism. Therefore, on epistemological grounds, there is no reason to reject the unified theory and we may accept it as a good theory to explain the functioning of capitalism, although only provisionally, until new empirical evidence (that can refute the theory) or a superior theory becomes available.

According to the unified theory, the capitalist system operates as follows:

A. In the short run, the capitalist system functions with excess labor sup-ply. The profit motive underlies this as excess labor supply is used by firms for labor effort extraction. Excess labor supply takes on differ-ent forms according to the type of capitalism: unemployment in the First World and unemployment and underemployment in the Third World. Because these forms lead to inequality among homogeneous workers, inequality among workers constitutes the generalized under-lying labor discipline device in the capitalist system.

B. In the short run, the capitalist system operates with excessive income inequality (within-country inequality and between the First World and Third World inequality), which leads to corresponding degrees of social disorder. Inequality is not merely an ethical problem; it gen-erates social costs in the form of social disorder and thus matters for the quality of society. Note that income inequality internalizes the inequality that excess labor supply generates.

C. In the long run, the capitalist system is able to grow endogenously, so that income levels increase everywhere over time. However, First World and Third World countries follow separate paths. The reason for this is, in the economic growth process there exists path depen-dence, that is, history prevails. The initial conditions under which countries started their capitalist growth process determine separate and hierarchical growth frontier curves: a high level curve for the First World and a low level curve for the Third World. Countries do not reach the same growth frontier independent of how they started. Overall income inequality persists in the growth process. European colonial legacy is, according to the unified theory, the main factor underlying this path-dependent economic growth. After the colonial system was removed, the colonial institutions have persisted, a social phenomenon that we could call social hysteresis, as it resembles the phenomenon of hysteresis in physics.

D. In the very long run, the economic growth process raises the rate of degradation of the biophysical environment. Economic growth is

Science-Based Public Policies l 179

an entropic and evolutionary process, not a mechanical one. Output growth cannot continue forever. There is no such thing as sustainable output growth. Therefore, in addition to maintaining excess income inequality, economic growth has another side effect: environment degradation, which in turn implies increasing inequality between generations and reducing the duration of the human society, as we know it.

E. In the very long run, economic growth does not bring continuous social progress. Social progress or quality of society, measured by healthy life expectancy, increases in the initial stages of capitalist growth, but later on the side effects tend to dominate. The unified theory predicts that the relation between growth in income levels and quality of society takes the form of an inverted-U curve. The fact that people live longer but are sicker indicates a trend that is consistent with the theory. The models that explain these different runs are all logically consistent with each other; moreover, in these models macrobehavior has microfoundations and microbehavior has macrofoundations; thus we have attained a unified theory of capitalism.

F. Why does the capitalist system operate thus? The common exoge-nous variable that is able to explain the functioning of capitalism in the short run, long run, and very long run is the initial inequality in the distribution of economic and political assets among individuals. This initial inequality constitutes the power structure of society. In the very long run, power structure alone is the exogenous variable. Therefore, the ultimate factor that explains the functioning of the capitalist system is the highly concentrated power structure. Power structure is more concentrated in the Third World, since it origi-nates from the legacy of the European colonial systems. This dif-ference in power structure explains why the Third World countries operate with higher degrees of income inequality and why the capi-talist system as a whole is a very unequal society. It also explains why markets and democracy, the basic institutions of capitalism, operate differently in the First World and the Third World countries. The power structure does not change endogenously in the process of eco-nomic growth, for there are no mechanisms for that; education, for one thing, is not income equalizing; hence, power structure is truly an exogenous variable of the unified theory. The capitalist system will continue to operate as shown above, with economic growth but uncertain social progress, as long as the power structure remains unchanged.


According to the unified theory, the capitalist system operates with power relations. In the case of the capitalist class, the theory has shown the following power mechanisms: use of labor discipline devices in labor market relations and pressures to the government behavior through the so-called Kaleckian threats, such as capital flights. Another mechanism is market power, as phys-ical capital concentration usually leads to monopolistic or monopsonistic power in market exchange. Market exchange implies voluntary exchange, free choice. However, free choice does not imply absence of market power, as in the case of the monopolist, who can choose his most advantageous price from the set of prices that buyers are willing to pay for different quantities. However, the models of the unified theory have assumed perfect competi-tion; hence, even ignoring market power, the theory has shown that power structure constitutes the essential factor in the functioning of capitalism.

The economic advantage that large capital ownership gives to the eco-nomic elites leads to the reproduction of the class structure and power in society. Capitalists have a high capacity to bear large losses, which leads them to undertake investment projects with the highest returns even if the risk is high, together with the capacity to protect their membership in the capitalist class using their social networks. Therefore, there is nothing in the economic process that is going to reduce endogenously the initial power concentration. As to the political class, governments are given political power by virtue of the representative democracy. This political power is exercised upon citizens in general through the mechanisms of asymmetric information and lack of accountability of state institutions, together with propaganda.

The unified theory assumes that people act motivated by self-interest. This is the force, the mechanism, that moves society. Given that the unified theory is a good theory, this assumption is a good approximation of the real world. Therefore, the economic process in the capitalist system is governed by the selfish motive of people, more precisely, by the self-interested motives of the economic and political elites.

In what follows, science-based policies will then be discussed, which will take into account the causality relationships discovered by the unified the-ory. On epistemological grounds, this procedure is justified because the uni-fied theory is a valid theory.

Power Structure and Institutions

The Market System

The famous statement about the “invisible hand” by Adam Smith (1776) constitutes the foundation of neoclassical economics and the justification for


relying upon market institutions. It can be summarized as follows: Everyone acting motivated by self-interest will lead, as by an invisible hand, to the com-mon good. The market system is not only self-regulated and needs no plan-ning or any intervention, but also is conducive to the common good. This idea has become the doctrine of economic liberalism in capitalist societies.

Leon Walras (1883) and other mathematical economists showed later on that Smith’s statement could be transformed into a theorem, that is, it was valid under certain conditions only. As shown in the standard literature, these conditions assume Walrasian markets operating under perfect compe-tition (as the model presented in chapter 3, volume 1) and Pareto optimality as the criterion of the common good, which imply an absence of market power (monopolies and oligopolies) and externalities (unintended damage to others); no need for public goods in society; and perfect information.

According to neoclassical economics, under these conditions, individual market exchange will be conducive to the common good. Market prices will reflect efficient allocation of scarce resources, that is, market prices will reflect the marginal social cost of producing goods (not the marginal cost to the private firm). If producing one additional unit of wheat implies giv-ing up two units of corn in society, then the relative market price of wheat to corn should be double and the market system will generate this rela-tive market price. Thus, the production outcome of the market system will be economically efficient and Pareto optimality will be attained, which in other words can be said as follows: there can be no allocation of resources to make someone better off without making someone else worse.

If one of those conditions is not met, individual self-interest will not lead in the aggregate to the efficient utilization of scarce resources, to Pareto efficiency, to the common good; then it is said that the market system fails to attain Pareto efficiency. However, this is the mathematical argument. Coming back to epistemology, neoclassical theory assumes that those cases for market failure do exist, but the magnitude of the failures is not signifi-cant, that is, the market system operates essentially as if it led to the common good.

The theoretical findings and the corresponding facts presented in this book show that the market system operates in a different way. According to the unified theory, general equilibrium in the market system has two char-acteristics: it implies excess labor supply (labor markets are non-Walrasian) and an excessive degree of inequality. Therefore, the market system is able to solve production and distribution, but it is not self-regulatory. There are no market forces that can endogenously lead to full employment and socially tolerable income inequality. The reason is that both results come from the profit motive of the capitalist class. Excess labor supply is a necessity for


profit maximization; excess inequality is, in addition to profit maximiza-tion, determined by the high concentration of physical capital, which capi-talists seek as a necessity to remain as members of the class and to retain economic and political power.

The other characteristic of the market system is, according to the uni-fied theory, that human behavior based on the individual self-interest leads to economic growth, which in turn implies a faster rate of degradation of the biophysical environment. Neoclassical economics assumes a mechani-cal economic growth process. The unified theory, in contrast, assumes an entropic economic process. Therefore, the environmental problems of deple-tion and pollution go beyond the problem of externalities and beyond the public policy of introducing Pigouvian taxes to solve it.

It follows that the capitalist system does not operate as the neoclassical theory predicts; that is, neoclassical theory fails to explain the basic traits of capitalism. The empirical refutation of the neoclassical theory indicates that it is a logically correct system, but it is empirically false. Individual actions do not lead to the common good through market exchange. Because Pareto efficiency is logically derived from the neoclassical theory, it follows that the failure of the latter to explain the real world implies the failure of the former as welfare criterion. Therefore, the market system solution cannot be evalu-ated using the Pareto criterion.

What is now needed is a new social welfare criterion that is in accord with the unified theory. The common good is the quality of society for present and future generations, which can be measured by the indicator healthy life expectancy (chapter 9, this volume). A difference between the Pareto criterion and the quality of society criterion refers to the role (or no role) of income inequality. Income inequality is not part of the criterion of the com-mon good in Pareto optimality. Any degree of income inequality that results from market exchange will be efficient as long as market prices are equal to marginal social cost. To be sure: according to neoclassical economics, Pareto optimum can exist in a society with Gini coefficient equal to 0.60, which corresponds to the most unequal countries in the Third World!

According to the unified theory, the task of markets is to solve for prices and quantities of equilibrium, which reflect the solution to social interac-tions in the general equilibrium. The economic theory of markets assumes that such equilibrium exists and that the market system operates as if it were an equation-solving machine, or a big computer.

The market system will solve any set of equations in which particular social interactions and power structures are represented. If the solution is not socially desirable, we cannot say that the market system has failed, because the equation-solving machine has done its job: It has found the solution to


the system of equations and has produced the prices and quantities of equi-librium. Market failure would occur if for some reason the market system could not find the prices and quantities of equilibrium, that is, it would be like a broken computer leading to chaotic prices, not to a price system, in market exchange. An example is the hyperinflation situation.

What is usually called “market failure” in neoclassical economics does not have to do with the computer, but with the results of market exchange; the failure is in reference to a particular social valuation: Pareto optimality. In light of the unified theory, we could use the criterion of quality of society: the market solution implies social disorder and environment degradation. This result has to do with the equations to be solved, which reflect particu-lar power relations in society. Social interactions and social conflicts operate through market exchange.

If individuals interact in the marketplace under the particular context in which asset endowments are unequally distributed among people, which implies a highly concentrated power structure in society, then there will be a particular market solution of prices and quantities and the consequent income distribution; if asset endowments were less concentrated, then too there will be a market solution of prices and quantities, but it will be a differ-ent solution: other prices and quantities and thus other income distribution, less concentrated, will be the new outcome. The same logic applies to the market outcome of environment degradation.

Monopolistic and oligopolistic market structures, which reflect high concentration of physical capital in few hands, are also part of the mar-ket system. If the market solution of this structure is inefficient or socially undesirable, the problem is not the market system, but the particular mar-ket structure, the power structure, which determines the conditions under which the market system will operate and solve for prices, quantities, and income inequality. An analytical distinction needs to be made between mar-ket system (the equations-solving machine, the computer) and the market structure (the degree of market power and the corresponding equations to be solved). The market system is the servant, not the master; the market structure is the master.

However, there is confusion between these categories of market system and market structure. Very often we hear the economic elites saying that “the market is worried” about some possible state interventions, indicating that they see the market system as part of their property rights. We also very often hear workers complaining about the unjust distribution of the market system. Certainly, the enemy of workers cannot be the market sys-tem. Inequality is rather the outcome of power structures working through the market system. A society of workers would still use the market system,


which will determine prices and quantities of equilibrium, together with income distribution. To be sure, the market system—the big computer—will deliver a degree of income inequality as output depending on what went in as inputs, as structural equations.

Consider the fact that the market system delivers a lower degree of income inequality in the First World compared to that in the Third World. The basic reason, as explained by the unified theory, has to do with differences in the concentration of power structure. The market system is blind regarding social outcomes; it only solves for prices and quantities exchanged.

Democracy

Democracy is the other basic institution of capitalism. Democracy (from the Greek demos, people and kratos, government) is a form of government in which people have an equal say in the decisions that affect their lives: one individual, one vote. The American president Abraham Lincoln coined the definition for the concept of democracy: Democracy is the government of the people, by the people, and for the people.

While the market system is the mechanism used for the solution of the problem of production and distribution of private goods, democracy is intended to be the mechanism to solve the production and distribution of public goods, which constitute the common good in society. What are the factors that determine the quantity of public goods to be produced? What goods will be taken out of the market and delivered as public goods?

The solution to these problems is reached through social choice, public policies, and using democracy as the mechanism. According to the unified theory, in a capitalist system, people act motivated by self-interest, and they must do so if they are going to survive physically and socially, that is, it is rational to be selfish in a capitalist system. Therefore, free-riding behavior will dominate in society and thus the quantity supplied of public goods will accordingly be nil or small. Democracy is explicitly the mechanism for producing public goods, the common good. However, democracy is a political system that can deliver different types of output depending on who controls the state. Under representative democracy, voters do not control the state, governments do; voters do not decide on social choice directly, but only indirectly, through their representatives elected by them, which is the mechanism by which political power is created.

Democratic governments are thus run by politicians, who also act only out of self-interest, subject to the constraints given by the economic power structure (as shown in chapter 7, volume 1). Politicians are shortsighted, as they seek to maximize votes for the next elections. Thus the principal-agent


problem appears: the agent (government) has no incentives to do what is convenient for the principal (voters). In addition, voters have the incentive to act as free riders on public matters: “Everybody’s business is nobody’s business.” Thus, the equilibrium of the democratic system is also reached, but it will reflect mostly politicians’ interest and the influence of economic elites. The objective of producing the common good is subordinated to the interests of politicians; thus, governments have a perverse incentive system.

Therefore, the outcome of the democratic decision will depend upon the power structure underlying the democratic process. For example, and as implied by the unified theory, a democratic mechanism in which there are first-class and second-class citizens will turn up a different public choice compared to the case in which voters are all first-class citizens, that is, a democratic mechanism in which citizenship is homogeneous will have a more accountable government (strong democracy) and reach a different pub-lic choice compared to democracy with first-class and second-class citizens (weak democracy). A democratic mechanism in which citizens participate more directly will reach a different public choice compared to representative democracy.

As in the case of the market system, failure of the observed democracy does not imply failure of the democratic system itself. The democratic mech-anism will process what the dominant power structure will feed into the sys-tem; if the power structure were changed, the outcome would be different. Markets and democracy will process what the balance of power between capitalists, workers, and governments feed into these mechanisms in the economic process. If the government intervenes the market and sets addi-tional conditions, the market system will still come up with particular prices and quantities of equilibrium and a degree of income distribution and envi-ronment degradation; if democracy does not intervene, the outcome of the market system will be different.

According to the unified theory, the outcome of the economic process under capitalism is the result of the interactions between social actors through the mechanisms of both markets and democracy. Given the current power structure, the outcome does not lead to the common good. The market sys-tem produces private goods in quantities (and qualities) and prices that seek primarily profits of firms; thus the satisfaction of human necessities or the common good is a subordinate objective. The democratic system produces public goods in quantities (and qualities) that are distributed to the popu-lation as either universal public goods or as local public goods, according to their degree of citizenship and economic power. In the democratic process, politicians seek their own interest; thus, the common good objective becomes also a by-product of government behavior, not the primary one.


Suppose representative democracy as it is practiced today—by electoral voting—were abandoned and replaced by randomly selected citizens (rem-iniscent of the ancient Greek democracy). Then political power would be eliminated. The perverse incentive system embedded in the current repre-sentative democracy would disappear. Society would be better off. There would still be public debate on public issues, but science-based policies could be practiced in society. This type of democracy would reach public choices leading to the common good as direct objective, not as a subordi-nated one.

The objective of the social actors in a capitalist society is not the com-mon good; hence, capitalism has nothing to do with social responsibility of individual actions. Capitalists nowadays tend to express concern with social responsibility, which are just new strategies to seek profits with guile. On their part, in the current liberal epoch, governments tend to be less con-cerned with social responsibility and transfer social problems to the individ-ual (education and health qualities). In a capitalist society, altruistic behavior will tend to be the exception because under this system the egotistical drive of man’s makeup dominates his social drives.

Capitalist System as a Sigma Society

What type of society is the capitalist system when taken as a whole? According to the unified theory, the capitalist system is a large sigma society. The aggregation of epsilon, omega, and sigma societies would result in a large sigma society. Thus, the aggregate capitalist society is overpopulated because two of its components (omega and sigma societies) are so. It is also socially heterogeneous and hierarchical because political entitlements are unequally distributed in one of its components (sigma society), to which we should add the word citizenship inequality between people living in epsilon and sigma, which is also a European colonial legacy. Therefore, the degree of citizenship inequality in the capitalist system is much higher than that in sigma society. In sum, according to the unified theory, the capitalist sys-tem taken as a whole is socially heterogeneous and overpopulated, that is, a sigma society. Thus, the unified theory is the sigma theory.

The basic public goods, social order, and the environment quality are also global public goods. Global social order is relevant because the capitalist system is composed not of isolated parts but of integrated parts (First World and Third World). The notion of socially tolerable inequality is also part of globalization. Environment quality is also global, for the Earth is, according to the entropy law of physics, a close system. Therefore, quality of society is also a criterion of social welfare for the capitalist system as a whole.


In sum, the prediction of the unified theory about the functioning of the capitalist system taken as a whole, which has not been refuted by facts, is the following: individuals acting out of self-interest have not led society to the common good (as Adam Smith predicted), but to a society that operates with excess labor supply, excess degree of inequality and social disorder, and faster degradation of the biophysical environment. The economic process in the capitalist system is thus governed by the self-interest motive.

In light of the unified theory, under what conditions would people’s selfish behavior be conducive to the common good? We should recall that growth versus quality of society is the big tradeoff of our time. This relation-ship was represented in figure 9.1, chapter 9. An answer to this fundamental question is offered now.

Current Public Policies

In an ideal world, social scientists would present to society a feasible set of public choices together with the policy instruments. From that set, the social choice would then be decided. However, this is not how public policies work in the real world. Actually, social actors through the democratic system have already made public choices on the growth and quality of society tradeoff that was mentioned above. The current public policy can be characterized as the pro-growth choice. Certainly, we are living the era of output growth, with countries racing to win the first places in the track of output growth. No other criterion to evaluate the economic performance of countries seems to exist now but output growth.

How has this social choice come about? In a class society, such as capital-ism, policy alternatives are not socially neutral. Some policies benefit some social groups to a larger extent than others. According to the unified the-ory, policy makers are not altruists; they also act motivated by self-interest, as ordinary people do; moreover, democracy is the public choice mecha-nism, but it includes formal and informal rules (chapter 7, volume 1). Hence, there is social conflict in policy choices. The political and economic elites, national and international, dominate in the social choice process. Therefore, we could conclude that the pro-growth choice reflects the current power structure, the one dominated by the current economic and political elites. In the process of economic growth, the winners have indeed been the economic and political elites, as shown in this book.

Many structural changes have taken place in the process of capitalist economic growth, such as sectorial recomposition, regional recomposition, modern forms of production and consumption. In particular, the rate of technological progress has been spectacular. However, the power structure


has not changed. According to the unified theory, there are no mechanisms embedded in the economic growth process that can endogenously redistrib-ute economic and political assets as growth proceeds; on the contrary, the mechanisms operate in the direction of maintaining the power structure or increasing it. One can then understand why pro-growth public policies have been applied at the capitalist world scale.

How is this public policy choice legitimized in a democratic system? The use of a paradigm seems to be the subtle mechanism. The political and eco-nomic elites make people believe that growth is the best choice for society as a whole. In order to present it as “science-based policy,” the appropriate scientific backing is needed, which has to be an economic theory that is con-sistent with the policy. This theory becomes the paradigm.

According to science historian Thomas Kuhn (1970), a theory becomes a paradigm when the community of scientists accepts it. In the case of eco-nomics, the theory that has become paradigm goes beyond the scientific community and expands into the public opinion to become the public pol-icy paradigm. This is feasible because the mass media are in the hands of the elites. The economic theory becomes a paradigm not on scientific grounds (as Kuhn says), but as part of the power relations in society. The equilibrium situation on public policy is thus attained. Therefore, one could say that the economic paradigm utilized in public policies depends upon the dis-tribution of power structure, that is, different power structures will seek to use different economic theories and public policy paradigms. The economic paradigm is thus endogenous to the economic process.

An economic paradigm is not necessarily an economic theory that has survived the scientific process of falsification. In this case, the incentive sys-tem to accept a theory is not based on scientific knowledge but on vested interests. In fact, the process of scientific research in economics follows another path compared to applied research, which operates within the para-digm. Basic research and applied research (within the paradigm) in econom-ics are mostly independent processes in the real world.

The current public policy paradigm is that output growth is a necessary and sufficient condition to solve the social problems of individual capitalist countries and those of the world as a whole (growth is panacea); moreover, capitalism is the only system that can do it. Output growth with the per-sistence of high degree of inequality is politically legitimized by applying policies to reduce absolute poverty, which governments publicize and use as a mechanism to attract votes. Output growth thus becomes a paradigm.

The current pro-growth policy paradigm is based on neoclassical eco-nomics. A simple rule to recognize the current economic theory paradigm is to look at the content of the university textbooks in economics. Economics


is taught at the world scale using the same textbooks, which contain neoclas-sical and Keynesian theories. Economics is taught as if it were physics!

Within neoclassical economics, output growth is indeed the normative objective in the neoclassical theory, which is the dominant theory. Growth policy is considered to be even more important than short-run macroeco-nomic policies (Keynesian theory). As we can read in a popular textbook on neoclassical growth theory: “Growth policy options can contribute much more to improvement in standards of living than has been provided by the entire history of macroeconomic analysis of countercyclical policy and fine-tuning. Economic growth is the part of macroeconomics that really matters” (Barro and Sala-i-Martin, 2004, p.6). Some authors recognize that capitalist societies are not homogeneous, and thus propose “many recipes but one eco-nomics” (Rodrik, 2007); however, the concept of “one economics” refers to neoclassical economics.

Alternative Public Policies

According to the unified theory, output growth is no panacea. The cost of output growth is inequality and social disorder, together with environment degradation at a higher rate, which cannot ensure higher quality of society for the present and future generations. More importantly, the problem at hand involves the survival of the human species, as we know it. Therefore, public policy options should be discussed at the world level. For the sake of simplicity in the argument, assume that the entire world is organized in the form of capitalism and thus we will consider the capitalist system as a whole, and as a sigma society. So the policy implications of the unified theory can be utilized in a meaningful way.

As pointed out earlier, the current public policy at world scale has chosen one extreme in the feasible set of social objectives: to seek output growth maximization. Because output growth does not imply social progress, the alternative public policy consists in reversing the current priority on growth. The alternative involves changing the current public policy: to dethrone the unique social objective of output growth and to enthrone the objective of better quality of society. The alternative to the current public policy thus entails seeking slower growth rates or even zero-growth rates in per capita income at world scale.

The objectives of the alternative public policy can be stated analyti-cally with the help of figure 7.6, chapter 7, this volume. Consider that the main objective is to delay as much as possible the threshold period at which human society, as we know it, will collapse (period Tp*). This objective can be attained by generating technological innovations that can push outward


the constraint given by depletion of nonrenewable resources (curve BN) or push upward the constraint given by pollution (line HS). As discussed there, technological change can hardly defeat the laws of thermodynamics.

The great faith of neoclassical economics in technology can be put in the following statement: Seek a technological solution to a social problem. The alternative comes from the unified theory, which could be stated as follows: Seek a social solution to a technological problem. In this case, the challenge is to find the social innovations by which the growth curve (curve DR) could be shifted downward to a flatter curve. The critical threshold period given by the pollution limit (Tp*) would clearly be shifted outward. This is due to the fact that lower output per capita implies lower total output, which in turn implies lower pollution; therefore, the threshold period of pollution will appear much later.

If the policy objective were zero-growth, would the critical period T* be infinite? No. At zero-growth alternative, total output will keep growing (at the rate given by the population growth rate); hence the pollution and deple-tion effects of total output will be in operation and the critical period T* will be finite. Even if total output were constant (so that output per worker falls), this critical period will be finite. This was clearly shown in figure 7.1 (chapter 7).

How would a zero-growth world society function? This may sound socially unviable to the reader. However, zero growth does not mean the renunciation of a better quality of society. It does mean changes in the way of life of society, as pointed out by theorists who have studied the function-ing of “zero-growth societies” (cf. Olson and Landsberg, 1975). More signif-icantly, a zero-growth society would imply better net quality of society due to the effects of less income inequality and less environment degradation, as the unified theory predicts.

Does zero-growth society imply zero-growth for the Third World? No, it doesn’t. Under a situation of zero-growth in the global economy, over-all inequality could be reduced by two alternative ways. First, the positive output growth in the Third World could be offset by a negative rate in the First World. Second, both regions could have zero growth, but consumption would be redistributed from the First World to the Third World, to the poor masses of the Third World, to be more precise. Both options would imply a redistribution of consumption, one in the form of differences in output growth rate and the other in the form of direct transfer. Both alternatives would certainly imply a fall in the consumption level of the First World and of the elite groups and middle classes of the Third World countries. However, the gain is clear: The quality of society, the common good, would improve.


Would redistribution of output growth rates from the First World to the Third World imply a lower rate of environmental degradation? The answer is an empirical question. In poor and rich countries, greenhouse gas emis-sions will increase if income increases. This is the income effect on gas emis-sions. The redistribution effect assumes total income as given and just sees the effect of income transfers from the rich to the poor. If the consumption basket of a poor country had a lower content of mineral resources per dollar of expenditure than the basket of the rich, the total gas emissions would fall if income were transferred from the rich to the poor, that is, what the rich would reduce in emissions is a higher quantity than what the poor would increase. The global rate of environmental degradation would then depend on another variable: the inequality within current generation. The lower the degree of inequality, the lower will be the rate of degradation.

Available data indicate that the flow of emissions of CO2 per unit of output in the First World is not too different from that in the Third World for the period 1980–2006 (UNCTAD, 2009, Table 5.1, p. 136). This fact refutes the hypothesis known as the Environmental Kuznets Curve, which is an inverted-U curve, showing the following relation: As income per capita increases, emissions per capita also increase in poor countries, but decreases in rich countries, which would imply that emissions per unit of output is higher in poor countries than it is in rich countries, which is against the fact just mentioned. More importantly, the Kuznets curve has no theoretical foundations. In sum, according to these empirical data, the redistribution effect would not be significant. Income redistribution from the First World to the Third World would not increase the degree of degradation of the bio-physical environment.

The consequence of this empirical result is that there is no conflict between the social objectives of reducing current between-country inequal-ity and reducing the rate of environmental degradation. On the basis of the available data, we may conclude that a reduction in between-country inequality would not increase between-generation inequality; there is no tradeoff between these social objectives.

Dethroning output growth to low or zero-growth rates and enthron-ing quality of society as the policy goal would certainly involve qualitative changes on our current lifestyle. Instead of seeking mostly the maximiza-tion of private consumption goods, as we do now, society should also seek to improve the quality of society, the common good. This alternative pol-icy involves reducing superfluous consumption. A significant proportion of current consumption is unnecessary for good quality of life and merely generates an enormous amount of waste. The fetishism toward goods would need to be replaced by the search for the satisfaction of human basic needs.


A car, for example, satisfies the need for transport and other things, but if the goal is to satisfy the need for transportation, other forms of organization, as a good public transport system, can be environmentally more efficient in achieving this end. Health economist Philip Musgrove (2007) has shown that real income is not the most important factor in the individual health wellbeing in our societies. The main reason is that health status depends upon other factors besides individual income, such as public goods. Even the search for lower inequality can be seen not as an end in itself, but as a means to attain the common good.

Improving the quality of society in a context of slow growth or zero growth also involves the development of social prevention and protection systems against risk. Under the pro-growth paradigm, the gains in con-sumption level are subject to the risk of losses due to shocks upon society. These shocks can be endogenous or exogenous to the economic growth pro-cess. Most relevant shocks are endogenous, such as shocks associated with epidemics and diseases, financial crises, economic recessions, inflation, ter-rorism, drug wars, organized crime, civil wars, pollution, and international wars. Shocks from climate change (natural disasters) are mostly endogenous, as shown in chapter 9. Social protection systems would then be increasingly needed, which implies more supply of public goods than we have today (and less superfluous private goods to compensate for).

Environmental distress is another source of social conflict. Most invest-ment projects that seek to exploit natural resources use local resources—water, land, forest—and are thus resisted by rural communities who fear loss of their livelihoods. These communities are at the forefront of envi-ronmental movements in the world. For them, the environment problem is a matter of survival. They know that when the land is mined and the trees are cut by businesses, their water resources dry up or they lose grazing and farmland. Rural people are mostly Z-populations, which have no voice or limited voice. This social conflict is in accord with the entropic economic process developed in this book: there is no such thing as sustainable output growth. If output growth were sustainable, the costs of reproducing output could be calculated and social conflict would disappear. However, the eco-nomic process is entropic.

The apparatus of the intergenerational consumption frontier shows another social conflict: given the stock of mineral resources and the rate of technological progress, output growth now implies a higher degree of inequality between the current generation and future generations. Technological progress that is mineral resource saving cannot eliminate this social dilemma; it can only make the choice less dramatic. In the production and consumption process, the quantitative and qualitative degradation of


the biophysical environment will increase continuously and irrevocably. The only choice society has now is on the velocity of the degradation, as shown in figure 7.6 (chapter 7, this volume). Overall, the public policy dilemma consists in making social choices under the constraint and tradeoffs given by the intergenerational consumption frontier.

According to the unified theory, a capitalist society with better quality of society can be achieved without output growth; hence, output growth is not a necessary condition for building such a society for the present and future generations. As we have shown in this book, output growth has not helped to attain a better society for all; hence, output growth is not a suffi-cient condition either. In contrast, according to neoclassical economics, out-put growth is a necessary and sufficient condition for social progress. If no social progress is obtained, more rapid growth is needed! So the argument becomes tautological. The lesson to be learnt is that India has shown the fastest growth rate in the last three decades among Third World countries and yet no significant social progress has been attained (Drèze and Sen, 2013).

In light of the unified theory, public policy options are clear, and can be summarized as follows. Either we maintain the current pro-growth policies, which do not bring continuous social progress, or we use scientific knowl-edge contained in the unified theory of capitalism to change the exogenous variable in order to develop a new social world in which the quality of soci-ety is better for the present generation and also for future generations. The latter case implies replacing the current economic paradigm for another that is based on scientific knowledge. The implication is clear: to change public policies that are pro-growth toward pro-quality of society requires remov-ing the current economic paradigm (neoclassical economics), which in turn requires changing the power structure of society.

Breaking with History

The exogenous variables of a valid economic theory constitute instruments of public policies. In the case of the unified theory, the exogenous variable is the degree of inequality in the distribution of the economic and political assets or the power structure. As long as the power structure remains unchanged, the current path of output growth will not lead to social progress.

How can the current power structure be changed? How can the legacy of the initial inequality be eliminated or weakened? How does one break the history?

According to the unified theory if Third World countries had initi-ated the process of capitalist development as socially homogeneous, as the


First World did, they would have converged to the First World level. In the long run, overpopulation—the other initial condition—is not significant because, under that condition, it can be eliminated endogenously in the growth process. This is what the omega theory predicts, which is consis-tent with facts: most omega societies (Third World countries with weak or no colonial legacy) have either become epsilon societies (Japan) or are en route to becoming one (Table 13.1, Chapter 13). The fundamental problem for the large majority of Third World countries (sigma societies) is their European colonial legacy: these countries initiated capitalist development as socially heterogeneous societies. Consistent with the prediction of sigma theory, facts indicate that there is not even a single case of a Third World country with strong colonial legacy that has become a First World country in the two hundred years of capitalism.

In order to clarify the meaning of “breaking with the past”, the major features of the colonial system are now presented. The European colonial history of Third World countries is not uniform. The colonial systems of England, Portugal, and Spain in America prevailed during the sixteenth and seventeenth centuries and those of England and France (and in minor degree Belgium, Germany, Holland, and Italy), in Africa and Asia in the last third of nineteenth and part of the twentieth centuries. The European colonial systems took different forms and occurred at different periods; yet, the European colonial legacy is uniform: Third World countries tend to be the poorer and more unequal relative to the First World countries, as shown in this book.

The 23 countries that have been classified as the First World were never under colonial rule (some were colonial powers). The United States, Canada, Australia, and New Zealand were not colonies, but settler territo-ries. The analytical distinction between colonial system and settler territory is based on the criterion of population density of territories under domina-tion. Compared to that of the colonial systems, the population density in the settler territories was relatively low, as economic historians have shown (Engerman and Sokoloff, 1997).

Historians have also shown that, around 1825, at the beginning of democratic capitalism in the American continent, the white population represented 18 percent of total population in Spanish America, 23 percent in Portuguese Brazil, but 80 percent in the United States and Canada. The United States and Canada were not colonial systems based on the exploitation of the aboriginal population, but employed Africans as slaves as the colonial systems did. Around 1825, the proportions of black popu-lations in those territories were 23 percent, 56 percent, and 17 percent, respectively; that is, black population was a minority ethnic group in the


United States and Canada compared to the case of Brazil (Engerman and Sokoloff, 1997). Therefore, the initial conditions of the United States, Canada, Australia, and New Zealand were more of an omega rather than a sigma society.

In a sample of nearly 80 countries with European colonial and settler histories, there was a negative correlation between their per capita income in 1995 and the population density (population divided by arable land) in their territory in 1500 (Acemoglu, Johnson, and Robinson, 2001, Figure 2, p. 1248). Population density was also important to determine the initial inequality and the initial institutional rules. Europeans concentrated land and political power in a degree that depended on whether they were acting on territories of high or low population density, colonial or settler systems.

The inequality of citizenship in the Third World is a colonial legacy, the result of the persistence of some colonial institutions. Historians usu-ally point out this legacy by indicating the nature of the colonial institu-tions. It is worth repeating what Dutch historian H. L. Wesseling (2004) stated: “Colonial societies were generally characterized by apartheid and segregation and often were based on notions of innate racial inequalities” (pp. 242–243). However, once the colonial system was eradicated with the independence, the colonial institutions have continued; hence, we could say that the past is not past. This case of social hysteresis is what makes colonial history significant today.

For example, independence from colonial powers did not imply breaking with colonial rules. It was not a refoundational shock. A summary of the general view of historians of Latin America has been put as follows: “Latin America is not postcolonial in any meaningful sense. Its nineteenth-century revolutions were predominantly civil wars between creoles (individuals of European descent born in the Americas) and their ‘peninsular’ (Iberian) cousins. For the non-white majorities, little of import has changed since col-onization” (Graubart, 2004, p.217).

However, some historians challenge the essential role played by the colo-nial history of capitalist countries upon their development process. They think that comparing countries that were never colonized with others that were may help us in assessing the effect of colonial legacy on the economic development of countries. For example, historian Wesseling says, “If we take a dispassionate look at the facts, it is difficult to regard India and Indonesia, Nigeria, and Egypt—areas that were long and thoroughly colonized and dominated—as less developed than Ethiopia and Afghanistan. Taiwan and Korea, which were for a long time Japanese colonies, are now indus-trial countries whose economies belong to the fastest growing in the world” (2004, p. 243).


Weak and strong colonial legacies as analytical categories are impor-tant to respond to this argument. Taiwan and Korea were Japanese colonies and for a relatively short period only (1910–1945). In addition, one could put forward the hypothesis that the legacy of Japanese colonies is different from that of European colonies. For one thing, this colonial system was not based “on notions of racial inequality.” China, Korea, and Japan are not racially too different, as is the case between European whites and American browns, African blacks, or Asian yellows. Culturally, Koreans speak Korean today, not Japanese; Taiwanese speak their native Chinese, not Japanese. In contrast, Europeans left the legacy of European languages in their col-onies. Under these conditions, Japanese colonialism could not generate Z-populations, as European colonialism did.

The unified theory predicts that the income levels of capitalist countries as of today depend upon their European colonial history. Europeans are high-income countries. Countries that had a strong colonial legacy are the low-income countries, whereas those with weak or no colonial legacy are middle-income countries. However, as in any theoretical proposition, there are exceptions to this general relation. Afghanistan and Ethiopia were never colonies and have been classified as omega societies, yet they are among the poorest countries in the capitalist world.

Formally, most capitalist countries operate under the same institu-tions: private property, market system, and democracy. It is true that some colonial institutions persisted after independence, such as the case of forced labor and slavery; but today capitalist countries operate predom-inantly with labor markets, a capitalist institution. However, we have to consider the significance of the enforcement of the formal rule of law and the existence of informal rules in the workings of institutions. It is the enforcement of institutions that is relevant for understanding the eco-nomic process.

The unified theory says that the workings of institutions are endogenous and depend upon the degree of inequality in the asset endowments among individuals, including political power under the category of assets. The fun-damental colonial institution that persists today is the inequality in citizen-ship, in spite of what the formal democracy rules may say about citizenship equality within countries or as universal rights.

Breaking with history then has a well-defined meaning: It means break-ing with the social hysteresis, that is, ending the colonial legacies that persist in the postcolonial period, mainly the legacy of citizenship inequality within Third World countries and between the First World and the Third World. This is just what the unified theory implies as change in power structure in the capitalist system.


According to the unified theory, history matters in the process of capital-ist development. This prediction of the theory is consistent with facts. Most postcolonial countries are relatively poor and the relatively poor countries are mostly postcolonial countries. Economic growth implies path dependence. However, the existence of path dependence does not mean historical deter-minism. Economics is not physics. Public policies can be utilized to break with history. This implies the introduction of institutional innovations in the democratic system to eliminate the citizenship inequality—the legacy of the colonial history—within the Third World countries and between the Third World and the First World. Recall that the capitalist system taken as a whole constitutes a sigma society.

Reducing the current power concentration would bring social progress. Thus, the enforcement degree of the current democratic rules would be higher. New democratic rules for the common good could be created. Limits to concentration in the ownership of land, physical capital, and human cap-ital could be included in the new rules. In general, social choices would be different from those taken now. Public policies would give less weight to growth and more to the quality of society. Technological progress could be planned for the common good. Technological progress that is mineral saving would be given priority on the research agenda. Technologies for better quality of health and education services would also be given higher priorities.

A strong democratic government on the world scale is also needed because the basic public goods, social order, and environment quality are interna-tional public goods. The world democratic government would then imply one world society, with one class of citizens. In principle, this new demo-cratic government could implement public policies to supply those funda-mental public goods for improving the quality of society. This strong world democracy would be able to regulate the economic process for the common good. The market system would produce a new equilibrium of prices and quantities that imply a higher quality of society. Individual choice would then be consistent with the common good, not against the common good, as is the case now.

Take the case of the ILO Convention 169, which was created in 1989. This Convention deals with the rights of indigenous peoples of the world. Why was this Convention needed? As stated in the preamble, the fact is that they do not enjoy the fundamental human rights to the same degree as the rest of the populations of the states in which they live. Hence, it is aimed at eliminating any form of discrimination against, including, citizenship and property rights. The Convention requires that indigenous peoples are con-sulted on capitalist projects that affect them with the objective of achieving


agreement. The experience is that this Convention is not respected and indigenous peoples are now in continuous struggle against capitalist projects that invade their territories to exploit natural resources and, as consequence, have become the most important environmental activists in the world. With the current power structure, the Convention has had no significant effect in transforming the Z-populations of the Third World in first-class citizens at the world scale.

Neoclassical economics constitute the current paradigm. The public policies—the engineering of the science of economics—are derived from neoclassical economics. The public policy implication of neoclassical eco-nomics calls for output growth. Output growth is seen as necessary and sufficient conditions to solve the social problems of present and future generations. Therefore, the engineering of neoclassical economics deals with the problems of how to generate higher growth rates of total output. Complementary policies refer to how to reduce poverty and also how to cal-culate environmental costs to achieve “sustainable output growth,” which can only refer to the reposition costs of renewable natural resources, not to pollution and depletion of nonrenewable resources, as shown in this book. Hence, the engineering of neoclassical economics cannot deal with the problems of how to generate social progress for present and future genera-tions when the economic growth process is entropic and evolutionary.

In contrast, the implications of the unified theory include the possibil-ity of social progress without output growth. These views are new, outside the current paradigm. Therefore, the engineering of the unified theory is something that needs to be developed. This will not be an easy task. We have been living in the growth paradigm for centuries and we are used to thinking in that manner. Breaking an economic paradigm is not easy; it is like changing from the known Euclidean geometry to another that is yet to be learned.

Conclusions

The evolutionary model of the unified theory predicts that the continuous and irrevocable degradation of the biophysical environment, which would occur even in a static economic process, has been accelerated with output growth. Hence, there is no such thing as sustainable economic growth. The implication is that social progress cannot be achieved through economic growth policies, even if economic growth were panacea. However, economic growth is no panacea. The side effects of output growth—higher rate of degradation of the environment and higher degree of inequality—implies lower quality of society, which will tend to dominate the positive effects as


growth proceeds. Another side effect is the increase in consumption inequal-ity between the current and future generations, together with the risk of reducing the survival period of the human species, as we know it.

Nevertheless, output growth is the main objective of public policies in the capitalist world of today. Why does capitalism operates in this way? According to the unified theory, this is a reflection of the current power structure, the exogenous variable of the theory. As long as the current power structure remains unchanged, growth without social progress will tend to be the outcome of the economic process and pro-growth public policies will also continue. Therefore, another social world, a higher quality society, requires a change in the power structure.

The asset that is crucial in the current power structure is the inequality in the distribution of political assets—the existence of citizenship classes—within the Third World countries and between the First World and the Third World. This is the legacy of the European colonial history of capitalist countries. Therefore, the public policy to reduce the current power struc-ture would consist in the introduction of institutional innovations that seek to break with history: the equalization of citizenship, one capitalist world with one citizenship class, which would lead to a global and strong democ-racy. Institutional innovations are needed to shift the current voter-game democracy (plutocracy) to some form of citizen-based democracy. If these institutional innovations in the democratic system bring a revolution in the workings of democracy, and the equalization of citizenship at national and international levels, then there would be a break with history.

A strong democratic system (which needs to be global) will have the incentive to produce global public goods that are necessary for a better quality of society. Because economic elites operate at the international level through big corporations, while political elites do mostly at the national level, the local political power is generally subordinated to economic power. Capitalists would cut investment in a country that is not friendly; this is the so-called Kaleckian threat, a mechanism that disciplines governments, which today seems more significant than ever. The idea with the institu-tional innovation is that the power of democracy should prevail over the power of the capitalist class; moreover, it should prevail over the political class, so as to reach the common good.

Strong global democracy would also affect the workings of the market system by introducing new equations in which the common good would be embedded. Hence, the market system will solve a new set of equations and determine a new set of prices and quantities, which are, by construc-tion, consistent with the common good. Strong global democracy implies not only a higher degree of social control upon the workings of the market


system, but also upon government behavior; in this context, selfish behav-ior can be conducive to the common good. Market and democracy are the basic institutions of the capitalist system and the quality of society that they deliver depends upon the power structure, as the unified theory has discovered.

The following proposition is then derived from the unified theory: Under stronger democracy and weaker economic power structure, individu-als acting motivated by self-interest will more likely be led in the aggregate to the common good. This is in lieu of the well-known “invisible hand” proposition of neoclassical economics, which must be abandoned on the grounds that neoclassical theory is refuted by facts. This conclusion is scientific, that is, independent of what our ideological positions or self-interests are.

Economic freedom without the corresponding strong social obligations for the common good is the norm of the society in which we live today. Thus, this selfish economic rationality together with the power concentra-tion explains the functioning of capitalism and the limited social progress achieved. This is how capitalism operates. The proposition of Adam Smith has become the liberal doctrine (what capitalism ought to be) rather than a scientific theory (what capitalism really is).

The alternative policy is still based on the selfish behavior of people, but economic freedom will operate under more stringent democratic norms, so as to be conducive to the common good. People will still choose their best positions in the economic process, but under new social norms that seek the common good. Even individual choices about family size are included here, but it would be made under social innovations directed to a higher degree of social protection, which would reduce the need for people to have children to care for them in their old age.

What are the factors than can change the power structure? The unified theory has no answer. The reason has to do with epistemology: an economic theory leaves its exogenous variables unexplained. If the theory sought to explain the exogenous variables, other exogenous variables would be needed, but that would be another theory, which in turn would need new exogenous variables to explain the old ones, and so on. Thus, the logical problem of infinite regress would be reached.

Contrary to physics, economics cannot explain everything because of the existence of endogenous and exogenous variables in the economic process. A Theory of Everything is logically impossible in economics. Exogenous vari-ables come from outside the boundaries of the economic process. The impli-cation is that the solution to the economic problem lies outside economics. The unified theory is able to identify exactly where.


In sum, the book has presented an economic theory that is able to explain the functioning of the capitalist system. The outcomes of employment, con-sumption, inequality, environment degradation, and quality of society have jointly been given a theoretical explanation, in which capitalism has been analyzed by parts (First World and Third World) and then as a whole, and also in the short-run, long-run, and very long run processes; moreover, cau-sality relations have been established between these endogenous variables and the exogenous variables. The ultimate factor that explains these endog-enous variables in the very long run is power structure. The unified the-ory is able to explain the eight empirical regularities of capitalism presented in chapter 2 (volume 1). A unified scientific theory of capitalism, unity of knowledge in economics, has thus been attained in the book. On epistemo-logical grounds, because the unified theory has not been refuted by any of the available facts, there is no reason to reject the unified theory and we may accept it at this stage of the research process, although provisionally, until new empirical evidence or a superior theory becomes available. Scientific knowledge is an evolutionary process.

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alpha propositions (foundations) of unified theory of capitalism, 7–8

asset inequality. See initial inequality, power structure

aversion to risky gamesconcept of, 74vs risk aversion, 74

Barro and Sala-i-Martin’s convergence theorem, 32

Becker principle of wage discrimination, 19

biology and economics, 98, 117, 127, 154, 156

biophysical environment. See environment

breaking with history and institutional innovations, 193–8

capital flights and Kaleckian threat, 199capitalist class, composition of

high executives, 16owners of physical capital, 16

capitalist societies, types ofFirst World countries (epsilon

society), 4Third World countries with strong

colonial legacy (sigma society), 4Third World countries with weak

colonial legacy (omega society), 4

capitalist system, overall inequality rise along growth process in, 85–92

capitalist system as sigma society, 186, 189, 197

causality relations (beta propositions) in unified dynamic model, 39, 52, 64, 82

causality relations (beta propositions) in unified theory, 180, 201

China effect on environment degradation, 128

climate changeendogenous vs exogenous origin,

107, 170and entropy law, 170–1natural disasters, 110, 171, 192

colonial institutions, persistence of, 196–8

colonial vs settler systems, 4, 194–5corporate social responsibility, 186culture of inequality, 27

democracy, problem of principal-agent in, 184

democracy failure vs power relations via democracy, 184–6

dynamic equilibrium. See growth frontier curve

Index

Subject

212 l Index

ecological systemdisruption, 154, 161–3footprint, 150impossibility of equalizing First

World and Third World income levels, 150

unique resources, 110, 113economic growth process, side effects

of, 172–3, 179, 198declining quality of society, 157–61,

167, 171–2faster environment degradation,

123–7, 151, 159, 172higher global income inequality, 83,

151higher intergenerational income

inequality, 104, 119, 179, 192unsustainable output growth, 114,

154economics and biology, 98, 117, 127,

154, 156economics and physics, 3, 105, 178,

189, 197, 200education, equality of opportunity

problem in, 23, 26education, process analysis of, 11–13education, unequal cognitive capacity in

role of initial socio-economic inequality, 13–15

role of language proficiency inequality, 13–15

education and culture of inequality, 26–7

education and income inequality relation, role of social networks in, 19–20

education process, main traits ofnot citizenship equalizing (sigma

society), 26–7not human capital equalizing, 17–18,

20, 22, 26not income equalizing, 17–18, 22, 26not social network equalizing,

19–20, 22path dependent, 16

education process under democracy, 17

education theoryalpha proposition, 13beta propositions, 21–4falsification, 24–5static model, 21–2

empirical predictions of a theory. See beta propositions

employment. See excess labor supplyEngel law, 134, 147entropic economic process. See also

evolutionary economic processentropic economic process, 108–14entropic economic process, main traits

ofevolutionary economic growth

process, 123–7intergenerational inequality, 104,

119, 179social costs measurement problem,

154–5, 178unsustainable output growth, 104,

114, 154Entropy law and economic process,

105–8, 113, 186, 206See also entropic economic process

environment as problem of the commons, 113, 126, 209

environment degradation, 123, 130, 158, 172, 179, 183–5, 189–90, 201

environmental Kuznets curve, 191epsilon dynamic model, assumptions

of, 29epsilon society. See epsilon theoryepsilon theory, 4–5evolutionary economic growth process,

123–7evolutionary economic process. See also

entropic economic processexcess labor supply and economic

growthfalling self-employment (omega

theory), 54

Index l 213

falling X-self-employment, persistent Z-self-employment (sigma theory), 65, 160

persistent unemployment (epsilon theory), 29, 160

first law of thermodynamics and economic process, 105, 115, 117

First World and Third World countriesinfant mortality differences, 167–8life expectancy differences, 167–8

First World and Third World countries, citizenship inequality between, 196, 199

First World countries. See also epsilon society

First World vs Third World, income inequality level gaps persistence, 85–92

First World vs Third World, income level gaps persistence, 85–9

food market, Walrasian model of, 133–5

food scarcitypopulation effect on, 135–7soil erosion effect on, 142–5

food supply and technological change, 141–5

formal education. See educationfree-rider behavior, 23, 185

Georgescu-Roegen’s flow-fund production process, 98–103

Gini index and Lorenz curve relation, 53

global saving rate, 70government policies on education, 26growth frontier curve, definition, 36growth vs quality of society, the big

trade-off, 187

Harrod vs Hicks technological changes, 159–60

healthy life expectancyvs life expectancy, 156, 172

measure of quality of society, 156–7, 167–9, 172, 179, 182

heteroglossia, 14Hicks vs Harrod technological changes,

159–60historical time (T)

and entropy law, 107and evolutionary economic process,

98vs mechanical time (t), 98

human capital accumulation, mechanisms for

education (schooling), 32–6new technologies, 32–6

human species future and environment degradation, 110, 113, 118, 128, 131, 145, 148, 154, 161, 189, 199

income distribution. See income inequality

income distribution, categories offunctional, definition, 39personal, definition, 39

initial inequality, role ofin economic growth process, 4, 6–7,

15, 20–7, 41–2, 68, 70, 73–85, 88, 91–3

in evolutionary (entropic) growth process, 125, 127

in quality of society along growth process, 156, 164, 172, 179, 193, 195

See also power structureinitial inequality (power structure),

reproduction of, 84, 92–3intergenerational consumption frontier

concept of, 104determinants, 119–23and entropic economic process, 108,

112–13, 116–18and social costs, 154–5

intergenerational inequality and economic growth, 104, 119, 179

investment-saving relations, 70

214 l Index

Kaleckian threat, 199

labor saving technological change, Hicks vs Harrod, 159–60

labor skills. See human capitalland resources and entropic economic

process, 139–41, 145–8language proficiency and cognitive

capacity, 14–15limitational technology

concept of, 99production process with, 99

limits to output growth (models), role of

land resources depletion, 145–8mineral resources depletion, 123–7pollution, 123–7

Lorenz curve, concept of, 53Lorenz curve and Gini index relation,

53

market failure vs power relations via markets, 180–4

market system and entropic economic process, 118–19

market system as a big computer, 182–4

market system vs market structure, 183mechanical time (t)

and dynamic economic process, 98vs historical time (T), 98

mineral resources in production processdepletion of given stocks, 99indispensable production factor, 106,

115mineral resource-saving technological

progress, 122–3Moore principle, 7Mother Nature has no cashier, 118

neoclassical economicsgrowth theory, 33, 88Pareto optimality, 180–3pro-growth paradigm, 188–90, 193,

198, 200

no-growth societies, functioning of, 190–3

nonrenewable natural resources. See mineral resources

omega dynamic model, assumptions of, 43–4

omega society. See omega theoryomega theory, 4–5, 194on the job training, 33

partial theories (epsilon, omega, sigma) of capitalism, 3, 4–8, 27, 68–9

perverse incentive system in political class, 185–6

physics and economics, 3, 105, 178, 189, 197, 200

political classand democracy failure, 184–6perverse incentives, 185–6power origin, representative

democracy, 180, 184–6political entitlements by type of

capitalist societycitizenship equality (epsilon and

omega societies), 4first and second class citizens (sigma

society), 4Popperian epistemology, 8, 177population, initial conditions by type

of capitalist societyoverpopulated (omega and sigma

societies), 4underpopulated (epsilon society), 4

population effect on food scarcity, 135–7

population growth, endogenously determined, 75

power relations under capitalist institutions

democratic system, 184–6market system, 180–4

power structure, role ofin economic process, 179–80in public policy choice, 187–9

Index l 215

in workings of democracy, 184–6in workings of market system, 180–4See also initial inequality

power structure and economic paradigm relationship, 188–9

power structure in unified theory of capitalist system

exogenously determined, 179power relations system, 180ultimate factor in the long run, 179

principal-agent problem and democracy, 184

private investment theoryalpha propositions, 71falsification, 75model and beta propositions, 71–5

problem of the commons, the environment as, 113, 126, 209

pro-growth public policiesdominant government policies,

187–9neoclassical paradigm based, 188–9power structure reflection, 187–9, 193

public policies, main traits ofeconomic paradigm based, 188–9limitations of democracy, 184–6power structure reflection, 187–9, 193vs science-based, 180, 186, 188

public policies, types ofbreaking with history (institutional

change), 193–8class interest-based (paradigm), 88–9doctrine-based, 200science-based, 180, 186, 188

quality of life (individualistic approach), limitations of

fallacy of composition, 155free-riders problem, 155negative externalities, 155neoclassical economics based, 165–7Compare quality of society

quality of societyas common good, 156concept of, 155–6

endogenous variable in economic process, 157

inverted-U curve, 157–8Compare quality of life,

individualistic approachquality of society, role of public goods,

155–7quality of society and technological

change, 158–64quasi-Walrasian markets, credit and

insurance as, 20

renewable natural resources and economic process, 116–17

Ricardian diminishing returns and mineral supplies, 110, 126, 129, 161

risk aversion vs aversion to risky games, 74

schooling vs human capital, 16–18Schultz principle of education

economic value, 33science-based policies, unified theory

implications forbreaking with history, institutional

innovations, 193–8concept of, 180, 186, 188enthroning quality of society, 189–83growth vs quality of society, 189

scientific theory (the world is) vs normative theory (the world ought to be), 177

second law of thermodynamics and economic process, 105–6

See also entropy lawselfish motivation vs altruistic

motivation under capitalism, 186sigma dynamic model, assumptions of,

57–8sigma society. See sigma theorysigma society, structure of

X-workers, definition of, 57Z-subsistence sector, the persistence

of, 67–8Z-workers, definition of, 57

sigma theory, 4–5, 89, 186, 194

216 l Index

sigma theory as unified theory of capitalism, 186

social costs in entropic economic processmeasurement problems, 154–5, 178Mother Nature has no cashier, 118not included in market prices, 118–19Compare social costs in neoclassical

economicssocial costs in neoclassical economics, 181–2

vs social costs in entropic process, 154–5, 178

social hysteresis and colonial legacy, 178, 195–6

social network as economic asset, 19social progress. See quality of societysoil erosion, determinants of

anthropogenic factors (endogenous), 140–5

natural factors (exogenous), 140–5theoretical model, 140–5

technological change, main traits ofendogenously determined, 164energy-intensive in food production,

163–4incentives for high-risk technologies,

159–62labor saving, 159–60

technological change and quality of society, 158–64

technological change in food production, 141–5

technological innovations vs social innovations

social solutions to technological problems, 190

technological solutions to social problems, 190

technology frontier, definition, 33theory of everything, 3, 20Third World colonial legacy, 5, 25, 85,

88, 89, 91–3, 178, 186, 194–6Third World countries, citizenship

inequality in, 196, 199

Third World countries with strong colonial legacy. See also sigma society

Third World countries with weak colonial legacy. See also omega society

time and economic processhistorical time (T) in evolutionary

process, 98, 107mechanical time (t) in dynamic

process, 98transition dynamics, concept of, 32, 37–8

unified dynamic model of capitalism, income inequality in

beta propositions, 83–4changes in inequality by type of

capitalist society, 80–3falsification, 85–92

unified dynamic model of capitalism, output growth in

beta propositions, 83–4convergence (epsilon and omega

societies), 76–80falsification, 85–90separate growth frontiers (epsilon

and sigma societies), 76–80unified evolutionary model of

economic growth and the environment

beta propositions, 127–8falsification, 128–30model, 123–7

unified evolutionary model of food production

beta propositions, 148–9falsification, 149–51model, 145–8

unified evolutionary model of quality of society

beta propositions, 157–8, 164–5falsification, 167–72model, 156–7, 164–5

unified theory, dynamic model of growth and distribution, assumptions, 8–9

Index l 217

unified theory, growth and distribution dynamic model of

vs neoclassical theory of growth, 88proximate factors, 76ultimate factors, 76

unified theory as scientific theory, 167, 177, 200, 201

unified theory of capitalism, 3, 89, 92–3, 153, 177, 179, 193, 201

unified theory of capitalism, alpha propositions of, 7–8

unified theory of capitalism as family of models

growth and distribution (dynamic), 76–83

growth and food supplies (evolutionary), 145–8

growth and quality of society (evolutionary), 156–7, 164–5

growth and the environment (evolutionary), 123–7

unified theory of capitalism as sigma theory, 186

unified theory vs theory of everything, 200

unity of knowledge in economics, 93, 153, 155, 172, 201

See also unified theory of capitalism

wage discriminationethnic prejudices, 19for given levels of human capital,

18–19for given years of schooling,

18–19Walrasian market, food as, 135water resources and entropic

economic process, 145

Z-workers, definition of, 13

Countries (excluding mentions in tables)

Afghanistan, 195–6Australia, 194–5

Belgium, 194Brazil, 194–5

Canada, 194–5China, 169–70, 196

Egypt, 195England, 194Ethiopia, 195–6

France, 92, 194

Germany, 194

Holland, 194

India, 193, 195

Indonesia, 195Italy, 194

Japan, 88, 194

New Zealand, 194–5Nigeria, 195

Peru, 24Portugal, 194

South Korea, 88, 195Spain, 194Sweden, 92

Taiwan, 88, 195

United Kingdom, 92United States, 90, 92, 194–5

218 l Index

Acemoglu, D., 191Aeschbach-Hertig, W., 171Akinbami, L., 169Alesina, A., 89

Barret, S., 169Barro, R., 32, 86, 88, 91,

189Baumgärtner, S., 116Becker, G., 19Bonaiuti, M., 127, 162Boulding, K., 107

Carbaugh, R., 88Chen, Y., 170Chilingar, G. V., 171Ciaian, P., 150Clugston, C. O., 129–30Currie, J., 170

Dadvand, P., 170Dasgupta, P., 165Davies, J., 90Deaton, A., 165, 168Deininger, K., 90Diamond, J., 25Dominici, F., 169Doyal, L., 167Drèze, J., 166, 193

Emmott, S., 151, 163, 171Engerman, S., 194–5

FAO, 90, 149Figueroa, A., 20, 24, 41, 79Fitoussi, J., 155Fleurbaey, M., 155Forinash, K., 107, 130, 162–3Forssell, O., 169

Galor, O., 88Gardner, H., 12Gellner, E., 89

Georgescu-Roegen, N., 97, 105–6, 126, 162

GFN, 150Gollin, D., 90Gough, I., 167Graubart, K., 195

Hawking, S., 3Hertz-Picciotto, I., 169Hudson, R. A., 13, 15

IHME, 168–9IPCC, 171

Janda, K., 150Johnson, S., 195Jones, C., 33, 86, 88

Kancs, A., 150Karabarbounis, L., 91Khilyuk, L. F., 171Kristoufek, L., 150Kuhn, T., 188

Lafforgue, G., 115–16Landsberg, H., 190Lee, J., 91Li, H., 90Lucas, R., 74

Maddison, A., 86Markusen, J., 75Mc Connell, R., 169Mohai, P., 169Mukhopadhyaya, K., 169Muller, E., 107, 170Munich, R. E., 171Musgrove, P., 192

Neiman, B., 91

OECD, 24Olson, M., 23, 190

Authors (Volume II only)

Index l 219

Parker, J., 169Piketty, T., 92Pimentel, D., 149

Ratey, J., 12, 14Robinson, J., 195Rodrik, D., 189Rousseau, J., 12

Sala-i-Martin, X., 32, 86, 88, 189Salomon, J., 169Samuelson, P., 7Schultz, T., 33Searle, J., 14Sen, A., 155, 166, 193Sheffield, P., 169Smith, A., 180, 187, 200Sokoloff, K., 194Solow, R., 114Sorokhtin, O. G., 171, 195Squire, L., 90

Stavins, R., 113, 171Stewart, F., 91Stiglitz, J., 155

UNCTAD, 75, 191UNDP, 167

Vollrath, D., 86, 88

Walras, L., 181Weale, M., 165Wesseling, H. L., 91, 195Wilson, E., 150Wolf, E., 90Woodruff, T., 169World Bank, 129, 168

Yim, S., 169

Zilberman, D., 150Zou, H. F., 90

Growth, Employment, Inequality, And the Environment Unity of Knowledge in Economics Volume II

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