The Marginal “Revolution”:Jevons Menger Walras

History of Economic ThoughtBoise State University

Fall 2015Prof. D. Allen Dalton

William Stanley Jevons (1835-1882)– born Liverpool, merchant– undergrad work at University College,

London in chemistry and metallurgy– 1854, leaves school to become assayer at

Sydney (Australia) mint– private research meteorology, railroads,

economics, national statistics– 1859, returns to London to finish

university education – 1863, tutor at Owens College, Manchester– 1866, professor of political economy at

Owens– 1876, professor University College,

London– 1880, retires due to ill health

Jevons’ Minor Works• “Notice of a General Mathematical Theory of Political

Economy” (1862)– sketch of ideas to be later fleshed out in Theory of Political

Economy, paradoxically without any mathematics

• (pamphlet) A Serious Fall in the Value of Gold Ascertained and its Social Effects set forth (1863)– pioneering methodological and empirical contribution to

index numbers, showing gold discoveries were source of commodity price rises

• The Coal Question (1865)– alarmist argument that coal was being exhausted and would

limit British economic growth– bestseller, widely debated, brought him instant fame

• Investigations in Currency and Finance (1884)– exogenous business cycle theory (“sunspot cycle”)

Jevons’ Contributions• The Theory of Political Economy (1871)• Value and Exchange; Capital and Interest• Value and Exchange

– starting point: “to maximize pleasure is the problem of economics”

– utility is function of quantity of goods consumed, u = u(x); disutility a function of “discommodities” (x) = du/dx = u’(x) is defined as degree of utility• the “degree of utility” of the last increment consumed is

termed the final degree of utility (marginal utility)

– degree of utility diminishes as quantity increases– for good with alternate uses, optimal allocation

occurs when same final degree of utility occurs in all uses (weak form of Gossen’s Second Law)

Jevons’ Contributions• Utility maximization is basis of theory of exchange

– relative price () defined as ratio in which small quantities of goods exchanged against one another; = px/py = dy/dx

– for homogenous goods in well-functioning markets, one price will prevail - Jevons’ Law of Indifference (Law of One Price)

– implies that total quantities exchanged by given trader stand in same ratio as any small quantities; y/x=dy/dx = .

– Thus, “the ratio of exchange of any two commodities will be the reciprocal of the ratio of the final degrees of utility of the quantities of commodity available for consumption after the exchange is completed”

Jevons’ Contributions• Let be given, as well as

quantities of x and y (a and b, respectively).

• If b expressed in terms of a, total resources are R = a + b/.

• Blue curve represents MU of x; Black curve represents utility of marginal unit of x exchanged for Y (and exchange occurs at ratio )

• Optimality requires (x) = (y), or (x)/(y) = , and = px/py, so...

R = a + b/

(x) (y)

(x)/(y) = = px/py

Jevons’ Contributions• but this is true for every individual, so the price ratio

between commodities equals the ratio of marginal utility between those commodities for all individuals

(x)1/(y)1 = = px/py = (x)2/(y)2

• Capital and Interest– capital regarded as stock of goods waiting to be

consumed (directly or indirectly-machines)

– essential function of capital is to allow an interval between labor input and final consumption

– “capital is concerned with time”

– to measure the interval Jevons introduces concept of “average interval of investment”• anticipates Bohm-Bawerk’s “average period of

production”

Jevons’ Contributions• Capital and Interest

– output increasing function of interval of investment [Q = F(t), where F’(t) > 0]and the interest rate is equal to the increment in output obtainable from the last increment in time, divided by output [ i = F’(t)/F(t)]

– given the length of production time, the market rate of interest will equal the rate of growth of output from waiting

– marginal productivity principle and Jevonian Triangles

MPK

KK

i

Capital income

Labor income

Slope equals i

Time

Value of output

Jevons’ Contributions• The Principles of Science - a Treatise on

Logic and Scientific Method (1874)– laws of science begin from creative act of

inventing hypothesis from which logical implications are deduced and tested against observation

– certainty of science can never be attained; probability plays a crucial role

– reads like early Popper

Carl Menger (1840-1921)– born Galicia (Poland)– studied law at Vienna and

Prague, obtained doctorate at Cracow

– financial journalist, civil servant– 1873, professor extraordinary in

Faculty of Law at Vienna– 1876, tutor to Crown Prince

Rudolph– 1879, chair of political economy

at Vienna– 1903, retires

• controversy over reasons for retirement

Menger’s Contributions• Principles of Economics (1871) - Grundsatze– first volume in planned four volume work, others

never written

• Investigations on the Method of the Social Sciences (1883)– response to Schmoller’s unkind review of the

Grundsatze which argued theory had no place in political economy

• founder of the Austrian School– emphasis on causal-genetic explanations– centrality of subjective utility, uncertainty,

adjustments in disequilibrium, and time

Menger’s Contributions• Principles of Economics (1871)– Chapter 1: “The General Theory of the

Good”• characteristics of goods in general

– need, property of satisfaction, knowledge, access

• first-order (consumer) goods v. higher-order (producer) goods• value of higher orders derived from first-order

goods• necessary complementarity in time-consuming

production process

Menger’s Contributions• Principles of Economics (1871)– Chapter 3: “The Theory of Value”• extensive discussion of subjectivity of utility• analysis of economizing by single individual of

lumpy alternatives of equal-expenditure bundles of alternative goods• value of any good in comparison with another

is determined by its least dependent use• extended discussion of uncertainty, error and

changes in knowledge upon economizing process

Menger’s Contributions• Principles of Economics (1871)– Chapter 4: “The Theory of Exchange”

• purpose of exchange; mutual beneficence of exchange

• exchange as result of inverted subjective evaluations

– Chapter 5: “The Theory of Price”• analysis of price formation, progressing from

monopoly to competition

– Chapter 6: “Use Value and Exchange Value”• reemphasis of difference between subjective

utility and objective exchange ratio

Menger’s Contributions• Principles of Economics (1871)– Chapter 7: “The Theory of the Commodity”• commodities are goods intended for sale• extensive discussion of marketability

– Chapter 8: “The Theory of Money”• money arises on the market as a commodity• the commodity money arises as a

consequence of its being the most marketable of all commodities

Léon Walras (1834-1910)– father, Auguste Walras, disappointing

career as teacher and economic writer• father championed notion that price

reflects relative scarcity

– rejected by Ecole Polytechnique, enrolls in Ecole des Mines but neglects studies and does not graduate

– 1858 conversation with father leads to interest in economic matters

– 1860, wins fourth prize in essay contest at International Tax Congress in Lausanne

– 1870, appointed professor of political economy in law faculty at Lausanne

– 1892 retires; Pareto succeeds him

Walras’ Contributions• Elements of Pure Political Economy (1874,

1877)– first volume in planned three volume work,

dealing with pure, applied, and social economics; latter two never written

– Minor Works: Etudes d’économie sociale (1896) and Etudes d’économie politique appliqué (1898)• develop views of ideal society, role of government and

private property• favored land nationalization; government to provide

public goods and control natural monopolies from land rent; abolition of taxes; abolition of paper currency and institution of managed gold standard (stabilize prices via changing supply of overvalued silver coins); otherwise free competition.

Walras’ Contributions• Elements of Pure Political Economy (1874,

1877)• General Equilibrium Analysis

– begins with analysis of exchange under partial equilibrium (two goods); arrives at Gossens’ Second Law, allowing him to explain why prices are determined by scarcity (solving his father’s problem)

– generalization from two goods to n goods; explicit analysis of general equilibrium

– view of money as numeraire good

– derivation of demand from utility maximization

– general equilibrium defined as zero excess demand in all market simultaneously

Walras’ Contributions• General Equilibrium Analysis

– Tâtonnement process • iterative process to solve simultaneous equations;

disallows false trading (exchange at nonequilibrium prices) by use of auctioneer who changes prices due to excess demand conditions

• stability questions understood but not analyzed

– Extension of model to production• assumed fixed coefficients of production• profits and losses are signal for expansion or

contraction of input usage and output production• households endowed with factors that produce

incomes• incomes replace endowments on demand for output

side

Walras’ Contributions• General Equilibrium Analysis– Extends model to account for growth through

investment and saving• investment defined as value of new capital goods; price

of each capital good is capitalized value of rental income it provides (therefore inverse relation between investment and interest rate)

• saving is income not consumed, determined by marginal equality of present consumption foregone and future income gained

– Treats money as an asset held as inventory to accomplish function of exchange over a time period• demand for cash balance is diminishing function of

interest rate

Influences/Differences• Influence– Menger had greatest initial influence in spreading

“marginalist” ideas– Walras and Jevons mathematical versions

eventually became more widespread and influential– Walras had greatest impact on mainstream modern

economist’s toolkit

• Differences– Menger’s emphasis on causality in time differs from

simultaneous equations approach of Walras– Menger emphasizes uncertainty, error and

processes rather than Jevons’ and Walras’ emphasis upon equilibrium

Additional Contributions• Friedrich von Wieser

– cost is marginal utility foregone from application of unit of input to produce one good rather than another

– imputation problem; expected prices of first-order goods determine the prices of higher order goods

• John Bates Clark– extension of emphasis on marginal

productivity theory of distribution as applied to all factors of production

– argued marginal productivity pricing of factors was just

Additional Contributions• Philip Wicksteed

– mathematical presentation of marginal productivity theory

– used Euler’s Theorem to show that in equilibrium, when production function is homogeneous and linear, that shares to wages, rent, and interest exhaust the revenue of the firm

• Francis Ysidro Edgeworth– extension of exchange analysis to note

multiplicity of possible equilibria from original endowments; contract curve