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General Equilibrium AnalysisGeneral Equilibrium Analysis
USAID Reform ProjectUSAID Reform Project
Dr. Brijesh C. PurohitDr. Brijesh C. Purohit
November 2005November 2005
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General equilibrium theory is a branch of theoretical microeconomics.
It seeks to explain production, consumption and prices in a whole economy.
General equilibrium tries to give an understanding of the whole economy
using a bottom-up approach, starting with individual markets and agents.
Macroeconomics, as developed by so-called Keynesian economists,
uses a top-down approach where the analysis starts with larger aggregates.
Since modern macroeconomics has emphasized microeconomic
foundations, this distinction has been slightly blurred.
However, many macroeconomic models simply have a 'goods market' and
study its interaction with for instance the financial market.General equilibrium models typically model a multitude of different goods
markets. Modern general equilibrium models are typically complex and
require computers to help with numerical solutions.
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Under capitalism, the prices and production of all goods are interrelated.
A change in the price of one good, say bread, may affect another price,
for example, the wages of bakers.
If bakers differ in tastes from others, the demand for bread might be
affected by a change in bakers' wages, with a consequent effect onthe price of bread.
Calculating the equilibrium price of just one good, in theory,
requires an analysis that accounts for all of the millions of different goods
that are available.
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History of general equilibrium modellingHistory of general equilibrium modelling
The first attempt inThe first attempt in Neoclassical economicsNeoclassical economics to modelto modelprices for a whole economy was made byprices for a whole economy was made by Leon WalrasLeon Walras..Walras' 'Walras' 'Elements of Pure EconomicsElements of Pure Economics provides aprovides a
succession of models, each taking into account moresuccession of models, each taking into account moreaspects of a real economy (two commodities, manyaspects of a real economy (two commodities, manycommodities, production, growth, money). Many thinkcommodities, production, growth, money). Many thinkWalras was unsuccessful and the later models in thisWalras was unsuccessful and the later models in thisseries inconsistent. Nevertheless, Walras first laid downseries inconsistent. Nevertheless, Walras first laid down
a research programme much followed by 20th centurya research programme much followed by 20th centuryeconomists. In particular, Walras' agenda included theeconomists. In particular, Walras' agenda included theinvestigation of when equilibria are unique and stable.investigation of when equilibria are unique and stable.
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In partial equilibrium analysis, the determination of the price of a good is
simplified by just looking at the price of one good, and assuming that theprices of all other goods remain constant.
The Marshallian theory ofsupply and demand is an example of partial
equilibrium analysis.
Partial equilibrium analysis is adequate when the first-order effects of a shift
in, say, the demand curve do not shift the supply curve.
Anglo-American economists became more interested in general equilibrium
in the late 1920s and 1930s afterPiero Sraffa's demonstration that
Marshallian economists cannot account for the forces thought to account forthe upward-slope of the supply curve for a consumer good.
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If an industry uses little of a factor of production,
a small increase in the output of that industry will not bid the price of that factor up.
To a first order approximation, firms in the industry will not experience decreasing
costs and the industry supply curves will not slope up. If an industry uses an
appreciable amount of that factor of production,
an increase in the output of that industry will exhibit increasing costs.
But such a factor is likely to be used in substitutes for the industry's product,
and an increased price of that factor will have effects on the supply of those
substitutes. Consequently, the first order effects of a shift in the supply curve of
the original industry under these assumptions include a shift in the original industry'sdemand curve.
General equilibrium is designed to investigate such interactions between markets.
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Continential European economists made important advances in the
1930s. Walras' proofs of the existence of general equilibrium often
were based on the counting of equations and variables.
Such arguments are inadequate for non-linear systems of equationsand do not imply that equilibrium prices and quantities cannot be
negative, a meaningless solution for his models.
The replacement of certain equations by inequalities and
the use of more rigorous mathematics improved general equilibrium
modeling.
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Modern concept of general equilibrium inModern concept of general equilibrium in
economicseconomics
The modern conception of general equilibrium isThe modern conception of general equilibrium is
provided by a model developed jointly byprovided by a model developed jointly by
Kenneth ArrowKenneth Arrow andand Gerard DebreuGerard Debreu in the 1950s.in the 1950s.
Gerard Debreu presents this model in Theory ofGerard Debreu presents this model in Theory ofValue (1959) as an axiomatic model, followingValue (1959) as an axiomatic model, following
the style of mathematics promoted bythe style of mathematics promoted by BourbakiBourbaki..
In such an approach, the interpretation of theIn such an approach, the interpretation of the
terms in the theory (e.g., goods, prices) are notterms in the theory (e.g., goods, prices) are notfixed by the axioms.fixed by the axioms.
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Types of GEA and LimitationsTypes of GEA and Limitations
One of the major virtues of the general equilibrium modelOne of the major virtues of the general equilibrium modelis its ability to trace the consequences of large changesis its ability to trace the consequences of large changesin a particular sector throughin a particular sector through-- out the entire economy.out the entire economy.
It shares this property with inputIt shares this property with input--output analysis butoutput analysis butpermits a more flexible treatment of the consumer side ofpermits a more flexible treatment of the consumer side ofthe economy and is less rigid in the requirements placedthe economy and is less rigid in the requirements placedon the productive side.on the productive side.
Major policy changes frequently have significant impactsMajor policy changes frequently have significant impactson the distribution of incomeon the distribution of income -- indeed, they may beindeed, they may bedesigned with this consequence in minddesigned with this consequence in mind -- and require,and require,for their analysis, a conceptual framework that allows forfor their analysis, a conceptual framework that allows forthe possibility of variations in income.the possibility of variations in income.
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The consequences of a change in economic policy are frequently
analyzed by assuming the changes to be small and using local linearapproximations based on estimates of the relevant elasticities.
If the number of sectors is small, diagrammatic techniques or explicit
analytical results may also be available as in the two-sector models so
frequently used in international trade theory.
But if the model is disaggregated, and if the changes - possibly more
than one are large, there is no recourse other than the construction
and explicit solution of a numerical general equilibrium model.
The imperfections of the general equilibrium model as a description of
economic reality are well known to economists and in a less informed
way to the general public.
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The model is inadequate in its treatment of money and financial
institutions, it has great difficulty in allowing for unemployed resources,
and it is unable to cope with large-scale industrial enterprises that are
capable of exerting a significant influence on prices.
Investments and roundabout methods of production are poorly treated if
the model is formulated in static terms, and any attempt to rectify this by
a dynamic model must find a replacement for the unrealistic assumptionof perfect futures markets.
But there are no competing formulations that avoid these shortcomings
and provide the flexibility and conceptual wealth of the general
equilibrium model.
In spite of its imperfections, this method of analysis will retain its
usefulness until economic theory is capable of providing compelling
alternative formulations.
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eight different applied general equilibrium models dealing with taxation.
The sensitivity of such models to the level of disaggregation in production
is investigated.
Several aspects of the eight models including :
their treatments of saving,
the labor-leisure choice,foreign de, and the household sector.
For instance, a model of the Mexican economy that is used to analyze
the effect of introducing a value-added tax of the consumption type on
income distribution and resource allocation.
Main result is that the welfare of rural consumer groups increases after this
reform.
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Borges and Goulder have used a model of the United States to simulate
the impact of higher energy prices economic growth and to test the
relative importance of several channels through which higher-priced
energy affects growth.
Bell and Harrison develops a regional model that predicts the incidence
of fiscal policy in the California economy.
Ginsburgh and Waelbroeck discuss planning models and activity analysis.
They propose that linearized economic models that can be formulated as
optimization problems have advantages over computable general
equilibrium models in the analysis of developing countries.
Dixon, Parmenter, and Rimmer also deals with a linearized model, but its
most distinctive feature is its level of detail.
This model of Australia identifies 113 industries, 230 commodities, 9 types
of or, and 7 types of land.
It has been used for policy evaluation by several of the agencies of
the Australian government.
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general equilibrium refers to the equilibrium in
which production, consumption, prices, and international trade are
determined simultaneously for allgoods produced and consumedin
the economy.
Assumptions-
1. Economic agents, consumers, and producers-
firms- exhibit rational behavior in the sense that
given all the available information, consumers
maximize utility from consumption, and firms
try to maximize profits.
2. Two countries in the world, A, and B. Two
goods, C, and W. Some of each good is consumed
in each country.
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3. Consumers and producers when they make
decisions about consumption and production look
at the real prices not the nominal prices.
This assumption excludes the possibility of what is
known as money illusion.
Money illusion meansthat economic agents make decisions by
only looking at some of the prices not all the
prices in the economy.
We are assuming hereagents base their decisions on relative prices not
on nominal prices.
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4. In each country factors of production is fixed
and the level of technology in each country is con-stant. Note this does not mean that each country
to have the same amount of factor endowments
or each have the same level of technology.
Under assumptions 1-
4we can illustrate thesupply conditions of a country by PPF.
Draw PPF to illustrate the supply conditions in each country.
PPF:
We can assume that either the economy issubject to increasing OCs or the constant OCs.
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5. Perfect competition prevails in each indus-
tries in each country. There are no externalities.
We know that under perfect competition firmswill maximize their profits when P= MC. Then
market prices reflect the true social (opportu-
nity) costs of production. Illustrate this graph-
ically by drawing PPF and price line together.
6. Factors of production are perfectly mobile
between the two industries within each country.
This assumption implies that factors of produc-
tion can freely move between industries when
there is a potential difference in factor payments
within a country.
What does then this suggest for
say wages in different industries within a coun-
try?
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7. Community preferences in consumption can
be represented by a consistent set of community
indifference curves.
Or alternatively we can assume that there is a representative agent for each
country whose indifference curve represents that
countrys community indifference curve.
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Dynamic General Equilibrium ModelDynamic General Equilibrium Model
Most of the empirical work in economics has relied onMost of the empirical work in economics has relied onpartial equilibrium analysis.partial equilibrium analysis.
This type of analysis concentrates on a single marketThis type of analysis concentrates on a single marketand quantifies the changes in supply, demand, prices,and quantifies the changes in supply, demand, prices,quantities and welfare brought about by exogenousquantities and welfare brought about by exogenousshocks and/or parametric changes.shocks and/or parametric changes.
This approach is well suited to markets with limited sizeThis approach is well suited to markets with limited sizeor with weak linkages to other economic sectors.or with weak linkages to other economic sectors.
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Many economic problems do not fit easily into this category, however.
The economic sector analyzed is often large, and changes in that sector
can have important repercussions economy-wide.
Such problems are more appropriately dealt with using general
equilibrium analysis in which all the sectors in the economy are seen asone linked system where changes in any part affect prices and output
economy-wide.
Mathematically, an interlinked economy cannot be described in one or
two equations, but rather by a large system of simultaneous equations.
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More precisely, in an economy with n markets, n-1 equations are
required to solve for all of the prices and outputs in the system.
Although the theory behind general equilibrium can be described fairly
easily,
the computations involved in solving such a system are fairly complex
and difficult.
Indeed, it was not until the advent of high-speed computers and efficient
solution algorithms that large economy-wide problems could be solved.
In a simple static model, the actual solution of a general equilibriumproblem requires that the modeler construct a social accounting matrix
(SAM). In the SAM, all production in all markets, all tax revenue of the
government and all consumption by all household for a specific base year
has to be replicated exactly first.
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Hence, for a country such as India,
one must specify the amount of manufacturing, agricultural, energy and
all the other sectoral outputs that occurred in the base year.
Supply and demand elasticities must also be specified, and the model
calibrated through constants in each equation so that each consumer
group is assigned the amount they consumed in that year.
The equations are solved and the results are checked to see that thebase year is indeed replicated.
The model is then run under a counterfactual scenario.
One or more supply, demand, or tax is altered and the results from
resolving the model are compared with the original benchmark run to
show the changes in prices and output in each of the models sectors.
In both runs, the total level of consumer welfare and GDP are also
calculated and the two are compared to see the impact of the
exogenous changes on these economy-wide variables.
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The policies that have been analyzed through these models include
changes in various types of taxes and tariffs, technological change,
natural resource policy, and employment policy. Both efficiency and
distribution impacts are presented in these studies
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Table.1 An Example of Classification of Producing Sectors, Production
and Consumer Goods and Services (in CGE)
Producing Sectors Production Goods Consumer Goods and Services
1. Manufacturing Manufacturing Goods 1. Food
2. Coal Mining Coal 2. Energy
3. Chemicals and Plastics Chemicals and Plastics 3. Autos
4. Agriculture Agricultural goods 4. Gasoline
5. Services Producer Services 5. Consumer Transport6. Transportation Transportation for production6. Consumer Services
7. Electricity Electricity 7. Housing and Household goods
8. Oil and Gas 1. Crude Petroleum
2. Natural Gas
9. Refining /petrochemicals 1. Coke2. Diesel
3. Fuel oil
4. LPG
5. Gasoline
6. Kerosene
7. Petrochemicals
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Table 2. Household Categories Based on Income
Category Income
Agent 1 Bottom 2 deciles: 8-10
Agent 2 Deciles 6-8Agent 3 Deciles 3-5
Agent 4 Top 2 deciles: 1-2
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The extension of a static CGE model to a dynamic one is fairly
straightforward.
Although computationally more complex, a dynamic CGE model differs
from its static counterpart only by the inclusion of a driving force to move
the economy from period to period.
In most dynamic models, this force is provided by the growth in theunderlying labor force and/or a change in the level of technology in one or
more sectors of the economy.
These changes are facilitated by new investments and the growth of the
capital stock in the economy.
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As with the static model, the actual output for each sector in a specific base
year is replicated through the calibration.
In addition, however, the economy is now expected to grow, and in the initial
benchmark run all sectors, quantities, and factors of production are required
to grow at the same steady-state rate.
When a counterfactual shock is then given to a dynamic CGE model, two
things occur.
First, the affected prices and quantities traverse to a new growth path in the
years following the shock.
Second, the new growth path itself returns to a steady state but with
economic variables at a level different from that in the benchmark case.
Generally, the interest in these dynamic models is on that new path and how
much higher or lower it is than the original benchmark path.
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Nonetheless,
because of their heavy computational requirements, true dynamic
extensions of CGE models are a fairly recent development.
In the past few years, authors such as Summers and Goulder (1989),Jorgenson and Wilcoxen (1990), and Rutherford and others (1997)
have begun to use dynamic CGE models to explore a variety of policy
issues using a single consuming agent.