General Equilibrium Analysis

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General Equilibrium Analysis

• USAID Reform Project
• Dr. Brijesh C. Purohit
• November 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 on the
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 modelling

• The first attempt in Neoclassical economics to
  model prices for a whole economy was made by Leon
  Walras. Walras' 'Elements of Pure Economics
  provides a succession of models, each taking into
  account more aspects of a real economy (two
  commodities, many commodities, production,
  growth, money). Many think Walras was
  unsuccessful and the later models in this series
  inconsistent. Nevertheless, Walras first laid
  down a research programme much followed by 20th
  century economists. In particular, Walras' agenda
  included the 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 the prices of all other
goods remain constant. The Marshallian theory
of supply 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 after Piero Sraffa's
demonstration that Marshallian economists cannot
account for the forces thought to account for the
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's demand
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 equations and 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 in
economics

• The modern conception of general equilibrium is
  provided by a model developed jointly by Kenneth
  Arrow and Gerard Debreu in the 1950s. Gerard
  Debreu presents this model in Theory of Value
  (1959) as an axiomatic model, following the style
  of mathematics promoted by Bourbaki. In such an
  approach, the interpretation of the terms in the
  theory (e.g., goods, prices) are not fixed by the
  axioms.

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Three important theorems have been proved in this
framework. First, existence theorems show that
equilibria exist under certain abstract
conditions. The first fundamental theorem of
welfare states that every market equilibrium is
Pareto optimal under certain conditions. The
second fundamental theorem of welfare states that
every Pareto optimum is supported by a price
system, again under certain conditions. These
conditions were stated in the language of
mathematical topology. The proofs used such
concepts as separating hyperplanes and fixed
point theorems.
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Types of GEA and Limitations

• One of the major virtues of the general
  equilibrium model is its ability to trace the
  consequences of large changes in a particular
  sector through- out the entire economy.
• It shares this property with input-output
  analysis but permits a more flexible treatment of
  the consumer side of the economy and is less
  rigid in the requirements placed on the
  productive side.
• Major policy changes frequently have significant
  impacts on the distribution of income - indeed,
  they may be designed with this consequence in
  mind - and require, for their analysis, a
  conceptual framework that allows for 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 linear approximations
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 assumption of
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 consumed
in 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
means that economic agents make decisions
by only looking at some of the prices not all
the prices in the economy. We are assuming
here agents 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 1-4 we can
illustrate the supply conditions of a country by
PPF. Draw PPF to illustrate the supply
conditions in each country. PPF We can assume
that either the economy is subject 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 firms will 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 Model

• Most of the empirical work in economics has
  relied on partial equilibrium analysis.
• This type of analysis concentrates on a single
  market and quantifies the changes in supply,
  demand, prices, quantities and welfare brought
  about by exogenous shocks and/or parametric
  changes.
• This approach is well suited to markets with
  limited size 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 as one 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
equilibrium problem 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 the base 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 Transport 6.
Transportation Transportation for
production 6. Consumer Services 7. Electricity
Electricity 7. Housing
and Household goods 8. Oil and Gas 1.
Crude Petroleum 2.
Natural Gas 9. Refining /petrochemicals 1.
Coke
2. 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 6-8 Agent 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 the
underlying 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.