general equilibrium analysis[1]

8/8/2019 General Equilibrium Analysis[1]

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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.

general equilibrium analysis[1]

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