Chapter 10

General Equilibrium and Welfare

Introduction Partial vs. General equilibrium analysis Partial Equilibrium: narrow focus General equilibrium: framework of analysis that

considers the working of several markets together

Objective General Equilibrium model of exchange Given an economy where individuals are

allocated a certain amount of goods, we willo Investigate barter exchangeo Define equilibrium tradeo Investigate the emergence of competitive markets

Harvesting & Gathering: Need for Trade

Primitive, two-person economyo Geoffrey, Elizabeth o Harvest & gather fruit

• Apples, raspberries o Voluntary trade – beneficial o Options

• Consume all• Trade some

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Edgeworth Box & Feasible Trades

Edgeworth boxo Graphical device to analyze the process of tradeo Its size equals the total amount of goodso A point in the box represents a possible/ feasible

allocation of goods

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Edgeworth Box & Feasible Trades

No-trade allocationo Feasible allocationo No tradeo Individuals consume their own harvest

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The Edgeworth box: Dimensions

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Dimensions of the Edgeworth box represent total amount of each good. There are 10 apples and 8 raspberries

Raspberries0 8

App

les

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The Edgeworth box: Geoffrey and Elizabeth

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Raspberries to Geoffrey 0 2 8

Apples toGeoffrey

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Raspberries to Elizabeth 06

Geoffrey

Elizabeth

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Finding Equilibrium Trades

Equilibrium allocationo Once reachedo No incentive to further trade

Block o Prevent a tradeo Coalition – each gets more

Individually rational tradeo Higher utility - than no trade

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Utility-improving trades

10The shaded, lens-shaped area represents the set of allocations that do not lower either agent’s utility relative to the no-trade allocation at point f .

Raspberries to Geoffrey 0 2 4 8

Apples toGeoffrey

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Apples toElizabeth

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Raspberries to Elizabeth 06 4

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Efficient / Pareto-Optimal Allocation

Pareto-optimal (efficient) allocationo Allocation of goods across peopleo No other allocation can make one person better off

without making the other worse off. Not an efficient allocation

o Indifference curves cross Efficient allocation

o Indifference curves – tangento MRS the same for both

Contract curveo Curve in Edgeworth boxo All efficient trades

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The Contract Curve

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Contract Curve

The core

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For any initial allocation we can see where trade may lead.

The Core Core of economy

o Set of equilibrium tradeso Portion of contract curve

• Between no-trade indifference curveso Individually rationalo Cannot be blocked

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Efficiency and Equity

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F is the “fair” allocation and E is the initial allocation.

E

F

It is not possible with voluntary exchange. Coercion would make Smith better off but Jones worse off.

A Simple General Equilibrium Model

Assume a simple economy comprised ofo Identical consumerso 2 Firmso Two goods X and Yo Consumers own all factors of production/ all firms

A Simple General Equilibrium Model

Quantity of X

Quantity of YPPF: shows the combinations of X and Y that can be produced if resources are used efficiently

It also shows the relative opportunity cost of good X in terms of Y

A Simple General Equilibrium Model

Quantity of X

Quantity of YThe indifference curves represent consumer preferences: “demand curve”

U1

U2

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A Simple General Equilibrium Model

Quantity of X

Quantity of Y

E

Point E is economically efficient: it both is productively efficient (on the PPF) and it maximizes utility.

U1

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Compare point E to point F

F

A Simple General Equilibrium Model

The slope of the PPF shows the opportunity cost of X in terms of Y. As more X is produced, the opportunity cost rises. The slope is the rate of product transformation.

The slope of the indifference curve shows the rate at which consumers are willing to trade one good for another in consumption. The slope is the marginal rate of substitution.

At the efficient point the RPT = MRS

The Efficiency of Perfect Competition

We now have an idea of where we want to be: point E.

How do we get there?

First Welfare Theorem says that a perfectly competitive price system will bring about an economically efficient allocation of resources.

The Efficiency of Perfect Competition

How to find a perfect competitive equilibrium?o It is a price vector that clears the marketo Given the prices of the two goods

• Producers supply an amount of x and y• Consumers demand an amount of x and an amount of y• Demand for x by all consumers= total production of x• Demand for y by all consumers= total production of y

A Perfectly Competitive System

Consumers own all resources Consumers offer resources to firms Firms produce goods and sell them Revenue from sales used to pay all resource

owners Consumers earn an income where

Income = value of goods

Firm’s Side

Quantity of X

Quantity of YFirms will maximize profits by producing here.

• Lets assume prices for both goods, and and see if these prices constitute a perfect competitive equilibrium

• The prices can be represented graphically by many straight lines with a slope - /

• Firms choose a combination of X and Y that maximizes Profit

• All points on the PPF cost the same, since all resources are used.

The budget line for consumers

Total product of firms represent income to consumers

Consumers income isM= +

The budget equation + =

+ = +

The budget line has a slope of - /and goes through point ,

The Economy’s Budget line

Quantity of X

Quantity of Y The budget line for consumers:

• Represents all points possible to consume at the price ratio

• Goes through the point of production of firms

Consumers’ Side

Quantity of X

Quantity of Y

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• Consumers maximize utility given the prices observed and their income

Consumers will want to consume at this point

The Efficiency of Perfect Competition

Quantity of X

Quantity of Y

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Excess demand for X

The Efficiency of Perfect Competition

Quantity of X

Quantity of Y

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Excess supply of Y

The Efficiency of Perfect Competition

What’s the problem?o At the initial set of prices the decisions of firms and

consumers don’t match up.o There is an excess demand for X and an excess supply

of Y. What will happen to the prices of X and Y?

o The price of X will increase and the price of Y will decrease.

o The budget line will pivot and become steeper.

The Efficiency of Perfect Competition

Quantity of X

Quantity of Y

U2

U3Firms will maximize profits by producing here.

Consumers will want to consume at this point

But we still have excess demand for X and excess supply of Y

The Efficiency of Perfect Competition

Quantity of X

Quantity of Y

U2

U3

Firms will maximize profits by producing here.

Consumers will want to consume at this point

The Efficiency of Perfect Competition

At equilibrium:o Firms are maximizing profits.o Given the income consumers earn from that level of

production consumers are maximizing utility.o At equilibrium the amount of X and Y producers wish to

supply is equal to the amount of X and Y that consumers demand.

Prices, Efficiency and Laissez Faire

The natural effort of every individual to better his own condition, when suffered to exert itself with freedom and security, is so powerful a principle that it is alone, and without any assistance, not only capable of carrying on the society to wealth and prosperity, but of surmounting a hundred impertinent obstructions with which the folly of human laws too often encumbers its operations.

Why Markets Fail to Achieve Efficiency

What do we mean by “market failure”? Imperfect Competition

o A market in which some buyers and/or sellers have some influence on the prices of goods and services

Externalitieso The effect of one party’s economic activities on another party

that is not taken into account by the price system (pollution) Public Goods

o Goods that are both non-exclusive and non-rival Imperfect Information