© 2005 Pearson Education Canada Inc. 13.1 Chapter 13 Competitive General Equilibrium.

© 2005 Pearson Education Canada Inc.13.1

Chapter 13Chapter 13

Competitive General EquilibriumCompetitive General Equilibrium


General EquilibriumGeneral Equilibrium

Earlier chapters dealt with a partial equilibrium Earlier chapters dealt with a partial equilibrium framework (characterized by a market-to framework (characterized by a market-to market equilibrium).market equilibrium).

This chapter widens the perspective by fitting This chapter widens the perspective by fitting all the analytical pieces together into one large all the analytical pieces together into one large picture of efficiency in an economy wide picture of efficiency in an economy wide context.context.

This framework considers all markets in the This framework considers all markets in the economy simultaneously and is known as a economy simultaneously and is known as a general equilibrium analysis.general equilibrium analysis.


Preference AssumptionsPreference Assumptions

1.1. Indifference curves are convex to Indifference curves are convex to the appropriate origin.the appropriate origin.

2.2. Indifference curves are smooth.Indifference curves are smooth.

3.3. Both goods are essential for all Both goods are essential for all consumers.consumers.

4.4. The thing that affects well-being are The thing that affects well-being are the quantities of the two goods the quantities of the two goods consumed.consumed.


Figure 13.1 The Edgeworth box diagramFigure 13.1 The Edgeworth box diagram


The Edgeworth BoxThe Edgeworth Box

When indifference curves are smooth When indifference curves are smooth and convex, if two are tangent at a and convex, if two are tangent at a point in an Edgeworth Box, that point point in an Edgeworth Box, that point is a Pareto-optimal allocation. is a Pareto-optimal allocation.

Given smooth indifference curves, if Given smooth indifference curves, if MRS at some allocation is identical MRS at some allocation is identical for two individuals then that for two individuals then that allocation is Pareto-optimal.allocation is Pareto-optimal.


Efficiency in ConsumptionEfficiency in Consumption

Given the assumptions previously Given the assumptions previously stated:stated:

An allocation of goods is Pareto-An allocation of goods is Pareto-optimal in a many person exchange optimal in a many person exchange economy if MRS is identical for all economy if MRS is identical for all individuals. individuals.


The Contract CurveThe Contract Curve

All the points in the Edgeworth box All the points in the Edgeworth box where the indifference curves are where the indifference curves are tangent describes the entire set of tangent describes the entire set of Pareto-optimal allocations.Pareto-optimal allocations.

A line connecting all these points of A line connecting all these points of tangency is call the tangency is call the contract contract curvecurve..


Figure 13.2 The contract curveFigure 13.2 The contract curve


Figure 13.3 Budget lines in an exchange economyFigure 13.3 Budget lines in an exchange economy


Figure 13.4 Competitive equilibrium in Figure 13.4 Competitive equilibrium in an exchange economyan exchange economy


From Figure 13.4From Figure 13.4

The initial allocation is at point A.The initial allocation is at point A. Given the announced price, line AE* is the Given the announced price, line AE* is the

budget line for Shelly and Marvin.budget line for Shelly and Marvin. Since they will both choose E*, the Since they will both choose E*, the

announced price is a competitive announced price is a competitive equilibrium price and E* is a competitive equilibrium price and E* is a competitive allocation.allocation.

Since E* is on the contract curve, the Since E* is on the contract curve, the competitive equilibrium is Pareto-optimal. competitive equilibrium is Pareto-optimal.


Walras’ LawWalras’ Law

When there are When there are n n markets in a markets in a general equilibrium model, Walras’ general equilibrium model, Walras’ law states that if demand is equal to law states that if demand is equal to supply in supply in n-1 n-1 markets, then the markets, then the demand is equal to supply in the demand is equal to supply in the nth nth market as well.market as well.


First Theorem of Welfare First Theorem of Welfare EconomicsEconomics

Given the assumptions made, the Given the assumptions made, the competitive equilibrium allocation of competitive equilibrium allocation of a many person exchange economy is a many person exchange economy is Pareto-optimal.Pareto-optimal.

In other words, all gains from trade In other words, all gains from trade are realized in a competitive are realized in a competitive equilibrium.equilibrium.


Second Theorem of Welfare Second Theorem of Welfare EconomicsEconomics

With the assumed preferences, given any With the assumed preferences, given any Pareto-optimal allocation, there is an initial Pareto-optimal allocation, there is an initial allocation such that, given the initial allocation such that, given the initial allocation, the Pareto-optimal allocation is allocation, the Pareto-optimal allocation is the competitive equilibrium allocation.the competitive equilibrium allocation.

(From Figure 13.4, this says that any (From Figure 13.4, this says that any allocation on the budget line will produce E*, allocation on the budget line will produce E*, the competitive equilibrium).the competitive equilibrium).


Efficiency in General Equilibrium Efficiency in General Equilibrium with Productionwith Production

Production Assumptions:Production Assumptions:

1.1. Isoquants are smooth and convex.Isoquants are smooth and convex.

2.2. Both inputs are essential in Both inputs are essential in producing both goods.producing both goods.

3.3. Production functions exhibit Production functions exhibit constant returns to scale.constant returns to scale.

4.4. Production involves no externalities.Production involves no externalities.


Efficiency in Consumption Efficiency in Consumption ConditionCondition

Efficiency in consumption requires Efficiency in consumption requires that MRS is identical for all that MRS is identical for all individuals.individuals.

In other words, the allocation to In other words, the allocation to individual consumers of the goods individual consumers of the goods produced in an economy must be produced in an economy must be Pareto-optimal.Pareto-optimal.


Figure 13.5 The production possibilities setFigure 13.5 The production possibilities set


Efficiency In ProductionEfficiency In Production

Efficiency in production Efficiency in production requires that requires that the combination of goods actually the combination of goods actually produced must be on the production produced must be on the production possibility frontier (PPF).possibility frontier (PPF).

Efficiency in production Condition:Efficiency in production Condition:

Efficiency in production requires that Efficiency in production requires that the MRTS must be identical for all the MRTS must be identical for all firms.firms.


Figure 13.6 An Edgeworth box for productionFigure 13.6 An Edgeworth box for production


Efficiency in the Product MixEfficiency in the Product Mix

This condition concerns the interface This condition concerns the interface between production and consumption.between production and consumption.

The absolute value of the slope of the PPF The absolute value of the slope of the PPF is known as the is known as the marginal rate of marginal rate of transformation (MRT).transformation (MRT).

The MRT The MRT measures the measures the opportunity cost opportunity cost of the economy as a whole for a small of the economy as a whole for a small increase in the amount of good 1 relative increase in the amount of good 1 relative to good 2.to good 2.


Figure 13.7 The marginal rate of transformationFigure 13.7 The marginal rate of transformation


Marginal Rate of TransformationMarginal Rate of Transformation

The marginal rate of transformation The marginal rate of transformation can be expressed in terms of the can be expressed in terms of the marginal products in two different marginal products in two different but equivalent ways:but equivalent ways:

MRTS=MPMRTS=MP1122/MP/MP11

11 = MP = MP2222/MP/MP22

11


Efficiency in the Product MixEfficiency in the Product Mix

Efficiency in the Product Mix Condition:Efficiency in the Product Mix Condition:

Efficiency in the product mix requires Efficiency in the product mix requires that each consumer’s MRS be identical that each consumer’s MRS be identical to the economy’s MRT. to the economy’s MRT.


Figure 13.8 Efficiency in product mixFigure 13.8 Efficiency in product mix


Efficient Allocation of resourcesEfficient Allocation of resources

Each of the three efficiency conditions is Each of the three efficiency conditions is necessary for an efficient allocation of necessary for an efficient allocation of resources:resources:

1.1. Efficiency in consumption requires that MRS is Efficiency in consumption requires that MRS is identical for all individuals.identical for all individuals.

2.2. Efficiency in production requires that the Efficiency in production requires that the MRTS must be identical for all firms.MRTS must be identical for all firms.

3.3. Efficiency in the product mix requires that Efficiency in the product mix requires that each consumer’s MRS be identical to the each consumer’s MRS be identical to the economy’s MRT.economy’s MRT.


Efficiency and General Competitive Efficiency and General Competitive EquilibriumEquilibrium

First Theorem of Welfare Economics: First Theorem of Welfare Economics: Given the assumptions made, the Given the assumptions made, the competitive equilibrium of this competitive equilibrium of this general equilibrium model with general equilibrium model with production is efficient.production is efficient.


Figure 13.9 Efficiency in product mix for Figure 13.9 Efficiency in product mix for general competitive equilibriumgeneral competitive equilibrium


Second Theorem of Welfare Second Theorem of Welfare EconomicsEconomics

Given the assumed preferences, given any Given the assumed preferences, given any Pareto-optimal allocation (POA) of goods, that Pareto-optimal allocation (POA) of goods, that is attainable in the model, there is a is attainable in the model, there is a distribution of ownership of inputs (DOI) such distribution of ownership of inputs (DOI) such that POA is a competitive equilibrium that POA is a competitive equilibrium allocation associated with DOI.allocation associated with DOI.

In other words, to achieve equity, redistribute In other words, to achieve equity, redistribute the ownership of inputs; to achieve the ownership of inputs; to achieve efficiency, use competitive markets.efficiency, use competitive markets.


Figure 13.10 Trade between Two CountriesFigure 13.10 Trade between Two Countries


Sources of InefficiencySources of Inefficiency

What produces an inefficient allocation What produces an inefficient allocation of resources?of resources?

There are many potential sources of There are many potential sources of inefficiencies, one is a monopoly.inefficiencies, one is a monopoly.


Monopoly and InefficiencyMonopoly and Inefficiency

For a monopoly the first 2 efficiency For a monopoly the first 2 efficiency conditions still hold:conditions still hold:

1.1. Because all firms face the same Because all firms face the same input prices, each chooses an input input prices, each chooses an input bundle so that MRTS=wbundle so that MRTS=w11

ee/w/w22ee

2.2. Because all consumers face the Because all consumers face the same product prices, each chooses same product prices, each chooses a bundle at which the MRS=pa bundle at which the MRS=p11

ee/p/p22ee


Monopoly and InefficiencyMonopoly and Inefficiency

For a monopoly the inefficiency For a monopoly the inefficiency arises from a distortion of the arises from a distortion of the product mix.product mix.

The inefficiency arises because the The inefficiency arises because the profit maximizing monopolist profit maximizing monopolist produces where MR<P.produces where MR<P.

Therefore for all consumers, the Therefore for all consumers, the MRS>MRT and the allocation of MRS>MRT and the allocation of resources is inefficient.resources is inefficient.

© 2005 Pearson Education Canada Inc. 13.1 Chapter 13 Competitive General Equilibrium.

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Transcript of © 2005 Pearson Education Canada Inc. 13.1 Chapter 13 Competitive General Equilibrium.