The Problem of Exchange. Given an economy where individuals are allocated a certain amount of...

Chapter 21

The Problem of Exchange

Objective 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

3

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

4

Edgeworth Box & Feasible Trades

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

5

The Edgeworth box: Dimensions

6

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

Raspberries0 8

App

les

10

The Edgeworth box: Geoffrey and Elizabeth

7

Raspberries to Geoffrey 0 2 8

Apples toGeoffrey

8

10

f

Apples toElizabeth

2

Raspberries to Elizabeth 06

Geoffrey

Elizabeth

I1g

I1e

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

8

Utility-improving trades

9The 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

6

8

10

f

Apples toElizabeth

2

4

Raspberries to Elizabeth 06 4

h

g

j

i

I1g

I1eI2e

I3eI3g

I2g

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 efficient allocation

o Indifference curves cross Efficient allocation

o Indifference curves - tangent

10

Marginal Conditions for Efficient Trades

Efficient allocationo Tangency point - indifference curveso Marginal rates of substitution - same

Contract curveo Curve in Edgeworth boxo All efficient trades

11

OG

OE

The contract curve

12The contract curve is a locus of all efficient trades, i.e., of all tangency points

Apples toElizabeth

Raspberries to Elizabeth

Apples toGeoffrey

Raspberries to Geoffrey

l

k

The contract curve Contract curve

o Set of efficient / Pareto optimal trades o No more voluntary trade will take place.

13

OG

OE

The Core of an Economy

14The 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 .

f

C

A

Apples toElizabeth

Raspberries to Elizabeth

Apples toGeoffrey

Raspberries to Geoffrey

I1g

I1em

l

n

k

Blocked byElizabeth

Blocked byGeoffrey

Marginal Conditions for Efficient Trades

Core of economyo Set of equilibrium tradeso Portion of contract curve

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

15

A Growing Population and the Core

Economy – grows through replication

As we add agentso Set of core allocation – diminisho Points on original core – eliminated

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The core of a four- person economy

17G1 and G2 will negotiate with E2 a better deal: Each G offers 2.5 apples and gets in return 0.5 raspberries

f

C

A

Apples toElizabeth

Raspberries to Elizabeth

Apples toGeoffrey

Raspberries to Geoffrey

m

n

z

3

5

512

212

3 7

8 2

2

6

An Economy with Many Agents

Economy – grows largero Set of core allocations – one point

Competitive behavioro Price-taking behavioro Individuals take prices as given o Based on the value of their endowments decide how much

of each good to buy

Competitive Equilibriumo Set of prices that clear markets (QD=QS of each good)o Determined by the endowment and individual preferences

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A Competitive Equilibrium

19

f

C

A

Apples toElizabeth

Raspberries to Elizabeth

Apples toGeoffrey

Raspberries to Geoffrey

e

Not A Competitive Equilibrium

20Point e

f

D

CB

A

Apples toElizabeth

Raspberries to Elizabeth

Apples toGeoffrey

Raspberries to Geoffrey

y

z

Conditions for Competitive Equilibrium A Competitive Equilibrium is defined by a set of

prices such thato For any goodo Total Quantity demanded= Total Quantity Suppliedo At those prices

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Conditions for Competitive Equilibrium To solve:

o Find the demand for each good by each individual• Use the utility function• Individual income evaluated at the competitive prices

o Calculate market demand by adding up all individual demand

o Total supply is total amount of good i.o Set total demand = total supply

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