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Chapter 21. The Problem of Exchange. Objective. Given an economy where individuals are allocated a certain amount of goods, we will Investigate barter exchange d efine equilibrium trade Investigate the emergence of competitive markets . Harvesting & Gathering: Need for Trade.

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chapter 21

Chapter 21

The Problem of Exchange

objective
Objective
  • Given an economy where individuals are allocated a certain amount of goods, we will
    • Investigate barter exchange
    • define equilibrium trade
    • Investigate the emergence of competitive markets
harvesting gathering need for trade
Harvesting & Gathering: Need for Trade
  • Primitive, two-person economy
    • Geoffrey, Elizabeth
    • Harvest & gather fruit
      • Apples, raspberries
    • Voluntary trade – beneficial
    • Options
      • Consume all
      • Trade some
edgeworth box feasible trades
Edgeworth Box & Feasible Trades
  • Edgeworth box
    • Graphical device to analyzethe process of trade
    • Its size equals the total amount of goods
    • A point in the box represents a possible/ feasibleallocation of goods
edgeworth box feasible trades1
Edgeworth Box & Feasible Trades
  • No-trade allocation
    • Feasible allocation
    • No trade
    • Individuals consume their own harvest
the edgeworth box dimensions
The Edgeworthbox: Dimensions

10

Apples

0

8

Raspberries

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

the edgeworth box geoffrey and elizabeth
The Edgeworth box: Geoffrey and Elizabeth

Raspberries to Elizabeth

Elizabeth

6

0

10

f

8

2

Apples

to

Elizabeth

Apples

to

Geoffrey

I1e

0

2

8

I1g

Raspberries to Geoffrey

Geoffrey

finding equilibrium trades
Finding Equilibrium Trades
  • Equilibrium allocation
    • Once reached
    • No incentive to further trade
  • Block
    • Prevent a trade
    • Coalition – each gets more
  • Individually rational trade
    • Higher utility - than no trade
utility improving trades
Utility-improving trades

Raspberries to Elizabeth

6

4

0

f

g

10

i

h

j

8

2

Apples

to

Elizabeth

Apples

to

Geoffrey

4

6

I3e

I3g

I1e

I2e

I2g

0

2

4

8

I1g

Raspberries to Geoffrey

The 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 .

efficient pareto optimal allocation
Efficient / Pareto-Optimal Allocation
  • Pareto-optimal (efficient) allocation
    • Allocation of goods across people
    • No other allocation can make one person better off without making the other worse off.
  • Not efficient allocation
    • Indifference curves cross
  • Efficient allocation
    • Indifference curves - tangent
marginal conditions for efficient trades
Marginal Conditions for Efficient Trades
  • Efficient allocation
    • Tangency point - indifference curves
    • Marginal rates of substitution - same
  • Contract curve
    • Curve in Edgeworth box
    • All efficient trades
the contract curve
The contract curve

Raspberries to Elizabeth

l

k

OE

Apples

to

Geoffrey

Apples

to

Elizabeth

Raspberries to Geoffrey

OG

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

the contract curve1
The contract curve
  • Contract curve
    • Set of efficient/ Pareto optimal trades
    • No more voluntary trade will take place.
the core of an economy
The Core of an Economy

Raspberries to Elizabeth

C

l

k

f

m

Blocked

by

Elizabeth

OE

n

Apples

to

Geoffrey

Apples

to

Elizabeth

Blocked

by

Geoffrey

I1e

Raspberries to Geoffrey

I1g

OG

A

The 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 .

marginal conditions for efficient trades1
Marginal Conditions for Efficient Trades
  • Core of economy
    • Set of equilibrium trades
    • Portion of contract curve
      • Between no-trade indifference curves
    • Individually rational
    • Cannot be blocked
a growing population and the core
A Growing Population and the Core
  • Economy – grows through replication
  • As we add agents
    • Set of core allocation – diminish
    • Points on original core – eliminated
the core of a four person economy
The core of a four- person economy

5

6

Raspberries to Elizabeth

C

n

z

f

m

Apples

to

Geoffrey

Apples

to

Elizabeth

5

2

1

2

1

2

3

8

7

2

Raspberries to Geoffrey

2

3

A

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

an economy with many agents
An Economy with Many Agents
  • Economy – grows larger
    • Set of core allocations – one point
  • Competitive behavior
    • Price-taking behavior
    • Individuals take prices as given
    • Based on the value of their endowments decide how much of each good to buy
  • Competitive Equilibrium
    • Set of prices that clear markets (QD=QS of each good)
    • Determined by the endowment and individual preferences
a competitive equilibrium
A Competitive Equilibrium

Raspberries to Elizabeth

f

C

e

Apples

to

Geoffrey

Apples

to

Elizabeth

Raspberries to Geoffrey

A

not a competitive equilibrium
Not A Competitive Equilibrium

Raspberries to Elizabeth

z

f

B

C

Apples

to

Geoffrey

y

Apples

to

Elizabeth

Raspberries to Geoffrey

D

A

Point e

conditions for competitive equilibrium
Conditions for Competitive Equilibrium
  • A Competitive Equilibrium is defined by a set of prices such that
    • For any good
    • Total Quantity demanded= Total Quantity Supplied
    • At those prices
conditions for competitive equilibrium1
Conditions for Competitive Equilibrium
  • To solve:
    • Find the demand for each good by each individual
      • Use the utility function
      • Individual income evaluated at the competitive prices
    • Calculate market demand by adding up all individual demand
    • Total supply is total amount of good i.
    • Set total demand = total supply