

The Problem of Exchange

Given an economy where individuals are allocated a certain
amount of goods, we will
o Investigate barter exchange
o define equilibrium trade
o Investigate the emergence of competitive markets

Primitive, two-person economy
o Geoffrey, Elizabeth
o Harvest & gather fruit
• Apples, raspberries
o Voluntary trade – beneficial
o Options
• Consume all
• Trade some
3

Edgeworth box
o Graphical device to analyze the process of trade
o Its size equals the total amount of goods
o A point in the box represents a possible/ feasible allocation of
goods
4

No-trade allocation
o Feasible allocation
o No trade
o Individuals consume their own harvest
5
Apples
10
0
8
Raspberries
Dimensions of the Edgeworth box represent total amount of each good. There
are 10 apples and 8 raspberries
6
Elizabeth
Raspberries to Elizabeth
6
10
8
0
f
2
Apples
to
Elizabeth
Apples
to
Geoffrey
I1e
I1g
0
Geoffrey
2
8
Raspberries to Geoffrey
7

Equilibrium allocation
o Once reached
o No incentive to further trade

Block
o Prevent a trade
o Coalition – each gets more

Individually rational trade
o Higher utility - than no trade
8
10
6
4
Raspberries to Elizabeth
0
f
2
8
Apples
to
6
Geoffrey
g
i
4
Apples
to
Elizabeth
j
h
I3g I3e
I1g
0
I2g
I2e
I1e
2
4
8
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 .
9

Pareto-optimal (efficient) allocation
o Allocation of goods across people
o 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
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
Efficient allocation
o Tangency point - indifference curves
o Marginal rates of substitution - same

Contract curve
o Curve in Edgeworth box
o All efficient trades
11
Raspberries to Elizabeth
l
Apples
to
Geoffrey
OE
Apples
to
Elizabeth
k
OG
Raspberries to Geoffrey
The contract curve is a locus of all efficient trades, i.e., of all tangency points
12

Contract curve
o Set of efficient / Pareto optimal trades
o No more voluntary trade will take place.
13
Raspberries to Elizabeth
C
Blocked
by
Elizabeth
f
Apples
to
Geoffrey
Blocked
by
Geoffrey
A
OE
Apples
to
Elizabeth
n
k
OG
l
I1e
m
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 .
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
Core of economy
o Set of equilibrium trades
o Portion of contract curve
• Between no-trade indifference curves
o Individually rational
o Cannot be blocked
15

Economy – grows through replication

As we add agents
o Set of core allocation – diminish
o Points on original core – eliminated
16
5
6
Apples
to
Geoffrey
f
8
5
Raspberries to Elizabeth
n
z
1
2
C
2
Apples
to
Elizabeth
3
7
m
A
2
1
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3
Raspberries to Geoffrey
G1 and G2 will negotiate with E2 a better deal: Each G offers 2.5 apples and
gets in return 0.5 raspberries
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
Economy – grows larger
o Set of core allocations – one point

Competitive behavior
o Price-taking behavior
o Individuals take prices as given
o Based on the value of their endowments decide how much of each
good to buy

Competitive Equilibrium
o Set of prices that clear markets (QD=QS of each good)
o Determined by the endowment and individual preferences
18
Raspberries to Elizabeth
C
Apples
to
Geoffrey
f
Apples
to
Elizabeth
A
Raspberries to Geoffrey
19
Raspberries to Elizabeth
B
Apples
to
Geoffrey
C
f
Apples
to
Elizabeth
y
A
Raspberries to Geoffrey
D
Point e
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
A Competitive Equilibrium is defined by a set of prices such
that
o For any good
o Total Quantity demanded= Total Quantity Supplied
o At those prices
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
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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