the problem of exchange. given an economy where individuals are allocated a certain amount of...
TRANSCRIPT
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
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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
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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
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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
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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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