Transcript Chapter 21

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
General Equilibrium and Welfare
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Partial vs. General equilibrium analysis
Partial Equilibrium: narrow focus
General equilibrium: framework of analysis that considers
the working of several markets together
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General Equilibrium model 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
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Primitive, two-person economy
o Geoffrey, Elizabeth
o Harvest & gather fruit
• Apples, raspberries
o Voluntary trade – beneficial
o Options
• Consume all
• Trade some
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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
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No-trade allocation
o Feasible allocation
o No trade
o Individuals consume their own harvest
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Apples
10
0
8
Raspberries
Dimensions of the Edgeworth box represent total amount of each good. There
are 10 apples and 8 raspberries
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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
8
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Equilibrium allocation
o Once reached
o No incentive to further trade
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Block
o Prevent a trade
o Coalition – each gets more
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Individually rational trade
o Higher utility - than no trade
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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 .
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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.
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Not an efficient allocation
o Indifference curves cross
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Efficient allocation
o Indifference curves – tangent
o MRS the same for both
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Contract curve
o Curve in Edgeworth box
o All efficient trades
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0J
U J1
U J2
Contract Curve
US3
U J3
US2
US1
0S
0J
U J1
U J2
US3
U J3
US2
US1
0S
For any initial allocation we can see where trade may lead.
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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
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0J
F is the
“fair”
allocation
and E is
the initial
allocation.
U J1
U J2
F
US3
U J3
US2
E
US1
0S
It is not possible with voluntary exchange. Coercion would
make Smith better off but Jones worse off.
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Assume a simple economy comprised of
o Identical consumers
o 2 Firms
o Two goods X and Y
o Consumers own all factors of production/ all firms
Quantity of Y
PPF: shows the combinations of X and Y
that can be produced if resources are used
efficiently
It also shows the relative opportunity cost
of good X in terms of Y
Quantity of X
Quantity of Y
The indifference curves represent
consumer preferences: “demand curve”
U3
U2
U1
Quantity of X
Point E is economically efficient: it both is
productively efficient (on the PPF) and it
maximizes utility.
Quantity of Y
F
Compare point E to point F
E
U3
U2
U1
Quantity of X
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The slope of the PPF shows the opportunity cost of X in
terms of Y. As more X is produced, the opportunity cost
rises. The slope is the rate of product transformation.
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The slope of the indifference curve shows the rate at which
consumers are willing to trade one good for another in
consumption. The slope is the marginal rate of
substitution.
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At the efficient point the RPT = MRS
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We now have an idea of where we want to be: point E.
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How do we get there?
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First Welfare Theorem says that a perfectly competitive
price system will bring about an economically efficient
allocation of resources.
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How to find a perfect competitive equilibrium?
o It is a price vector that clears the market
o Given the prices of the two goods
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Producers supply an amount of x and y
Consumers demand an amount of x and an amount of y
Demand for x by all consumers= total production of x
Demand for y by all consumers= total production of y
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Consumers own all resources
Consumers offer resources to firms
Firms produce goods and sell them
Revenue from sales used to pay all resource owners
Consumers earn an income where
Income = value of goods
Quantity of Y
Firms will maximize
profits by producing
here.
𝑌
𝑋
Quantity of X
• Lets assume prices for
both goods,𝑃𝑋1 and 𝑃𝑌1
and see if these prices
constitute a perfect
competitive equilibrium
• The prices can be
represented graphically by
many straight lines with a
slope -𝑃𝑋1 /𝑃𝑌1
• Firms choose a
combination of X and Y
that maximizes Profit
• All points on the PPF cost
the same, since all
resources are used.
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Total product of firms represent income to consumers
Consumers income is
M= 𝑃𝑋1 𝑋+ 𝑃𝑌1 𝑌
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The budget equation
𝑃𝑋1 𝑋+ 𝑃𝑌1 𝑌 = 𝑀
𝑃𝑋1 𝑋+ 𝑃𝑌1 𝑌 = 𝑃𝑋1 𝑋+ 𝑃𝑌1 𝑌
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The budget line has a slope of -𝑃𝑋1 /𝑃𝑌1 and goes through
point 𝑋 , 𝑌
Quantity of Y
The budget line for
consumers:
𝑌
• Represents all
points possible to
consume at the
price ratio
• Goes through the
point of
production of
firms
𝑋
Quantity of X
Quantity of Y
Consumers will
want to consume
at this point
𝑌
U3
U2
𝑋
Quantity of X
• Consumers
maximize utility
given the prices
observed and
their income
Quantity of Y
𝑌
U3
U2
Excess demand for X
𝑋
Quantity of X
Quantity of Y
Excess
supply of Y
U3
U2
Quantity of X
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What’s the problem?
o At the initial set of prices the decisions of firms and consumers
don’t match up.
o There is an excess demand for X and an excess supply of Y.
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What will happen to the prices of X and Y?
o The price of X will increase and the price of Y will decrease.
o The budget line will pivot and become steeper.
Quantity of Y
Consumers will want to consume at
this point
Firms will maximize
profits by producing
here.
U3
U2
But we still have excess demand for X and excess
supply of Y
Quantity of X
Quantity of Y
Consumers will want to consume at
this point
Firms will maximize
profits by producing
here.
U3
U2
Quantity of X
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At equilibrium:
o Firms are maximizing profits.
o Given the income consumers earn from that level of production
consumers are maximizing utility.
o At equilibrium the amount of X and Y producers wish to supply is
equal to the amount of X and Y that consumers demand.
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The natural effort of every individual to better his own
condition, when suffered to exert itself with freedom and
security, is so powerful a principle that it is alone, and
without any assistance, not only capable of carrying on the
society to wealth and prosperity, but of surmounting a
hundred impertinent obstructions with which the folly of
human laws too often encumbers its operations.
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What do we mean by “market failure”?
Imperfect Competition
o A market in which some buyers and/or sellers have some influence on the
prices of goods and services
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Externalities
o The effect of one party’s economic activities on another party that is not
taken into account by the price system (pollution)
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Public Goods
o Goods that are both non-exclusive and non-rival
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Imperfect Information