Chapter Ten
General
Equilibrium
and Economic
Welfare
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口尚未定論。
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10–2
General Equilibrium
and Economic Welfare
• In this chapter, we examine five main
topics
– General equilibrium
– Trading between two people
– Competitive exchange
– Production and trading
– Efficiency and equity
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10–3
General Equilibrium
• partial-equilibrium analysis
– an examination of equilibrium and changes
in equilibrium in one market in isolation
• general-equilibrium analysis
– the study of how equilibrium is determined
in all markets simultaneously
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10–4
Feedback Between Competitive
Markets
• Sequence of Events
– We can demonstrate the effect of a shock
in one market on both markets by tracing
the sequence of events in the two markets.
– Whether these steps occur nearly
instantaneously or take some times
depends on how quickly consumers and
producers react.
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10–5
Figure 10.1
Relationship
Between the
Corn and
Soybean
Markets
(a) Corn Market
Sc
0
Sc
3
ec
0
$2.15
Dc
0
ec
1
$1.9171
$1.9057
ec
3
Dc
1
8.227 8.2613
8.44
Corn, Billion bushels per year
(b) Soybean Market
Ss
0
es
0
$4.12
Ds
0
Ss
2
Ss
4
es
$3.8325
$3.8180
2
es
4
Ds
2
Ds
4
© 2007 Pearson Addison-Wesley. All rights reserved.
2.0505 2.0514
2.07
Soybeans, Billion bushels per year
Minimum Wages With Incomplete
Coverage
• Minimum Wages With Incomplete
Coverage
– In the absence of a minimum wage, the
equilibrium wage is w1 .
– Applying a minimum wage, w, to only one
sector causes the quantity of labor
services demanded in the covered sector
to fall.
– The extra labor moves to the uncovered
sector, driving the wage there down to w2.
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10–7
Figure 10.2 Minimum Wage with
Incomplete Coverage
(a) Covered Sector
(c) Total Labor Market
(b) Uncovered Sector
S
w
–
Su
w1
w1
w1
w2
Dc
L c2
L c1
Lc, Annual hours
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Du
Lu1 Lu2
Lu, Annual hours
D
L1 = Lc1+ Lu1
L, Annual hours
10–8
Trading Between Two People
• Endowments
– an initial allocation of goods
• Pareto efficient
– describing an allocation of goods or
services such that any reallocation harms
at least one person
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10–9
Figure 10.3 Endowments in an
Edgeworth Box
(a) Jane’
s Endowment
ej
30
I1j
0j
Jane’
s candy
20
Candy, Bars
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10–10
Figure 10.3 Endowments in an
Edgeworth Box (cont’d)
(b) Denise’
s Endowment
ed
20
0d
Denise’
s candy
I1d
60
Candy, Bars
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10–11
Figure 10.3 Endowments in an
Edgeworth Box (cont’d)
(c) Edgeworth Box
80
50
Denise’
s candy
60
0d
A
I1d
e
30
20
f
B
C
I1j
a
0j
Jane’
s candy
30
20
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40
50
80
10–12
Mutually Beneficial Trades
• We make four assumptions about their
tastes and behavior:
– Utility maximization
– Usual-shaped indifference curves
– Nonsatiation
– No interdependence
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10–13
Figure 10.4 Contract Curve
80
50
60
Denise’
s candy
40
g
I 0d
I 1d
30
d
Contract curve
I 4j
e
20
I 2d
c
I 3d
f
20
B
b
I 1j
a
0j
0d
Jane’
s candy
20
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40
I 2j
I 3j
30
50
80
10–14
Mutually Beneficial Trades
•
Trades are possible where indifference
curves intersect because marginal
rates of substitution are unequal.
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10–15
Mutually Beneficial Trades
• To summarize, we can make four
equivalent statements about allocation f :
1.The indifference curves of the two parties
are tangent at f .
2.The parties’ marginal rates of substitution
are equal at f .
3.No further mutually beneficial trades are
possible at f .
4.The allocation at f is Pareto efficient: One
party cannot be made better off without
harming the other.
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10–16
Mutually Beneficial Trades
• Indifference curves are also tangent at
Bundles b , c, and d , so these
allocations, like f , are Pareto efficient.
• By connecting all such bundles, we
draw the contract curve: the set of all
Pareto-efficient bundles.
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10–17
Bargaining Ability
• All the allocations in area B are
beneficial.
• Where will they end up on the contract
curve between b and c ?
• That depends on who is better at
bargaining.
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10–18
Competitive Exchange
• The First Theorem of Welfare
Economics
– The competitive equilibrium is
efficient: Competition results in a
Pareto-efficient allocation—no one can
be made better off without making
someone worse off—in all markets.
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10–19
Competitive Exchange
• The Second Theorem of Welfare
Economics
– Any efficient allocations can be
achieved by competition: All
possible efficient allocations can be
obtained by competitive exchange,
given an appropriate initial allocation
of goods.
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10–20
Competitive Equilibrium
•
The initial endowment is e.
a) If, along the price line facing Jane
and Denise, pw  $2 and pc  $1 ,
they trade to point f , where Jane’s
2
indifference curve, I j , is tangent to
the price line and to Denise’s
indifference curve, I d2 .
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10–21
Competitive Equilibrium
b) No other price line results in an
equilibrium, If pw  $1.33 and pc  $1,
Denise wants to buy 12 (=32－20)
cords of firewood at these prices, but
Jane wants to sell only 8 (=30－22)
cords. Similarly, Jane wants to buy
10 (=30－20) candy bars, but Denise
wants to sell 17 (=60－43). Thus
these prices are not consistent with a
competitive equilibrium.
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10–22
Figure 10.5 Competitive Equilibrium
(a) Price Line That Leads to a Competitive Equilibrium
80
50
60
40
Denise’
s candy
0d
40
I1d
30
e
20
I2d
f
20
30
I2j
I1j
Price line
a
0j
Jane’
s candy
20
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40
50
80
10–23
Figure 10.5 Competitive Equilibrium
(cont’d)
(b) Prices That Do Not Lead to a Competitive Equilibrium
80
50
60
43
Denise’
s candy
0d
45
I1d
30
e
I2d
20
j
22
d
32
I2j
I1j
Price line
a
0j
Jane’
s candy
20
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30
60
50
80
10–24
The Efficiency of Competition
• In a competitive equilibrium, the slope
(MRS) of each person’s indifference
curve equals the slope of the price line,
so the slopes of the indifference curves
are equal:
pc
MRS j  
 MRSd
pw
• We have demonstrated the First
Theorem of Welfare Economics:
Any competitive equilibrium is Pareto efficient.
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10–25
The Efficiency of Competition
• The first welfare theorem tells us that
society can achieve efficiency by
allowing competition.
• The second welfare theorem adds that
society can obtain the particular efficient
allocation it prefers based on its value
judgments about equity by appropriately
redistributing endowments (income).
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10–26
Production and Trading
Comparative Advantage
• Production Possibility Frontier
– Jane’s production possibility frontier
( PPF j ; Chapter 7), which shows the
maximum combinations of wood and candy
that she can produce from a given amount
of input.
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10–27
Production and Trading
Comparative Advantage
• Marginal Rate of Transformation
– The slope of the production possibility
frontier is the marginal rate of
transformation (MRT).
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10–28
Production and Trading
Comparative Advantage
• comparative advantage
– the ability to produce a good at a lower
opportunity cost than someone else
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10–29
Production and Trading
Comparative Advantage
• Benefits of Trade
– Because of the difference in their marginal
rates of transformation, Jane and Denise
can benefit from a trade.
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10–30
Production and Trading
•
Comparative Advantage and
Production Possibility Frontiers.
j
PPF
a) Jane’s production possibility frontier,
,
shows that in a day, she can produce 6
cords of firewood or 3 candy bars or any
combination of the two. Her marginal rate
of transformation (MRT) is -2.
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10–31
Production and Trading
b) Denise’s production possibility
1
d

frontier, PPF , has an MRT of 2 .
c) Their joint production possibility
frontier, PPF, has a kink at 6 cords
of firewood (produced by Jane) and
6 candy bars (produced by Denise)
and is concave to the origin.
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10–32
Figure 10.6 Comparative Advantage
and Production Possibility Frontiers
(a) Jane
(c) Joint Production
(b) Denise
9
6
1
1
1
MRT = – –
2 (Denise)
PPF
6
MRT = –2
1
3
2
PPFj
2 3
Candy, Bars
2
MRT =
–2
(Jane)
PPFd
1
2
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1
MRT = – –
2
6
Candy, Bars
6
9
Candy, Bars
10–33
Comparative Advantage
• Optimal Product Mix.
– The optimal product mix, a , could be
determined by maximizing an individual’s
utility by picking the allocation for which an
indifference curve is tangent to the
production possibility frontier.
– It could also be determined by picking the
allocation where the relative competitive
price, pc / p f , equals the slope of the PPF.
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10–34
Figure 10.7 Optimal Product Mix
I2
Price line
–1
–
2
1
I1
PPF
a
50
b
80
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Candy, Bars
10–35
Comparative Advantage
• The marginal rate of transformation
along this smooth PPF tells us about
the marginal cost of producing one good
relative to the marginal cost of
producing the other good.
MCc
MRT  
MCw
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10–36
Comparative Advantage
• Each price-taking consumer picks a
bundle of goods so that the consumer’s
marginal rate of substitution equals the
slope of the consumer’s price line (the
negative of the relative prices):
pc
MRS  
pw
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10–37
Comparative Advantage
• If candy and wood are sold by
competitive firms, pc  MCc and pw  MCw
in the competitive equilibrium, the MRS
equals the relative prices, which equals
the MRT:
pc
MRS  
 MRT
pw
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10–38
Comparative Advantage
• Because competition ensures that the MRS
equals the MRT, a competitive equilibrium
achieves an efficient product mix: The rate at
which firms can transform one good into
another equals the rate at which consumers
are willing to substitute between the goods,
as reflected by their willingness to pay for the
two goods.
• In this competitive equilibrium, supply equals
demand in all markets.
• The consumers buy the mix of goods at f .
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10–39
Figure 10.8 Competitive Equilibrium
Price line
–1
–
2
1
PPF
s candy
40 Denise’
50
a
Ij
40
Id
f
20
30
–1
–
2
0j
Jane’
s candy
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40
Price line
1
80
Candy, Bars
10–40
Efficiency and Equity
• Role of the Government
– By altering the efficiency with which goods
are produced and distributed and the
endowment of resources, governments
help determine how much is produced and
how goods are allocated.
– By redistributing endowments or by
refusing to do so, governments, at least
implicitly, are making value judgments
about which members of society should get
relatively more of society’s goodies.
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10–41
Efficiency
• We can use the Pareto principle to rank
allocations or government policies that
alter allocations.
• The Pareto criterion ranks allocation x
over allocation y if some people are
better off at x and no one else is
harmed.
• If that condition is met, we say that x is
Pareto superior to y .
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10–42
Efficiency
• The Pareto principle cannot always be
used to compare allocations.
• Because there are many possible
Pareto-efficient allocations, however, a
value judgment based on interpersonal
comparisons must be made to choose
between them.
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10–43
Equity
• If we are unwilling to use the Pareto
principle or if that criterion does not
allow us to rank the relevant allocations,
we must make additional value
judgments to rank these allocations.
• A way to summarize these value
judgments is to use a social welfare
function that combines various
consumers’ utilities to provide a
collective ranking of allocations.
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10–44
Equity
• Who decides on the welfare function?
• In most countries, government leaders
make decisions about which allocations
are most desirable.
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10–45
Figure 10.9 Welfare Maximization
(b)
(a)
a
UPF
UPF
e
b
W3
c
W1
W2
Jane’
s utility
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W1
W2
W3
Jane’
s utility
10–46
Equity
• Voting.
– In a democracy, important government
policies that determine the allocation of
goods are made by voting.
– Such democratic decision making is often
difficult because people fundamentally
disagree on how issues should be resolved
and which groups of people should be
favored.
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10–47
Equity
• Unfortunately, sometimes voting does
not work well, and the resulting social
ordering of allocations is not transitive.
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10–48
Equity
• Arrow’s Impossibility Theorem.
• Arrow suggested that a socially
desirable decision making system, or
social welfare function, should satisfy
the following criteria:
– Social preferences should be complete
(Chapter 4) and transitive, like individual
preferences.
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10–49
Equity
– If everyone prefers Allocation a to
Allocation b, a should be socially preferred
to b.
– Society’s ranking of a and bshould
depend only on individual’s ordering of
these two allocations, not on how they rank
other alternatives.
– Dictatorship is not allowed; social
preferences must not reflect the
preferences of only a single individual.
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10–50
Equity
• Although each of these criteria seems
reasonable—indeed, innocuous—Arrow
proved that it is impossible to find a
social decision-making rule that always
satisfies all of these criteria.
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10–51
Equity
• Social Welfare Functions.
– How would you rank various allocations if
you were asked to vote?
• Jeremy Bentham (1748-1832) and his
followers (including John Stuart Mill),
the utilitarian philosophers, suggested
that society should maximize the sum of
the utilities of all members of society.
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10–52
Equity
• If U i is the utility of Individual i and there
are n people, the utilitarian welfare
function is
W  U1  U 2    U n .
• A generalization of the utilitarian
approach assigns different weights to
various individuals’ utilities.
• This generalized utilitarian welfare
function is
W  1U1   2U 2     nU n .
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10–53
Equity
• John Rawls (1971), a philosopher at
Harvard, believes that society should
maximize the well-being of the worst-off
member of society, who is the person
with the lowest level of utility.
• The Rawlsian welfare function is
W  min U1 ,U 2 , ,U n .
Rawls’s rule leads to a relatively
egalitarian distribution of goods.
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10–54
Efficiency Versus Equity
• Given a particular social welfare function,
society might prefer an inefficient
allocation to an efficient one.
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10–55
Efficiency Versus Equity
• Competitive equilibrium may not be very
equitable even though it is Pareto
efficient.
• Consequently, societies that believe in
equitable may tax the rich to give to the
poor.
• If the money taken from the rich is given
directly to the poor, society moves from
one Pareto-efficient allocation to
another.
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10–56
Efficiency Versus Equity
• Unfortunately, there is frequently a
conflict between a society’s goal of
efficiency and the goal of achieving an
equitable allocation.
• Even when the government
redistributes money form one group to
another, there are significant costs to
this redistribution.
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10–57