chapter ten general equilibrium and economic welfare

Chapter Ten

General Equilibrium and Economic Welfare

© 2007 Pearson Addison-Wesley. All rights reserved. 10–2

焦點新聞

• 政院稅改方案大幅調降營所稅綜所稅• 鋼價狂漲暫不限制出口

–由於國內外鋼價急驟上揚，近期陸續有營造等相關業界建議政府希望限制廢鋼、鋼筋等出口。經濟部工業局表示，按照 WTO精神，禁止出口有可能損及台灣形象，同時也會打亂台灣既有鋼鐵產銷體系，造成業界的反彈，甚至危及單軋廠的生存，因此，是否禁止出口尚未定論。


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


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


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.

© 2007 Pearson Addison-Wesley. All rights reserved.

Figure 10.1 Relationship Between the Corn and Soybean Markets Corn, Billion bushels per year

e0c

e1c

e3c

D0c

D1c

S3c

S0c

$2.15

$1.9171$1.9057

8.448.26138.227

(a) Corn Market

Soybeans, Billion bushels per year

e0s

e2s

e4s

D4s

D2s

S4s

S2s

S0s

D0s

$4.12

$3.8325$3.8180

2.072.05142.0505

(b) Soybean Market


Minimum Wages With Incomplete Coverage

• Minimum Wages With Incomplete Coverage– In the absence of a minimum wage, the

equilibrium wage is . – Applying a minimum wage, , 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 .

1w

2w

w


Figure 10.2 Minimum Wage with Incomplete Coverage

(b) Uncovered Sector

w1

w2

Lu2Lu

1

Du

Su

Lu, Annual hours

(a) Covered Sector

w1

w–

Lc2 Lc

1

Dc

Lc, Annual hours L, Annual hours

(c) Total Labor Market

w1

S

Lc1 Lu

1L1 = +

D


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


Figure 10.3 Endowments in an Edgeworth Box

I1j

(a) Jane’s Endowment

Jane’s candy20

30

Candy, Bars

0j

ej


Figure 10.3 Endowments in an Edgeworth Box (cont’d)

I1d

(b) Denise’s Endowment

Denise’s candy60

20

Candy, Bars

0d

ed


Figure 10.3 Endowments in an Edgeworth Box (cont’d)

(c) Edgeworth Box

Jane’s candy

Denise’s candy

C

A

B

20 40

608050

30e

a

f

8050

30

20

0j

0d

I1j

I1d


Mutually Beneficial Trades

• We make four assumptions about their tastes and behavior:– Utility maximization– Usual-shaped indifference curves– Nonsatiation– No interdependence


Figure 10.4 Contract Curve

Jane’s candy

Denise’s candy

20 40

608050

30

20

40g

c

d

e

b

a

fB

8050

30

20

Contract curve

0j

0d

I1jI2j

I3j

I4j

I 0d

I1dI2d

I3d



• Trades are possible where indifference curves intersect because marginal rates of substitution are unequal.



• To summarize, we can make four equivalent statements about allocation :1.The indifference curves of the two parties

are tangent at .2.The parties’ marginal rates of substitution

are equal at .3.No further mutually beneficial trades are

possible at .4.The allocation at is Pareto efficient: One

party cannot be made better off without harming the other.

f

f

f

ff



• Indifference curves are also tangent at Bundles , , and , so these allocations, like , are Pareto efficient.

• By connecting all such bundles, we draw the contract curve: the set of all Pareto-efficient bundles.

bf

c d


Bargaining Ability

• All the allocations in area B are beneficial.

• Where will they end up on the contract curve between and ?

• That depends on who is better at bargaining.

b c


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.


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.


Competitive Equilibrium

• The initial endowment is .

a) If, along the price line facing Jane and Denise, and , they trade to point , where Jane’s indifference curve, , is tangent to the price line and to Denise’s indifference curve, .

$2wp $1cp

2jI

2dI

f

e


Competitive Equilibrium

b) No other price line results in an equilibrium, If and , 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.

$1.33wp $1cp


(a) Price Line That Leads to a Competitive Equilibrium

Jane’s candy

Denise’s candy

Price line

20 40

608050

30

40

20

40

e

a

f

8050

30

20

0j

0d

I1j

I2j

I1d

I2d

Figure 10.5 Competitive Equilibrium


Figure 10.5 Competitive Equilibrium (cont’d)

80

(b) Prices That Do Not Lead to a Competitive Equilibrium

Jane’s candy

Denise’s candy

Price line

20 30

608050

30

45

22

43

e

a

j

d

6050

32

20

0j

0d

I1j

I2j

I1d

I2d


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:

• We have demonstrated the First Theorem of Welfare Economics:

Any competitive equilibrium is Pareto efficient.

cj d

w

pMRS MRS

p


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).


Production and Trading

Comparative Advantage

• Production Possibility Frontier– Jane’s production possibility frontier (

; Chapter 7), which shows the maximum combinations of wood and candy that she can produce from a given amount of input.

jPPF




• Marginal Rate of Transformation– The slope of the production possibility

frontier is the marginal rate of transformation (MRT).




• comparative advantage– the ability to produce a good at a lower

opportunity cost than someone else




• Benefits of Trade– Because of the difference in their marginal

rates of transformation, Jane and Denise can benefit from a trade.



• Comparative Advantage and Production Possibility Frontiers.

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.

jPPF



b) Denise’s production possibility frontier, , has an MRT of .

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.

dPPF1

2


Figure 10.6 Comparative Advantage and Production Possibility Frontiers

PPFd

Candy, Bars

3

2

(b) Denise

1

62

MRT = – 1–2

MRT = –2

6

PPFj

Candy, Bars

2

(a) Jane

1

2 3

PPF

MRT =–2(Jane)

Candy, Bars

6

9

(c) Joint Production

1

96

MRT = – (Denise)1–2

1



• Optimal Product Mix.– The optimal product mix, , 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, , equals the slope of the PPF.

a

/c fp p


Figure 10.7 Optimal Product Mix

I 1

I 2

Price line

PPF

1

80

50

Candy, Bars

a

b

1–2

–



• 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.

c

w

MCMRT

MC



• 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):

c

w

pMRS

p



• If candy and wood are sold by competitive firms, and in the competitive equilibrium, the MRS equals the relative prices, which equals the MRT:

w wp MCc cp MC

c

w

pMRS MRT

p



• 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


Figure 10.8 Competitive Equilibrium

Ij

Id

Jane’s candy

Price line

Price line

PPF

40

40

1

1–2

–

1

80

40

20 30

50

Candy, Bars0j

f

a

1–2

–

Denise’s candy


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.


Efficiency

• We can use the Pareto principle to rank allocations or government policies that alter allocations.

• The Pareto criterion ranks allocation over allocation if some people are better off at and no one else is harmed.

• If that condition is met, we say that is Pareto superior to .

xy

x

xy


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.


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.


Equity

• Who decides on the welfare function?

• In most countries, government leaders make decisions about which allocations are most desirable.


Figure 10.9 Welfare Maximization

UPF

c

a

b

(a)

Jane’s utility

W 1 W 2

W 3

UPF

e

(b)

Jane’s utility

W 1 W 2 W 3


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.


Equity

• Unfortunately, sometimes voting does not work well, and the resulting social ordering of allocations is not transitive.


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.


Equity

– If everyone prefers Allocation to Allocation , should be socially preferred to .

– Society’s ranking of and should 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.

ab a

ba b


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.


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.


Equity

• If is the utility of Individual and there are people, the utilitarian welfare function is

• A generalization of the utilitarian approach assigns different weights to various individuals’ utilities.

• This generalized utilitarian welfare function is

iUn

i

1 2 . nW U U U

1 1 2 2 . n nW U U U


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

Rawls’s rule leads to a relatively egalitarian distribution of goods.

1 2min , , , . nW U U U


Efficiency Versus Equity

• Given a particular social welfare function, society might prefer an inefficient allocation to an efficient one.



• 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.



• 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.

chapter ten general equilibrium and economic welfare

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