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Chapter Ten

General Equilibrium

and Economic

Welfare

© 2009 Pearson Addison-Wesley. All rights reserved. 10-2

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

Corn and soybean markets using supply

and demand curves estimated by Holt

(1992).

© 2009 Pearson Addison-Wesley. All rights reserved.

Figure 10.1

Relationship

Between the

Corn and

Soybean

Markets

if demand for

corn decreased

….P

rice

, $

pe

rbu

sh

el

Corn, Billionbushels peryear

$2.15

$1.9171$1.9057

8.448.26138.227

(a) Corn Market

Pri

ce, $

pe

rbu

sh

el

Soybeans, Billionbushels peryear

$4.12

$3.8325$3.8180

2.072.05142.0505

(b) Soybean Market

S0

c

D0

c

D1

c

S3

c

e0

c

e3

ce1

c

S0

s

e0

s

D0

s

S2

s

S4

s

e2

s

e4

s

D2

s

D4

s


Table 10.1 Adjustment in the Corn

and Soybean Markets


Minimum Wages with Incomplete

Coverage

Result of partial-equilibrium analysis in

Chapter 2:

the minimum wage causes the quantity of

labor demanded to be less than the

quantity of labor supplied.

Workers who lose their jobs cannot find work

elsewhere, so they become unemployed.


Minimum Wages with Incomplete

Coverage (cont).

The story changes substantially if the

minimum wage law covers workers in

only some sectors of the economy.

When the U.S. minimum wage law was

first passed in 1938 it drove workers out

of manufacturing and other covered

industries into agriculture, which the law

did not cover. Why?


Figure 10.2 Minimum Wage with

Incomplete Coveragew

,W

age p

er

hour

(a) Covered Sector

w1

w–

Dc

Lc, Annual hours

w,W

age p

er

hour

(b) Uncovered Sector

w1

w2

Du

Su

Lu, Annual hours

w,W

age p

er

hour

L, Annual hours

(c) Total Labor Market

w1

S

L1

= +

D

Lc2 L

c1 L

u1 L

u2 L

u1L

c1


Solved Problem 10.1

After the government starts taxing the

cost of labor by τ per hour in a covered

sector only, the wage that workers in

both sectors receive is w, but the wage

paid by firms in the covered sector is w +

τ. What effect does the subsidy have on

the wages, total employment, and

employment in the covered and

uncovered sectors of the economy?


Solved Problem 10.1


Trading Between Two People: Scenario

Jane and Denise live near each other in the wilds of Massachusetts when a snowstorm strikes, isolating them from the rest of the world.

They must either trade with each other or consume only what they have at hand.

Collectively, they have 50 cords of firewood and 80 bars of candy and no way of producing more of either good.


Trading Between Two People:

Endowments

Endowment - an initial allocation of

goods

Jane’s endowment is 30 cords of

firewood and 20 candy bars.

Denise’s endowment is 20 (= 50 − 30)

cords of firewood and 60 (= 80 − 20)

candy bars.

So Jane has relatively more wood, and

Denise has relatively more candy.


Figure 10.3a Endowments in an

Edgeworth Box


Figure 10.3b Endowments in an

Edgeworth Box


Figure 10.3c Endowments in an

Edgeworth Box


Mutually Beneficial Trades

Four assumptions about their tastes and

behavior:

Utility maximization.

Usual-shaped indifference curves.

Nonsatiation.

No interdependence.


Figure 10.4 Contract Curve


Mutually Beneficial Trades

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.


Contract Curve

contract curve - the set of all Pareto-

efficient bundles


Solved Problem 10.2

Are allocations a and g in Figure 10.4

part of the contract curve?


Competitive Exchange

Two desirable properties:

The competitive equilibrium is efficient.

First Theorem of Welfare Economics

Any efficient allocations can be

achieved by competition.

Second Theorem of Welfare Economics


Competitive Equilibrium

If there were a large number of people

with tastes and endowments like Jane’s

and a large number of people with

tastes and endowments like Denise’s,

each person would be a price taker in

the two goods.


Figure 10.5a Competitive Equilibrium


Figure 10.5b Competitive

Equilibrium


Competitive Equilibrium (cont).

In a competitive market, prices adjust

until the quantity supplied equals the

quantity demanded.


The Efficiency of Competition

In a competitive equilibrium:

Thus, we have demonstrated the First Theorem

of Welfare Economics:

Any competitive equilibrium is Pareto efficient.

d

w

cj MRS

p

pMRS


Obtaining Any Efficient Allocation

Using Competition

Any Pareto-efficient bundle x can be obtained

as a competitive equilibrium if the initial

endowment is x.

That allocation can also be obtained as a

competitive equilibrium if the endowment lies

on a price line through x, where the slope of

the price line equals the marginal rate of

substitution of the indifference curves that are

tangent at x.

Thus, …..


Obtaining Any Efficient Allocation

Using Competition

we’ve demonstrated the Second

Theorem of Welfare Economics:

Any Pareto-efficient equilibrium can b obtained by competition, given an

appropriate endowment.


Comparative Advantage

Scenario: Jane and Denise can produce

candy or chop firewood using their own

labor. They differ, however, in how much

of each good they produce from a day’s

work.


Production Possibility Frontier.

Jane can produce either 3 candy bars or

6 cords of firewood in a day.

Denise can produce up to 3 cords of

wood or 6 candy bars in a day.


Production Possibility Frontier (cont).

Production Possibility Frontier -

shows the maximum combinations of

two goods that can be produced from a

given amount of input.

The slope of the production possibility

frontier is the marginal rate of transformation (MRT).


Figure 10.6 Comparative Advantage

and Production Possibility Frontiers


Production Possibility Frontier (cont).

comparative advantage - the ability to

produce a good at a lower opportunity

cost than someone else.

Because of the difference in their

marginal rates of transformation, Jane

and Denise can benefit from a trade.


Solved Problem 10.3

How does the joint production possibility

frontier in panel c of Figure 10.6 change

if Jane and Denise can also trade with

Harvey, who can produce 5 cords of

wood, 5 candy bars, or any linear

combination of wood and candy in a

day?


Solved Problem 10.3


Figure 10.7 Optimal Product Mix


The Number of Producers

Because the PPF is concave, the marginal rate

of transformation decreases (in absolute value)

as we move up the PPF.

Also,

where MCc and MCw are the marginal costs of

producing candy and wood respectively.

w

c

MC

MCMRT


Efficient Product Mix

If a single person were to decide on the

product mix, that person would pick the

allocation of wood and candy along the

PPF that maximized his or her utility.

For each consumer:

MRS = MRT,

if the economy is to produce the optimal

mix of goods for each consumer.


Competition

Each consumer picks a bundle of goods so,

consumption efficiency - we can’t redistribute

goods among consumers to make one consumer

better off without harming another one.

the competitive equilibrium lies on the contract curve.

w

c

P

PMRS


Competition (cont)

If candy and wood are sold by competitive firms,

pc = MCc

pw = MCw

Therefore,

MRSP

PMRT

P

PMRT

MC

MC

P

P

w

c

w

c

w

c

w

c


Competition (cont)

Since,

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.

MRSP

PMRT

w

c


Figure 10.8 Competitive

Equilibrium


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.


Application Wealth Distribution in the

United States



United States (a)



United States (b)


Efficiency

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.

Any policy change that leads to a Pareto-

superior allocation must increase W (welfare).

However, some policy changes that increase W are not Pareto superior: There are both winners and losers.


Equity

social welfare function - combines

various consumers’ utilities to provide a

collective ranking of allocations.

Sort of like a utility function for society.

Utility possibility frontier (UPF): the set

of utility levels corresponding to the

Pareto efficient allocations along the

contract curve.


Figure 10.9 Welfare Maximization


Application An Unequal World


Voting

Sometimes voting does not work well,

and the resulting social ordering of

allocations is not transitive.


Table 10.2 Preferences over

Allocations of Three People


Arrow’s Impossibility Theorem.

A social welfare function should satisfy the following criteria:

Social preferences should be complete and transitive, like individual preferences.

If everyone prefers Allocation a to Allocation b, a should be socially preferred to b.

Society’s ranking of a and b should depend only on individuals’ 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.


Arrow’s Impossibility Theorem (cont).

It is impossible to find a social decision-

making rule that always satisfies all of

these criteria.

Result indicates that democratic decision making may fail—not that democracy must

fail.


Social Welfare Functions

Utilitarian philosophers: suggested that

society should maximize the sum of the

utilities of all members of society.

Their social welfare function is the sum of

the utilities of every member of society.

If Ui is the utility of Individual i and there

are n people, the utilitarian welfare

function is:

W = U1 + U2 + . . . + Un.


Social Welfare Functions (cont).

The Rawlsian welfare function is:

W = min {U1, U2, . . . , Un}.

Rawls’ rule leads to a relatively egalitarian

distribution of goods.


Cross-Chapter Analysis: Outsourcing

and the World Trade Organization

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