General Equilibrium and Economic Welfare

Perloff Chapter 10

General Equilibrium

• Partial equilibrium– Changes in equilibrium are analysed in one (or

a few) markets in isolation.– Prices and quantities in ‘unrelated’ markets are

held fixed.

• General equilibrium– The study of how equilibrium is attained in all

markets simultaneously.

GE in Corn and Soya Beans

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

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

Pric

e, $

per

bus

hel

Pric

e, $

per

bus

hel

Min. wages with incomplete coverage

L, Annual hours

(a) Covered Sector (b) Uncovered Sector (c) Total Labor Market

w1 w1 w1

w2

w–

S

Lc2 Lc

1 Lu2Lu

1 Lc1 Lu

1L1 = +

D c Du

S u

D

Lc , Annual hours Lu , Annual hours

w, W

age

per

hour

w, W

age

per

hour

w, W

age

per

hour

Trade Between People: The Edgeworth Box

I1jI1d

(a) Jane’s Endowment

Jane’s candy20

30

Candy, Bars

0j

ej

(b) Denise’s Endowment

Denise’s candy60

20

Candy, Bars

0d

edFir

ewo

od,

Co

rds

Fir

ewo

od,

Co

rds

(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

Jane

’s w

ood

Den

ise’s w

oo

d

Obtaining the contract curve

Jane’s candy

Denise’s candy

20 40

608050

30

20

40

g

c

d

e

b

a

f

B

8050

30

20

Contract curve

0j

0d

I1j

I 2jI 3j

I 4j

I 0d

I1d

I 2d

I 3d

Jane

’s w

ood

Denise’s w

ood

Four equivalent statements about points on the contract curve

• The indifference curves are tangential.

• The marginal rates of substitution are equal.

• No further mutually beneficial trades are possible.

• The allocation is Pareto efficient: One person cannot be made better off without making the other worse off.

Price that doesn’t lead to equilibrium

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

I 2j

I1d

I 2d

Denise’s w

ood

Jane

’s w

ood

Price that leads to equilibrium(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

I 2j

I1d

I 2d

Jane

’s w

ood

Denise’s w

ood

• The competitive equilibrium is Pareto efficient.

• Any efficient allocations can be achieved by competition.– Any point on the contract curve can be achieved by

trade along the appropriate price line.– Achieving the desired point may involve some

redistribution (value judgements required)

Theorems of Welfare Economics

cj d

w

pMRS MRS

p

Production Possibilities

I 1

I 2

PPF

80

50

Candy, Bars

a

b

Fir

ew

oo

d,

Co

rds

c

w

MCMRS MRT

MC

Competition Ensures Efficiency

c

c c

w w

c c

w w

c

w

pMRS

p

p MC

p MC

p MCMRT

p MC

pMRS MRT

p

The whole picture

c c

w w

p MCMRT

p MC

’

Price line

PPF

1

80 Candy, Bars0j

1–2

–

Fire

wo

od

, C

ord

s

50a

Janes candy

Jan

e’s

wo

od

40

Ij

Id

Price line

40

1

1–2

–

40

20 30f

Denise’s candy

De

nise

’s wo

od

c

w

pMRS

p

Is efficiency enough?

• Many policies make somebody better off at the expense of somebody else.

• Producer surplus plus consumer surplus.– As long as producers gain more than consumers

lose, its efficient eg. first degree price discrimination.

– Weights producers and consumers equally.

Utility possibilities frontier

UPF

Jane’s utility

Den

ise’

s ut

ility

Jane s candy

Denise’s candy

0j

0d

Jane

’s w

ood

Denise’s w

ood

Welfare maximisation

UPF UPF

c

a

b

e

(a)

Jane’s utility

W 1 W 2

W 3

(b)

Jane’s utility

W 1 W 2 W 3

Den

ise’

s ut

ility

Den

ise’

s ut

ility

How do we arrive at a social preference ranking

• Individuals rankings are transitive• We need a rule which allows us to convert individual rankings into a social

ranking.– Majority voting

• 2 prefer a to b, 2 prefer b to c, transitivity would require 2 to prefer a to c.• But 2 prefer c to a.

Voting with non-transitive prefrences

• With non-transitive preferences result depends on order the vote is taken in.• a compared to b then compare winner to c

– a chosen in first vote– c chosen in second vote

• c compared to a then compare winner to b– c chosen in first vote– b chosen in second vote

Arrow’s impossibility theorem

• Desirable properties of a social preference ordering.– Complete– If everyone prefers a to b, the social ranking should do

the same– Social ranking of a to b should not depend on the what

other alternatives are available– Dictatorship is not allowed

• No rule exists which produces a ranking that always satisfies these properties