Chapter 10: General Equilibrium

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Chapter 10: General Equilibrium So far, we have studied a partial equilibrium analysis, wh

ich determines the equilibrium price and quantities in one market.

It ignores the repercussions of a price change in that market on equilibrium prices and quantities in other markets.

A general equilibrium analysis traces the effects of a change in demand or supply in one market on equilibrium prices and quantities in all markets. Note that if there are n goods, Xi

d=Xid(p1, p2, ……pn, Y).

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A general equilibrium exists when prices have adjusted to a change in either demand or supply so that quantities demanded and quantities supplied are equalized in all markets.

Used often in simulating the effect of policy intervention in trade analysis and environment literature.

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(0) Initial eq.: ec0, es

0

(1) An external shock to the corn demand, shifting

the demand from DC0 shifts

to DC1, causing PC to fall

(ec1)

(2) Consumers substitute toward corn, away from soybean, reducing the demand for soybean from Ds

0 to Ds2

Example: Corn & Soybean Markets

S

DC0

Corn Market

SSoybean Market

DC1

DS1

DS2

ec0

es0

ec1

es1

1

2Ps0

Pc1

Pc0

Ps1

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(3) Because the price of corn decreased relatively more than the price of soybean did, producers shift away from corn to soybeans, shifting the soybean supply curve to the right, reaching es

2.

(4) Because the decline of the price of soybeans, producers now produce more corn, shifting the corn supply curve to the right and reaching a new equilibrium. (ec

3)

(5) Because the decline of the price of corn, consumers shift away from soybeans, to DS

4 and producers produce more soybeans, shifting the soybean supply curve to the

right, reaching es4.

Adjustments continue…

SC0

DC0

Corn Market

SS0

Soybean Market

DC1

DS1

DS2

es2

ec3

4

3

Ps2

Pc1

Pc2

Ps1

SS2

SC3

5

es4 DS

4

5

5

• See the previous two slides.

Example: Corn & Soybean Markets

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Example: Minimum Wage Law

Initial wage rate.

Minimum wage rate is imposed.

Because of the high wage rate, the labor demand declines from L1C to L2

C

The unemployed workers move to uncovered sectors.

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Example: Minimum Wage Law

Workers move to uncovered sector, decreasing the wagerate.

Without the minimum wage rate.

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Trading between Two People

• Suppose two people have two goods that they may exchange if they wish.

• Their endowments:

Person A=(wA1, wA

2), Person B=(wB1, wB

2)

Good 1= wA1+ wB

1, Good 2= wA2+ wB

2

• Where do they end up?

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An Edgeworth box diagram

Person BGood 2

Person A

W

Good 1

10

An Edgeworth box diagram

X

Person BGood 2

xA2

Person A xA1

xB1

xB2

W

Good 1

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• They will trade until reaching to the Pareto optimum.

• Pareto optimum (efficient): an allocation of goods or services such that one cannot be made better off without worsening the other. This is where the MRS of two people are equalized.

• The set of Pareto optimum points is called the “contract curve.”

• Where they end up between the lens-shaped area depends upon their bargaining power.

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Contract Curve

The contract curvex2

B

x1AOA

ω2A

x1B

x2A

OB

ω2B

ω1B

ω1A

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Competitive Exchange• In a two-person exchange, the final allocation depends on

the bargaining power of the parties.

• However, when there are many sellers and buyers, each participant acts as a price-taker.

• In the competitive markets, prices respond automatically to excess demand and supply and will adjust until an equilibrium is reached such that Qs=Qd (no excess demand nor supply).

• Excess demand (supply) of a good puts pressure to raise (lower) its relative price, reducing the quantity demanded (supplied).

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Trade in Competitive Markets

1 1 2 2 1 1 2 2A A A Ap p p x p x

For consumer A

x*2A

ω2A

ω1Ax*1

A Good1OA

Good2

1

2A

pMRS

p

15

1 1 2 2 1 1 2 2B B B Bp p p x p x

For consumer BGood2

x*2B

ω2B

ω1B x*1

B Good1OB

1

2B

pMRS

p

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• In competitive equilibrium:

indicating that the competitive equilibrium should be on the contract curve.

→ First welfare theorem: “The competitive equilibrium is efficient.”

• Which Pareto-optimum is reached depends on the initial endowment. Any Pareto-optimum bundle can be obtained as a competitive equilibrium given an appropriate endowment.

→ Second welfare theorem: “Any efficient allocations can be achieved by competition.”

BA MRSp

PMRS

2

1

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Production and Trading

• We now consider the efficient use of inputs in the production using GE analysis.

• Suppose food (F) and clothing (C) are produced using labor (L) and capital (K). Total supply of L and K are fixed in the society.

• An Edgeworth box diagram in production shows every possible way that the existing K and L might be used to produce F and C.

• We will use isoquants for the two goods.

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An Edgeworth Box Diagram in Production

OF

OC

ACap

ital fo

r F

Cap

ital

fo

r C

Labor for C

Labor for F

Capitalin Cproduction

Capitalin Fproduction

Labor in C production

Labor in F production

Qf=10 Qf=15

Qc=7Qc=10

Qc=12

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• Many of the allocations in the Edgeworth box are technically inefficient.– it is possible to produce more F and more C by

shifting capital and labor around.

• The efficient allocations occur where the isoquants are tangent to one another (MRTSF=MRTSC) because output of one good cannot be increased without decreasing the output of another good in such allocations, i.e., Pareto optimum.

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Contract Curve in Production

At each efficient point (e), the MRTS is equal in both Food and Clothing production

OF

OC

Total Labor

To

tal C

apit

al

F’’F’

F’’’’

F’’’

C’’’’

C’’’

C’’

C’

e4

e3

e2

e1

The contract curve

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• The locus of efficient points shows the maximum output of C that can be produced for any level of F..

• We can transfer this information to construct a production possibility frontier (PPF).

• PPF shows the maximum amount of outputs (F and C) that can be produced with the fixed amount of inputs (K and L).

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Production Possibility Frontier

Quantity of F

Quantity of C

e4

e3

e2

e1

C’’’

C’’C’

F’

C’’’’

F’’ F’’’ F’’’’

e0

OF

OC

F’’F’

F’’’’

F’’’

C’’’’

C’’’

C’’

C’

e4

e3

e2

e1

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Production Possibility Frontier

Quantity of F

Quantity of C

e4

e3

e2

e1

C’’’

C’’C’

F’

C’’’’

F’’ F’’’ F’’’’

e0

OF

OC

F’’F’

F’’’’

F’’’

C’’’’

C’’’

C’’

C’

e4

e3

e2

e1

If all resources are used to produce C.

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• Marginal Rate of Transformation of F for C (slope of PPF):– measures how much C must be given up to produce one

additional unit of F.

As we increase the production of F by moving along the PPF, the MRT increases in absolute value (or becomes steeper), i.e., the PPF is concave.

Fof F forC

C

MCCMRT

F MC

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Optimal Product Mix

Food

Clo

thes

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• Output efficiency: For an economy to be efficient, goods must be produced not only at minimum cost but also to match people’s demands.

• An economy produces output efficiently only if, for each consumer, MRS = MRT, i.e., the conditions for the Pareto efficiency:

- P1/P2 = MRSA = MRSB = MRTi.e., the rate at which firms can transform one good into another = the rate at which consumers are willing to substitute between the goods.

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Production and the Edgeworth Box Diagram

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Comparative Advantage• The theory of comparative advantage

was first proposed by Ricardo

– Countries should specialize in producing those goods of which they are relatively more efficient producers

• these countries should then trade with the rest of the world to obtain needed commodities

– If countries do specialize this way, total world production will be greater.

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Efficient Choice of Output and Trade between Two Countries

Which country is relatively efficient in producing good 1?

Good 1

Good 2

Country A Country B

50 50

100 100

MRT= - 2/1 MRT= - 1/1

Good 2

Good 1

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Before trading, countries were producing at E0 and F0. Country A has a comparative advantage in producing Good 2, while the country B hasa comparative advantage in producing Good 1.

Good 1 Good 1

Good 2

Country A Country B

50 100

E0F0

IB

IA

50100

Good 2

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Suppose that the international price ratio of goods 1 and 2 is 2. Then, country A produces at E1 and consumes at E2. Country B produces atF1 and consumes at F2. Both countries are better off after the trade.

Country A Country B

50 100

100

60

E1

E2F1

F2

IB

IA

P1/P2=2

P1/P2=2

50

110

100

50

Import

Export

Good 2

Good 1 Good 1

Export

Import