Chapter 16 General Equilibrium. ©2005 Pearson Education, Inc.Chapter 162 General Equilibrium Analysis To study how markets interrelate, we can use general

Chapter 16

General Equilibrium

©2005 Pearson Education, Inc. Chapter 16 2

General Equilibrium Analysis

To study how markets interrelate, we can use general equilibrium analysis

The feedback effect is the price or quantity adjustment in one market caused by price and quantity adjustments in related markets


Two Interdependent Markets – Moving to General Equilibrium

ScenarioThe competitive markets of:

DVD rentalsMovie theater tickets

Changing prices in one market are likely to affect the other market


Two Interdependent Markets – Moving to General Equilibrium

ScenarioEquilibrium price of movies is $6.00Equilibrium price of DVD rentals are $3.00Government places a $1.00 tax on each

movie ticketNeed to look at effect of tax on

Market for DVDsFeedback effects in Movie market

©2005 Pearson Education, Inc. 5

Two Interdependent Markets – Movies and DVDs

DVDM

Price

Numberof Videos

Price

Number ofMovie Tickets

SMSV

$6.00

QMQV

$3.00

$6.35

Q’M

S*M

$1 tax on each movie ticket causes supply to

fall

D’V

Q’V

$3.50

General Equilibrium Analysis:Increase in movie ticket pricesincreases demand for videos.



Price

Numberof Videos

Price

Number ofMovie Tickets

DM

SM

$6.00

QM

$6.35

Q’M

S*M

The increase in the priceof videos increases the

demand for movies.

D’V

DV

SV

QV

$3.00

Q’V

$3.50

General Equilibrium Analysis:The Feedback effects continue.

D*M

$6.82

Q*MQ”M

$6.75

D’M

$3.58

Q*V

D*V



ObservationWithout considering the feedback effect with

general equilibrium, the impact of the tax would have been underestimated

This is an important consideration for policy makers.


Reaching General Equilibrium

Must be able to determine the equilibrium price of both movies and DVDs simultaneouslyWe must simultaneously find two prices that

equate quantity demanded and quantity supplied in all related markets

This requires finding the solution to four equations: demand and supply for DVDs and Movies


The Advantages of Trade

AssumptionsTwo consumers (countries)Two goodsZero transaction costsJames & Karen have a total of 10 units of

food and 6 units of clothing.


The Advantage of Trade

Individual Initial Allocation

Trade Final Allocation

James 7F, 1C -1F, +1C 6F, 2C

Karen 3F, 5C +1F, -1C 4F, 4C



There is room for tradeJames values clothing more than KarenKaren values food more than James

Actual terms of trade are determined through bargaining



From this analysis we obtain an important result:

An allocation of goods is efficient only if the goods are distributed so that the marginal rate of substitution between any pair of goods is the same for all

consumers.


The Edgeworth Box Diagram

A diagram showing all possible allocations of either two goods between two people is called an Edgeworth Box


The Edgeworth Box Diagram

Each point describes the market baskets of both consumersJames has 7 units of food and 1 unit of

clothing – point AKaren has 3 units of food and 5 units of

clothing – point A from different axis


Exchange in an Edgeworth Box

10F 0K

0J

6C

10F

6C

James’sClothing

Karen’sClothing

James’s Food

Karen’s Food

1C 5C

3F

7F

A

The initial allocation before trade is A: James has 7F and 1C & Karen

has 3F and 5C.


Exchange in an Edgeworth Box

10F 0K

0J

6C

10F

6C

James’sClothing

Karen’sClothing

James’s Food

Karen’s Food

1C 5C

3F

7F

A

The allocation after trade is B: James

has 6F and 2C & Karen has 4F and 4C.

4F

6F

+1C

-1F

2C 4CB


Efficient Allocations

A trade from A to B makes both Karen and James better off

If James’s and Karen’s MRS are the same at B the allocation is efficient.


Efficient Allocations

We can see both parties are better off at point B since they both end up on a higher indifference curve

Although a trade might make both parties better off, the new allocation is not necessarily efficient


A: UJ1 = UK

1,but the MRSis not equal.

All combinationsin the shaded

area arepreferred to A. Karen’s

Clothing

Karen’s Food

UK1

James’sClothing

James’s Food

UJ1

Efficiency in Exchange10F 0K

0J

6C

10F6C

Gains fromtrade

A


Efficiency in Exchange

Karen’sClothing

Karen’s Food

James’sClothing

James’s Food

10F 0K

0J

6C

10F6C

UK1

UJ1

A

Point B is on higher IC but

is not efficient

UJ2

UK2

B

At point C, MRSs are equal and

allocation is efficient

UK3

C

D is also a possible efficient

allocation depending on

bargaining

UJ3

D



Any move outside the shaded area will make one person worse off (closer to their origin).

B is a mutually beneficial trade--higher indifference curve for each person.

Trade may be beneficial but not efficient.

MRS is equal when indifference curves are tangent and the allocation is efficient.

A

Karen’sClothing

Karen’s Food

UK1UK

2UK3

James’sClothing

James’s Food

UJ1

UJ2

UJ3

B

C

D

10F 0K

0J

6C

10F6C



The Contract CurveTo find all possible efficient allocations of

food and clothing between Karen and James, we would look for all points of tangency between each of their indifference curves.

The contract curve shows all the efficient allocations of goods between two consumers, or of two inputs between two production functions


The Contract Curve

0J

James’sClothing

Karen’sClothing

0KKaren’s Food

James’s Food

E

F

G

ContractCurve

E, F, & G arePareto efficient .


Contract curve

All points of tangency between the indifference curves are efficient.MRS of individuals is the sameNo more room for trade

The contract curve shows all allocations that are Pareto efficient.Pareto efficient allocation occurs when

further trade will make someone worse off.


Consumer Equilibrium in a Competitive Market

We can show opportunities for trade for many consumersWhen prices of food and clothing are equal,

we can show the price line, PP’ with a slope of –1

James buys 2 clothing for 2 food: A to CKaren buys 2 food for 2 clothing: A to CBoth increase satisfaction



Price Line

10F 0K

0J

6C

10F

6C

James’sClothing

Karen’sClothing

Karen’s Food

James’s Food

C

A

Begin at A:Each James buys 2C and sells 2Fmoving from Uj1 to Uj2, which is preferred (A to C).

Begin at A:Each Karen buys 2F and sells 2C moving fromUK1 to UK2, which is preferred (A to C).

P

P’

UJ2

UJ1

UK1UK

2



The amount of clothing that Karen wanted to sell is equal to the amount of clothing that James wanted to buy

An equilibrium is a set of prices at which the quantity demanded equals the quantity supplied in every marketAlso called competitive equilibrium



In a general equilibrium setting where all markets are perfectly competitive, we can show the same resultBest example of Adam Smith’s invisible handEconomy will automatically allocate all

resources efficiently without need for regulatory control



Competitive equilibrium1. Because the indifference curves are tangent, all

MRSs are equal between consumers

2. Because each indifference curve is tangent to the price line, each person’s MRS is equal to the price ratio of the two goods

KFC

F

CJFC MRSP

PMRS



Difficult for efficient allocation with many consumer and producers unless all markets are perfectly competitive

Efficient outcomes can also be achieved by centralized system


Equity and Efficiency

Although there are many efficient allocations, some may be fairer than others

The difficult question is what is the most equitable allocation?

There is no reason to believe that efficient allocation from competitive markets will give an equitable allocation


The Utility Possibilities Frontier

From the Edgeworth box we showed a two person exchange

The utility possibilities frontier represents all allocations that are efficient in terms of the utility levels of the two individuals



James’ Utility

Karen’s Utility

E

F

G

OK

L

OJ

H

OJ – James has zero utilityOK – Karen has zero utilityE, F, G – points on contract curveH – inefficient – can do better in shaded areaL - unobtainable



James’ Utility

Karen’s Utility

E

F

G

OK

OJ

H

Are all efficient points equitable?•Efficient points E or F make both persons better off without making one worse off from H•If only possible points are H and G, can argue that one is more equitable to James and one to Karen



From previous example, we can see that an inefficient allocation might be more equitable than an efficient one.

But how do we define an equitable allocation?


Four Views of Equity

EgalitarianAll members of society receive equal amount of goods

RawlsianMaximize the utility of the least-well-off person

UtilitarianMaximize the total utility of all members of society

Market - Oriented

The market outcome is the most equitable


Equity and Perfect Competition

A competitive equilibrium can occur at any point on the contract curve depending on the initial allocation.

Since not all competitive equilibriums are equitable, we rely on the government to help reach equity by redistributing income.TaxesPubic services


Efficiency in Production

We can extend to the efficient use of inputs used for production.

Assume:Two fixed inputs: capital and laborProduce same two goods: food and clothingMany consumers own inputs to production

and earn income from selling themIncome allocated between goods


Efficiency in Production

Using the Edgeworth box diagram, we can show efficient use of inputs in productionLabor on horizontal axisCapital on vertical axis50 hours of labor and 30 hours of capital

available


Production in an Edgeworth Box

50L 0C

0F

30K

50L

30K

Capital in Food Production

Capital in Clothing

Production

Labor in Food Production

Labor in Clothing Production

5K 25K

15L

35L

A

The initial allocation is A.Every combination of labor and capital used to produce

two goods is represented as point in box



Can use production isoquants to show levels of output produced with each combination of inputs3 isoquants representing 50, 60 and 80 units

of food3 isoquants representing 10, 25 and30 units

of clothing



50L 0C

0F

30K

50L

30K


Capital in Clothing

Production



5K 25K

15L

35L

3 isoquants representing food production

3 isoquants representing clothing production

10C

60F

50F

25C

B

30C

80F

A



To find efficient production, we must find different combinations of inputs used to produce the two outputs

An allocation of inputs is technically efficient if the output of one good cannot be increased without decreasing the output of another goods



50L 0C

0F

30K

50L

30K


Capital in Clothing

Production



5K 25K

15L

35L

Can move from A to B or C which increases

efficiency.

10C

60F

50F

25C

30C C

80FD

AB

Any place in shaded area will increase efficiency

from allocation A.



Points B and C are efficient allocations and therefore lie on the production contract curveCurve showing all technically efficient

combinations of inputs.Curve connects the origins, OF and OC

All points on curve are tangencies between two isoquants



50L 0C

0F

30K

50L

30K


Capital in Clothing

Production



5K 25K

15L

35L

10C

60F

50F

25C

30C C

80FD

AB

Production Contract

Curve


Producer Equilibrium – Competitive Input Markets

If input markets are competitive, an efficient point will be achieved

In competitive input marketsWage rate, w, will be equal in all industriesRental rate of capital, r, will be equal in all

industries



If producers minimize costs, they will choose inputs to the point where the ratio of the marginal products of the two inputs is equal to the ratio of input prices:

r

w

MP

MP

K

L



Ratio of marginal products is the same as the marginal rate of technical substitution of labor for capital:

LKK

L MRTSr

w

MP

MP



The MRTS is the slope of the isoquant, so competitive equilibrium exists only if:Slopes of the isoquants are equal to one

anotherThese also equal the ratio of the prices of

two inputsCompetitive equilibrium lies on the

production contract curve, and the competitive equilibrium is efficient in production


Production Possibilities Frontier

PPF shows the various combinations of two goods that can be produced with fixed quantities of inputs.

Frontier is derived from the production contract curve

Points on PPF show efficiently produced levels of both goods



Clothing(units)

Food (units)

•Point A is inefficient•Points B, C and D are efficient•All points in triangle ABC completely utilize capital and labor but distortion in labor market leads to inefficient use

OF

OC

D

C

B

A



PPF is downward slopingIn order to produce more of one good, must

give up producing some of the other good

PPF is concaveSlope is the MRTS which increases as the

level of production of food increases



Marginal rate of transformation (MRT) of food for clothing is the magnitude of the slope of the frontier at each pointHow much clothing must be given up to

produce one additional unit of foodAs we increase the production of food my

moving along the PPF, the MRT increases


Marginal Rate of Transformation

The productivity of labor and capital differs depending on whether the inputs are used to produce more food or clothing.Starting where only clothing is produced, MP

of labor and capital are relatively lowTransferring some to food production where

MP are relatively highAs we do this, MP in food decreases and MP

in clothing increases



Clothing(units)

Food (units)

OF

OC

D MRT = 2

B MRT = 1

MRT < 1

MRT > 1


Marginal Rate of Transformation

Can also describe in terms of costsWhen producing at OF the MC of food is very low

and MC of clothing is very highWhen MRT is low, so is the ratio of the MC of

producing food to clothingSlope of PPF measures the MC of producing one

good relative to the MC of producing the other

C

F

MC

MCMRT


Output Efficiency

For efficiency, MRS = consumer’s WTP for additional food

by consuming less clothingMRT = cost of additional unit of food in terms

of producing less clothing

Efficiency means MRS = MRT


Output Efficiency

Clothing(units)

Food (units)

60

100

Indifference Curve

MRS = MRT

PPF


Efficiency in Output Markets

For perfectly competitive markets, all consumers allocate their budgets so their MRS between two good are equal to the ratio of prices

Profit maximizing firms produce output to the point where price is equal to MC

MRT is equal to the MRS

MRSPP

MCMCMRT

C

F

C

F


The Gains from Free Trade

We have showed gains from trade in an Edgeworth box, but what about gains from trade with two countries where one has the comparative advantageA country has a comparative advantage over

another country in the production of a good if the first country can produce the good at a lower opportunity cost than the other country



EX: Two countries producing two goodsHolland and ItalyCheese and WineHolland has comparative advantage in

cheese productionItaly as comparative advantage in wine

productionTrade is good for both countries



Hours of Labor Required to Produce Cheese and Wine

Cheese (1 LB)

Wine

(1 GAL)

Holland 1 2

Italy 6 3



When there is comparative advantage, free trade allows the country to consume outside their PPF

Before tradeProduces at A on indifference curve U1

where MRT and pre-trade price ratio is 2Holland would want to export 2 pounds of

cheese for 1 gallon of wine



After tradeSuppose they choose to trade 1 gallon of

wine for 1 pound of cheeseHolland will produce at the point of tangency

on the 1/1 price line and PPF – point BConsumption will occur at D, on a higher

indifference curve U2 tangent to the trade price line


The Gains from Trade

Cheese (lbs)

Wine (gal)

U1

Pre-Trade Prices

U2

World Prices

CBB

WB

A

WD

DCD

•Trade allows Holland to consume outside PPF

Exports

Imports


Overview – Efficiency of Competitive Markets

1. Efficiency in Exchange MRSJ

FC = MRSKFC

MRSJFC = PF/PC = MRSK

FC

2. Efficiency in the use of inputs in production MRTSF

LK = MRTSCLK

MRTSFLK = w/r = MRTSC

LK


Overview – Efficiency of Competitive Markets

3. Efficiency in the output market MRTFC = MRSPC (for all consumers)

PF = MCF, PC = MCC resulting in

MRTFC = MCF/MCC = PF/PC; therefore

MRSFC = MRTFC


Why Markets Fail

Market PowerThose with market power choose the price

and quantityLess output is sold than in competitive

marketsInefficiency


Why Markets Fail

Incomplete InformationConsumers must have accurate information

about market prices or production quality for markets to operate efficiency

Lack of information can change supplySome markets may never develop


Why Markets Fail

ExternalitiesConsumption or production has indirect

effect on other consumption or production not reflected in market prices


Why Markets Fail

Public GoodsNonexclusive, nonrival good that can be

made available cheaply but which, once available, is difficult to prevent others from consuming

Company thinking about researching a new technology if can’t get patent

Once it’s made pubic, others can duplicate it

Documents

Chapter 16 General Equilibrium. ©2005 Pearson Education, Inc.Chapter 162 General Equilibrium Analysis To study how markets interrelate, we can use general