16.4 Competitive Market Efficiency

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16.4 Competitive Market Efficiency

Pareto Efficient»No alternate allocation of inputs and goods makes one consumer better off without hurting another consumer

If another allocation improves AT LEAST ONE CONSUMER (without making anyone else worse off), the first allocation was Pareto Inefficient.

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Pareto Efficiency has three requirements:

1)Exchange Efficiency Goods cannot be traded to make a

consumer better off

2) Input Efficiency Inputs cannot be rearranged to

produce more goods

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3) Substitution Efficiency Substituting one good for another

will not make one consumer better off without harming another consumer

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1) Exchange Efficiency Model Assumptions

• Assumptions:–2 people–2 goods, each of fixed quantity

This allows us to construct an EDGEWORTH BOX – a graph showing all the possible allocations of goods in a two-good economy, given the total available supply of each good

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1) Edgeworth Box Example

• Two people: Maka and Susan• Two goods: Food (f) & Video Games (V)• We put Maka on the origin, with the y-axis

representing food and the x axis representing video games

• If we connect a “flipped” graph of Susan’s goods, we get an EDGEWORTH BOX, where y is all the food available and x is all the video games:

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1) Maka’s Goods Graph

Video Games

Food u

O xMaka

Ou is Maka’s food, and Ox is Maka’s Video Games

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1) Edgeworth Box

Video Games

Food u

O xMaka

O’w is Susan’s food, and O’y is Susan’s Video Games

w

r y O’Susan

s

Total food in the market is Or(=O’s) and total Video Games is Os (=O’r)

Each point in the Edgeworth Box represents one possible good allocation

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1) Edgeworth and utility

• We can then add INDIFFERENCE curves to Maka’s graph (each curve indicating all combinations of goods with the same utility) – Curves farther from O have a greater utility

• We can then superimpose Susan’s utility curves– Curves farther from O’ have a greater utility

Remember that: y

xxy MU

MUMRS

F

VVF MU

MUMRS

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1) Maka’s Utility Curves

Video Games

Food

OMaka

Maka’s utility is greatest at M3

M1

M2

M3

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1) Edgeworth Box and Utility

Video Games

Food

OMaka

Susan has the highest utility at S3

r O’Susan

s

At point A, Maka has utility of M3 and Susan has Utility of S2

M1

M2

M3

S1S2

S3

A

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Video Games

Food

OMaka

If consumption is at A, Maka has utility M1 while Susan has utility S3

r O’Susan

s

By moving to point B and then point C, Maka’s utility increases while Susan’s remains constant

M1M2

M3

S3A B

C

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1) Exchange Efficiency

Video Games

Food

OMaka

Point C, where the indifference curves barely touch is EXCHANGE EFFICIENT, as one person can’t be made better off without harming the other.

r O’Susan

s

M1M2

M3

S3C

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1) Pareto Improvement

• When an allocation is NOT exchange efficient, it is wasteful (at least one person could be made better off)…

• A PARETO IMPROVEMENT makes one person better off without making anyone else worth off (like the move from A to C)…

• However, there may be more than one pareto improvement:

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1) Pareto Improvements

Video Games

Food

OMaka

If we start at point A:-C is a pareto improvement that makes Maka better off-D is a pareto improvement that makes Susan better off-E is a pareto improvement that makes both better off

r O’Susan

s

M1M2

M3

S3C

S5S4

A

D

E

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1) The Contract Curve• Assuming all possible starting points, we can

find all possible exchange efficient points and join them to create a CONTRACT CURVE

• All along the contract curve, opposing indifferent curves are TANGENT to each other

• Since each individual maximizes where his indifference curve is tangent to his budget line:

F

VSusanVf

MakaVf P

PMRSMRS

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1) The Contract Curve

Video Games

Food

OMaka

r O’Susan

s

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1) Example: House and ChaseAssume that House and Chase have the following

utilities for books and coffee:CCChaseHHHouse CBUCBU ,

The Exchange Efficiency Condition therefore becomes:The Exchange Efficiency Condition therefore becomes:

CCHH

ChaseC

ChaseB

HouseC

HouseB

ChaseBC

HouseBC

BCBC

MUMU

MUMU

MRSMRS

//

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1) MATH – House and ChaseIf there are 10 books, and 4 cups of coffee, then the

contract curve is expressed as:

)10/()4(/

,HHHH

ChaseBC

HouseBC

BCBC

MRSMRS

If House has 6 books, an exchange efficient allocation If House has 6 books, an exchange efficient allocation would be:would be:

4.2

2410

)4(64

)610/()4(6/

H

H

HH

HH

C

C

CC

CC

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1) MATH – House and ChaseTherefore, House would have 6 books and 2.4 cups of coffee,

and Chase would have 4 (10-6) books and 1.6 (4-2.4) cups of coffee, for utilities of:

52.2)6.1(4

79.3)4.2(6

CCChase

HHHouse

CBU

CBU

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2) Input EfficiencyModel Assumptions

• Assumptions:–2 producers/firms–2 inputs (Labor and Capital), each of

fixed quantityThis lead to a EDGEWORTH BOX FOR

INPUTS– a graph showing all the possible allocations of fixed quantities of labor and capital between two producers

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2) Edgeworth Box For Inputs Example

• Two firms: Apple and Google• Two inputs: Labor (L) and capital (K)• We put Apple the origin, with the y-axis

representing capital and the x axis representing labor

• If we connect a “flipped” graph of Google’s inputs, we get an EDGEWORTH BOX FOR INPUTS, where y is all the capital available and x is all the labor:

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2) Apple’s Input Graph

Labor

Cap

ital

u

O xApple

Ou is Apple’s capital, and Ox is Apple’s labor.

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2) Edgeworth Box For Inputs

Labor

Cap

ital

u

O xApple

O’w is Google’s capital, and O’y is Google’s labor

w

r y O’Google

s

Total capital in the market is Or(=O’s) and total labor is Os (=O’r)

Each point in the Edgeworth Box represents one possible input allocation

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2) Edgeworth and Production

• We can then add ISOQUANT curves to APPLE’s graph (each curve indicating all combinations of inputs producing the same output) – Curves farther from O produce more

• We can then superimpose Google’s Isoquants– Curves farther from O’ produce more

Remember that the slope of the Isoquant is MRTS and:

K

LLK MP

MPMRTS

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2) Apple’s Isoquants

Labor

Cap

ital

OApple

Apple produces the mostat A3

A1

A2

A3

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2) Edgeworth Box for Inputs

Labor

Cap

ital

OApple

Google produces the most at G3

r O’Google

s

At point A, Apple makes A3 Google produces G2

A1

A2

A3

G1G2

G3

A

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O

If production is at A, Apple produces A1 while Google produces G3

r O’

s

By moving to point B and then point C, Apple produces more while Google’s production remains constant

A1A2

A3

G3A B

C

Labor

Cap

ital

Apple

Google

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2) Input Efficiency

O

Point C, where the isoquant curves barely touch is INPUT EFFICIENT, as one firm can’t produce more without the other firm producing less.

r O’

s

A1A2

A3

G3C

Labor

Cap

ital

Apple

Google

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2) Pareto Improvement

• When an input allocation is NOT input efficient, it is wasteful (at least one firm COULD produce more)…

• A PARETO IMPROVEMENT allows one firm to produce more without reducing the output of the other firm(like the move from A to C)

• However, there may be more than one pareto improvement:

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2) Pareto Improvements

O

If we start at point A:-C is a pareto improvement where Apple produces more-D is a pareto improvement where Google produces more-E is a pareto improvement where both firms produce more

r O’

s

A1A2

A3

G3C

G5G4

A

D

E

Labor

Cap

ital

Apple

Google

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2) Input Contract Curve• Similar to the goods market, a contract curve

can be derived in the input market:• All along the contract curve, opposing isoquant

curves are TANGENT to each other• Since each firm maximizes where their

isoquant curve is tangent to their isocost line:

rwMRTSMRTS Google

klApplekl ,,

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2) Input Contract Curve

O

r O’

sLabor

Cap

ital

Apple

Google

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2) Example: Apple and GoogleAssume that Apple and Google have the following

production functions:3/23/13/13/2 4, klQklQ GoogleApple

The Exchange Efficiency Condition therefore becomes:The Exchange Efficiency Condition therefore becomes:

Googlekl

Applekl MRTSMRTS ,,

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The isoquant slope for Apple is:The isoquant slope for Apple is:

Apple

AppleApplekl

Applekl

Applek

ApplelApple

kl

lk

MRTS

kl

klMRTS

MPMPMRTS

231

32

,

3/23/2

3/13/1

,

,

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The isoquant slope for Google is:The isoquant slope for Google is:

AppleTotal

AppleTotal

Google

GoogleGooglekl

Googlekl

Googlek

GooglelGoogle

kl

llkk

lk

MRTS

kl

klMRTS

MPMPMRTS

)(2238

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,

3/13/1

3/23/2

,

,

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2) MATH – Apple and GoogleIf there are 1000 workers, and 125 capital in Silicon

valley, then the contract curve is expressed as:

Apple

Apple

Apple

Apple

Googlekl

Applekl

lk

lk

MRTSMRTS

1000)125(22

,,

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2) MATH – Apple and GoogleIs the market input efficient if Apple has 200 workers and

50 capital?

16\316/82001000

)50125(2)200()50(2

1000)125(22

Apple

Apple

Apple

Apple

lk

lk

No – Apple needs fewer capital (Google needs more capital) AND/OR

Google needs fewer workers (Apple needs more workers)

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3) Substitution Efficiency• Substitution Efficiency can be analyzed using

the PRODUCTION POSSIBILITIES CURVE/FRONTIER– The PPC shows all combinations of 2 goods that

can be produced using available inputs– The slope of the PPC shows how much of one

good must be SUBSTITUTED to produce more of the other good, or MARGINAL RATE OF TRANSFORMATION (x for y) (MRTxy)

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Production Possibilities CurveR

obot

s

Pizzas

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

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10Here the MRTSpr is equal to (7-5)/(2-1)=-2, or two robots must be given up for an extra pizza.

The marginal cost of the 3rd pizza, or MCp=2 robots

The marginal cost of the 6th and 7th robots, or MCr=1 pizza

Therefore, MRTxy=MCx/MCy

Therefore, MRTpr=2/1=2

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3) Substitution Efficiency and Production• If production is possible in an economy, the

Pareto efficiency condition becomes:PersonBxy

PersonAxyxy MRSMRSMRT

Assume MRTpr=3 and MRSpr=2.-Therefore Maka could get 3 more robots by transforming 1 pizza-BUT Maka would exchange 2 robots for 1 pizzas to maintain utility-Therefore 1 pizza is sacrificed for 3 robots, increasing Maka’s utility through the 3rd robot-The Market isn’t Pareto Efficient

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The First Fundamental Theorem Of Welfare Economics

IF1) All consumers and producers act as perfect

competitors (no one has market power)and

2) A market exists for each and every commodity

ThenResource allocation is Pareto Efficient

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First Fundamental Theorem of Welfare Economics Proof:

• From microeconomic consumer theory, we know that:

y

xPersonAxy P

PMRS

Since prices are the same for all people:Since prices are the same for all people:PersonBxy

PersonAxy MRSMRS

Therefore perfect competition leads to Therefore perfect competition leads to exchange efficiencyexchange efficiency

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First Fundamental Theorem of Welfare Economics Proof:

• From microeconomic theory of the firm, we know that:

rwMRTS FirmAkl ,

Since each firm in an industry faces the same Since each firm in an industry faces the same wages and rents:wages and rents:

FirmBkl

FirmAkl MRTSMRTS ,,

Perfect competition leads to input efficiencyPerfect competition leads to input efficiency

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First Fundamental Theorem of Welfare Economics Origins

• From the PPF, we know that

xyxy MRSMRT Therefore a perfectly competitive market is Therefore a perfectly competitive market is

Pareto Efficient:Pareto Efficient:

y

xPersonBxy

PersonAxy

y

xxy P

PMRSMRSMCMCMRT

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Efficiency≠Fairness• If Pareto Efficiency was the only concern, competitive markets

automatically achieve it and there would be very little need for government:–Government would exist to protect property rights

• Laws, Courts, and National Defense• But Pareto Efficiency doesn’t consider distribution. One person could get

all society’s resources while everyone else starves. This isn’t typically socially optimal.

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Fairness

Video Games

Food

OMaka

r O’Susan

s

A

C

B Points A and B are Pareto efficient, but either Susan or Maka get almost all society’s resources

Many would argue C is better for society, even though it is not Pareto efficient

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Fairness• For each utility level of one person, there is

a maximum utility of the other

• Graphing each utility against the other gives us the UTILITY POSSIBILITIES CURVE:

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Utility Possibilities Curve

Susan’s Utility

Mak

a’s

Util

ity

OMaka

All points on the curve arePareto efficient, while all points below the curve are not.Any point above the curve is unobtainable

A

C

B

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Fairness•Typical utility is a function of goods consumed:

U=f(x,y)

•Societal utility can be seen as a function of individual utilities: W=f(U1,U2)

•This is the SOCIAL WELFARE FUNCTION, and can produce SOCIAL INDIFFERENCE CURVES:

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Typical Social Indifference Curves

Susan’s Utility

Mak

a’s

Util

ity

OMaka

An indifference curve farther from the origin represents a higher level of social welfare.

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Fairness• If we superimpose social indifference curves on top of the

utilities possibilities curve, we can find the Pareto efficient point that maximizes social welfare

• This leads us to the SECOND FUNDAMENTAL THEOREM OF WELFARE ECONOMICS

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Maximizing Social Welfare

Susan’s Utility

Mak

a’s

Util

ity

OMaka

ii is preferred to i, even though ii is not Pareto efficienti

ii

iii

The highest possible social welfare, iii, is Pareto efficient

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Second Fundamental Theorem of Welfare Economics

The SECOND FUNDAMENTAL THEOREM OF WELFARE ECONOMICS states that:

Society can attain any Pareto efficient allocation of resources by: 1) making a suitable assignments of original endowments, and then

2) letting people trade

54Video Games

Food

OMaka

r O’Susan

s

Second Fundamental Theorem of Welfare Economics

StartingPoint

Goal

By redistributing income, society can pick the starting point in the Edgeworth box, therefore obtaining a desired point on the Utility Possibility Frontier:

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Why Is Government so Big?

1) Government has to ensure property laws are protected. (1st Theorem)

2) Government has to redistribute income to achieve equity. (2nd Theorem)

3) Often the assumptions of the First Welfare Theorem do not hold (Econ 350)

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Why Trade and Not Tax?Taxes and penalties punish income-enhancing behavior, encouraging

people to work less.Subsidies and incentives give an incentive to stay in a negative state to

keep receiving subsidies and incentives.Lump sum transfers have the least distortion,

AND TRADE ALWAYS BENEFITS BOTH PARTIES…

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16.5 Gains From Free Trade• Trade ALWAYS makes society better off

by increasing the productivity of scarce resources

• The basis for the gains from specialization and trade is Comparative Advantage

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Theory of Comparative Advantage:• Production Possibilities :

–Carl and Mike: retired neighbours: hobbies are making wine and beer

Carl’s ProductionPossibilities

Mike’s ProductionPossibilitiesA B C

A B C

Wine (btls) 0 30 100Beer (btls.) 1,000 700 0

0 40 80 80 40 0

PPF’s for 1 month’s production:

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Carl’s Proposition

• “Lets each of us do what we do best and trade. This will give each of us more than we now have without either of us working any harder.”

• Notice that voluntary trade does not take place unless both parties benefit.

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Mike’s Production Possibilities/ Opportunity Costs

Bottles of beer

A•C

In a month Mike can produce either 80 bottles of wine or 80 bottles of beerOpp cost of 80 wine is 80 beer Opp cost of 1 wine is 1 beer Opp cost of 80 beer is 80 wine Opp cost of 1 beer is 1 wine

Bottles of wine

••BConsumption choice before trade8040

40 80

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Carl’s Production Possibilities/ Opportunity Costs

0

Bottles of beer

A•

C•

Opp cost 100 wine is 1000 beer Opp Cost 1 wine is 10 beerOpp cost of 1000 beer is 100 wine Opp Cost 1 beer is 1/10 wine

Bottles of wine

•B Consumption choice before trade700

100

30 100

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Opportunity Cost Table

Opportunity cost of 1 beer

Opportunity cost of 1 wine

Carl 1/10 wine 10 beer

Mike 1 wine 1 beer

• When producer A has a lower opportunity cost of producing good A compared to another producer, then producer A is said to have a comparative advantage in the production of good A.

Theory of Comparative Advantage:

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Comparative Advantage: Specialization• Carl has a “comparative advantage” (lowest

opportunity cost producer) in the production of beer and therefore specializes in beer production.

• Mike has a “comparative advantage” in the production of wine and therefore specializes in wine production

• As long as opportunity costs differ, there is comparative advantage

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Comparative Advantage: SpecializationComparative Advantage: Specialization

Theory of Comparative AdvantageTheory of Comparative Advantage • if specialization takes place according to comparative advantage (the lowest opportunity cost producer) and then trade takes place…. both parties can benefit: that is, move outside their current PPF’s.

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Carl & Mike Before Specialization & Trade

Carl Produces & Consumes

Mike Produces & Consumes

Total Consumption+ =

Wine (btls.)Beer (btls.)

30700

4040

70740

Carl & Mike After Specialization, but Before Trade

Mike Produces & Can

Consume+ =


01,000

800

801,000

Carl Produces & Can

Consume

Total Production & Consumptio

n

Total Gains

+10+260

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• Carl proposes, after specialization, that he trade Mike 175 beer for 35 wine.

Carl gets wine for a reduced sacrifice–35 wine for 175 beer instead of 350 beer, the opportunity cost before trade

Mike gets beer for a reduced sacrifice–175 beer for 35 wine instead of 175 wine, the opportunity cost before trade

(terms of trade: 5 beer for 1 wine)

Trade: The Benefits of Specialization

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Terms of Trade: 1 Wine for 5 Beer• Since voluntary trade requires that both parties

benefit from the trade.• Before trade:

• Carl: 1 wine “trades” for 10 beer

• Mike: 1 wine trades for 1 beer

After trade 1 wine “trades” for 5 beer

•The Terms of Trade are between the personal ones that exist before trade, thus producing gains for both parties participating in the trade

Carl is better off as he now only has to give up 5 beer for a wine

Mike is better off as he now only has to give up 1/5 wine for a beer

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Trade Between Carl & Mike

1 Wine trades for 5 Beeror

1 Beer trades for 1/5 WineMike

(specializes in wine)

Carl (specializes

in beer)

175 Bottles of Beer To

Trades away

35 Bottles of Wine Trades awayTo

Before trade Mike gave up 1 wine to get 1 beer, after trade1/5 wineBefore trade Carl gave up 10 beer to get a wine, after trade 5 beer

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Carl & Mike After Specialization & Trade

Carl

Mike

ProducesTradesFor (+)Away (-)

ConsumesAfterTrade

Produced & ConsumedBefore Trade

GainsfromTrade

Wine (btls.) Beer (btls.)

01,000

+35-175

35825

30700

+5+125

Produces

TradesFor (+)Away (-)

ConsumesAfterTrade

Produced & ConsumedBefore Trade

GainsfromTrade


800

-35+175

45175

4040

+5+135

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Mike’s Production Possibilities After TradeBottles of

beer

A•C

Bottles of wine

••B•D Consumption after trade

Mike produces 80 wine and then trades 35 wine for 175 beer, leaving him with 45 wine and 175 beer, point D

8040

40 80

175

45

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Carl’s Production Possibilities/ Opportunity Costs, After Trade

0

Bottles of beer

A•

C• Bottles of wine

•BD• Consumption after trade

Carl produces 1000 beer and trades 175 beerto Mike for 35 wine, leaving him with 825 beerand 35 beer, point D

700

100

30 100

825

35

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Absolute Advantage

• When a producer with of set of inputs can produce more output than another with the same inputs, the first producer has an absolute advantage in production of the output.

• Carl has an absolute advantage in the production of both wine and beer.

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Gains from Specialization and Trade

• Specialization produces gains for both traders, even when one trader enjoys an absolute advantage in both endeavors.

• Unless two people/firms/countries have IDENTICAL opportunity costs, Trade is always beneficial

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Why No Free Trade?1) Misunderstanding: people misunderstand the

facts or hold to political or ideological dogma, or confuse voluntary jobs with enforced slavery

2) Short-run effects: in the SHORT-RUN, there may be some unpopular adjustments:

a) Richer, developed countries may lose jobs to developing countries with a comparative advantage

b) Poorer, developing countries may have short-run environmental damage until the higher incomes lead to environmental protection

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Chapter 16 Conclusions1) General equilibrium requires

simultaneous equilibrium in multiple markets

2) One change can cause a cascade of changes through markets until a new equilibrium is reached

3) An equilibrium is Pareto Efficient if no other allocation of inputs can make one person better off without making another worse off.

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Chapter 16 Conclusions4) Pareto Efficiency requires exchange

efficiency (goods can’t be traded), input efficiency (more can’t be produced) and substitution efficiency (substituting production won’t improve outcome)

5) The First Fundamental Theorem of Welfare Economics states that if all perfectly competitive markets exist, allocations are Pareto Efficient

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Chapter 16 Conclusions6) The Second Fundamental Theorem of

Welfare Economics states that governments can redistribute wealth to reach any pareto efficient outcome

7) Free Trade is always beneficial to all parties

8) Economic truths, when properly applied and explained, can cut through ideologies and make people cry

Documents

16.4 Competitive Market Efficiency