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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

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slide1

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.
slide2

16.4 Competitive Market Efficiency

  • Pareto Efficiency has three requirements:
  • Exchange Efficiency
    • Goods cannot be traded to make a consumer better off
  • 2) Input Efficiency
    • Inputs cannot be rearranged to produce more goods
slide3

16.4 Competitive Market Efficiency

  • 3) Substitution Efficiency
    • Substituting one good for another will not make one consumer better off without harming another consumer
1 exchange efficiency model assumptions
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
1 edgeworth box example
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:
1 maka s goods graph
1) Maka’s Goods Graph

Ou is Maka’s food, and Ox

is Maka’s Video Games

u

Food

O

x

Video Games

Maka

1 edgeworth box
1) Edgeworth Box

Susan

y

O’

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

r

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

u

Food

w

Each point in the Edgeworth Box represents one possible good allocation

O

s

x

Video Games

Maka

1 edgeworth and utility
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:

1 maka s utility curves
1) Maka’s Utility Curves

Maka’s utility is greatest at M3

Food

M3

M2

M1

O

Video Games

Maka

1 edgeworth box and utility
1) Edgeworth Box and Utility

Susan

O’

Susan has the highest utility at S3

r

S1

A

S2

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

S3

Food

M3

M2

M1

O

s

Video Games

Maka

1 edgeworth box and utility1
1) Edgeworth Box and Utility

Susan

O’

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

r

A

B

S3

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

C

Food

M3

M2

M1

O

s

Video Games

Maka

1 exchange efficiency
1) Exchange Efficiency

Susan

O’

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

S3

C

Food

M3

M2

M1

O

s

Video Games

Maka

1 pareto improvement
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:
1 pareto improvements
1) Pareto Improvements

Susan

O’

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

A

S3

C

S4

Food

S5

E

M3

M2

D

M1

O

s

Video Games

Maka

1 the contract curve
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:
1 the contract curve1
1) The Contract Curve

Susan

O’

r

Food

O

s

Video Games

Maka

1 example house and chase
1) Example: House and Chase

Assume that House and Chase have the following utilities for books and coffee:

  • The Exchange Efficiency Condition therefore becomes:
1 math house and chase
1) MATH – House and Chase

If there are 10 books, and 4 cups of coffee, then the contract curve is expressed as:

  • If House has 6 books, an exchange efficient allocation would be:
1 math house and chase1
1) MATH – House and Chase

Therefore, 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:

2 input efficiency model assumptions
2) Input EfficiencyModel Assumptions
  • Assumptions:
    • 2 producers/firms
    • 2 inputs (Labor and Capital), each of fixed quantity
  • This lead to a EDGEWORTH BOX FOR INPUTS– a graph showing all the possible allocations of fixed quantities of labor and capital between two producers
2 edgeworth box for inputs example
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:
2 apple s input graph
2) Apple’s Input Graph

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

u

Capital

O

x

Labor

Apple

2 edgeworth box for inputs
2) Edgeworth Box For Inputs

Google

y

O’

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

r

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

u

Capital

w

Each point in the Edgeworth Box represents one possible input allocation

O

s

x

Labor

Apple

2 edgeworth and production
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:

2 apple s isoquants
2) Apple’s Isoquants

Apple produces the mostat A3

Capital

A3

A2

A1

O

Labor

Apple

2 edgeworth box for inputs1
2) Edgeworth Box for Inputs

Google

O’

Google produces the most at G3

r

G1

A

G2

At point A, Apple makes A3 Google produces G2

G3

Capital

A3

A2

A1

O

s

Labor

Apple

2 edgeworth box and utility
2) Edgeworth Box and Utility

Google

O’

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

r

A

B

G3

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

C

Capital

A3

A2

A1

O

s

Labor

Apple

2 input efficiency
2) Input Efficiency

Google

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

G3

C

Capital

A3

A2

A1

O

s

Labor

Apple

2 pareto improvement
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:
2 pareto improvements
2) Pareto Improvements

Google

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

A

G3

C

G4

Capital

G5

E

A3

A2

D

A1

O

s

Labor

Apple

2 input contract curve
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:
2 input contract curve1
2) Input Contract Curve

Google

O’

r

Capital

O

s

Labor

Apple

2 example apple and google
2) Example: Apple and Google

Assume that Apple and Google have the following production functions:

  • The Exchange Efficiency Condition therefore becomes:
2 math apple and google
2) MATH – Apple and Google

If there are 1000 workers, and 125 capital in Silicon valley, then the contract curve is expressed as:

2 math apple and google1
2) MATH – Apple and Google

Is the market input efficient if Apple has 200 workers and 50 capital?

  • No – Apple needs fewer capital (Google needs more capital) AND/OR
  • Google needs fewer workers (Apple needs more workers)
3 substitution efficiency
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)
production possibilities curve
Production Possibilities Curve

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

10

9

8

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

7

6

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

Robots

5

4

Therefore, MRTxy=MCx/MCy

3

2

Therefore, MRTpr=2/1=2

1

1

2

3

4

5

6

7

8

Pizzas

3 substitution efficiency and production
3) Substitution Efficiency and Production
  • If production is possible in an economy, the Pareto efficiency condition becomes:
  • 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
the first fundamental theorem of welfare economics
The First Fundamental Theorem Of Welfare Economics

IF

  • All consumers and producers act as perfect competitors (no one has market power)

and

2) A market exists for each and every commodity

Then

Resource allocation is Pareto Efficient

first fundamental theorem of welfare economics proof
First Fundamental Theorem of Welfare Economics Proof:
  • From microeconomic consumer theory, we know that:
  • Since prices are the same for all people:
  • Therefore perfect competition leads to exchange efficiency
first fundamental theorem of welfare economics proof1
First Fundamental Theorem of Welfare Economics Proof:
  • From microeconomic theory of the firm, we know that:
  • Since each firm in an industry faces the same wages and rents:
  • Perfect competition leads to input efficiency
first fundamental theorem of welfare economics origins
First Fundamental Theorem of Welfare Economics Origins
  • From the PPF, we know that
  • Therefore a perfectly competitive market is Pareto Efficient:
efficiency fairness
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.
fairness
Fairness

Susan

O’

r

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

B

C

Food

A

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

O

s

Video Games

Maka

fairness1
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:
utility possibilities curve
Utility Possibilities Curve

All points on the curve are

Pareto efficient, while all points below the curve are not.

Any point above the curve is unobtainable

B

Maka’s Utility

C

A

O

Susan’s Utility

Maka

fairness2
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:
typical social indifference curves
Typical Social Indifference Curves

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

Maka’s Utility

O

Susan’s Utility

Maka

fairness3
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
maximizing social welfare
Maximizing Social Welfare

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

i

ii

The highest possible social welfare, iii, is Pareto efficient

Maka’s Utility

iii

O

Susan’s Utility

Maka

second fundamental theorem of welfare economics
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

second fundamental theorem of welfare economics1
Second Fundamental Theorem of Welfare Economics

Susan

O’

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

r

Starting

Point

Goal

Food

O

s

Video Games

Maka

why is government so big
Why Is Government so Big?
  • Government has to ensure property laws are protected. (1st Theorem)
  • Government has to redistribute income to achieve equity. (2nd Theorem)
  • Often the assumptions of the First Welfare Theorem do not hold (Econ 350)
why trade and not tax
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…

16 5 gains from free trade
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
theory of comparative advantage

Mike’s Production

Possibilities

Carl’s Production

Possibilities

A B C

A B C

Wine (btls) 0 30 100

Beer (btls.) 1,000 700 0

0 40 80

80 40 0

Theory of Comparative Advantage:
  • Production Possibilities :
    • Carl and Mike: retired neighbours: hobbies are making wine and beer

PPF’s for 1 month’s production:

carl s proposition
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.
mike s production possibilities opportunity costs
Mike’s Production Possibilities/ Opportunity Costs

Bottles of beer

In a month Mike can produce either 80 bottles of wine or 80 bottles of beer

Opp 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

A

B

Consumption choice before trade

80

C

40

Bottles of wine

40

80

carl s production possibilities opportunity costs
Carl’s Production Possibilities/ Opportunity Costs

Opp cost 100 wine is 1000 beer Opp Cost 1 wine is 10 beer

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

Bottles of beer

A

100

B

Consumption choice before trade

700

C

30

100

0

Bottles of wine

opportunity cost table

Theory of Comparative Advantage:

Opportunity Cost Table
  • 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.
comparative advantage specialization
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
comparative advantage specialization1
Comparative Advantage: Specialization

Theory 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.
carl mike before specialization trade

Carl & Mike After Specialization, but Before Trade

Total Production & Consumption

Total Gains

Carl Produces & Can Consume

Mike Produces & Can Consume

+

=

Wine (btls.)

Beer (btls.)

+10

+260

0

1,000

80

0

80

1,000

Carl & Mike Before Specialization & Trade

Carl Produces & Consumes

Mike Produces & Consumes

Total Consumption

+

=

Wine (btls.)

Beer (btls.)

30

700

40

40

70

740

slide66

Trade: The Benefits of Specialization

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

(terms of trade: 5 beer for 1 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 1 wine for 5 beer
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

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

After trade 1 wine “trades” for 5 beer

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

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

175 Bottles of Beer

To

Trades away

To

Trades away

35 Bottles of Wine

Trade Between Carl & Mike

1 Wine trades for 5 Beer

or

1 Beer trades for 1/5 Wine

Mike (specializes in wine)

Carl (specializes in beer)

Before trade Mike gave up 1 wine to get 1 beer, after trade1/5 wine

Before trade Carl gave up 10 beer to get a wine, after trade 5 beer

carl mike after specialization trade
Carl & Mike After Specialization & Trade

Carl

Trades

For (+)

Away (-)

Consumes

After

Trade

Produced & Consumed

Before Trade

Gains

from

Trade

Produces

Wine (btls.) Beer (btls.)

0

1,000

+35

-175

35

825

30

700

+5

+125

Mike

Trades

For (+)

Away (-)

Consumes

After

Trade

Produced & Consumed

Before Trade

Gains

from

Trade

Produces

Wine (btls.)

Beer (btls.)

80

0

-35

+175

45

175

40

40

+5

+135

mike s production possibilities after trade

Consumption after trade

D

Mike’s Production Possibilities After Trade

Bottles of beer

Mike produces 80 wine and then trades 35 wine for 175 beer,

leaving him with 45 wine and 175 beer, point D

175

A

B

80

C

40

Bottles of wine

40

45

80

carl s production possibilities opportunity costs after trade

D

Consumption after trade

Carl’s Production Possibilities/ Opportunity Costs, After Trade

Bottles of beer

Carl produces 1000 beer and trades 175 beer

to Mike for 35 wine, leaving him with 825 beer

and 35 beer, point D

A

100

825

B

700

C

30

35

100

0

Bottles of wine

absolute advantage
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.
gains from specialization and trade
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
why no free trade
Why No Free Trade?
  • Misunderstanding: people misunderstand the facts or hold to political or ideological dogma, or confuse voluntary jobs with enforced slavery
  • Short-run effects: in the SHORT-RUN, there may be some unpopular adjustments:
    • Richer, developed countries may lose jobs to developing countries with a comparative advantage
    • Poorer, developing countries may have short-run environmental damage until the higher incomes lead to environmental protection
slide75

Chapter 16 Conclusions

  • General equilibrium requires simultaneous equilibrium in multiple markets
  • One change can cause a cascade of changes through markets until a new equilibrium is reached
  • An equilibrium is Pareto Efficient if no other allocation of inputs can make one person better off without making another worse off.
slide76

Chapter 16 Conclusions

4) 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

slide77

Chapter 16 Conclusions

6) 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