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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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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.


  • 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


    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


    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


    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.


    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


    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


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