Optimal Taxation Old Riddles Neoclassical Answers Copyright 2008 by Peter Berck.
A P.O. Is a C.E. © 1998, 2007 by Peter Berck. What Is It Good? Sum of surplus and profits allows...
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Transcript of A P.O. Is a C.E. © 1998, 2007 by Peter Berck. What Is It Good? Sum of surplus and profits allows...
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A P.O. Is a C.E.
© 1998, 2007 by Peter Berck
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What Is It Good?
• Sum of surplus and profits allows for policies that make income less evenly distributed.
• A dam that increases banana plantation owners incomes by more than it decreases native American’s incomes increases surplus plus profits.
• We can do better.
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Pareto Optimal (Easy Definition)
• An allocation is Pareto optimal if there is no way to make any agent better off without making some other agent worse off.
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The First Welfare Theorem
• A Competitive Equilibrium is a Pareto Optimum
• But first an example to introduce the machinery
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Smoker and Asthmatic
• In this example there are two consumers, smoker and asthmatic.
• There are two goods, clean air (CAS) and chocolate available in fixed supply.
• The initial allocation of the goods makes a big difference for how clean the air is.
• The initial allocation makes a big difference for how much each agent gets.
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Edgeworth-Bowley Box
• The width is the amount of CAS– Asthmatic uses CAS
to breathe– Smoker, to smoke
• The height is the amount of chocolate CAS
Cho
cola
teA
S
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Who Got What?
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Picture of a P.O.
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The “Lens” of Pareto Preferred
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A Possible Trade to a P.O.
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Which Are P.O.?
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All Possible P.O.’S
A
SDoes Endowment Matter Now???? Is there a Coase Theorem?
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Coase Theorem (Revised)
• When changes in income don’t change the demand for the environmental good.
• And the costs of transaction between agents is small.
• And the property rights in clean air services are defined.
• Then, trading in clean air will lead to a unique amount of clean air and pollution.
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The First Welfare Theorem
• When all the goods are freely traded, a competitive equilibrium is a Pareto optimum.
• There are many Pareto optima.– All of them can be achieved as competitive
equilibrium starting at SOME initial allocation.• Agent’s have very different incomes in the
different Pareto optima.
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Graphical Proof for 2 consumers
• Preliminary:• Suppose consumer starts with (e1,e2)
quantities of the two goods.• Then income is y = p1 e1 + p2 e2• Budget constraint is• p1 e1 + p2 e2 = p1 x1 + p2 x2• Budget constraint goes through point (e1,e2)
and has slope –p1/p2 as usual.
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Wrong Price
Pw = 1; Consumer starts with (10,40)
Other Consumer
Starts with (20,50)
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A Price Change
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CE is a PO
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First Welfare Theorem and Pollution
• The theorem applies to goods that are traded.• Consumers’ demand for clean air isn’t
effective because:– Costs to much to trade small amounts of CAS.– Benefits from buying it do not accrue only to the
consumer who bought it.• Government is needed to assure clean air.
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Free Rider Problem
• When I buy a candy bar, who benefits?• When I buy an SO2 certificate and retire it,
who benefits?– Do all the beneficiaries contribute to the cost of
buying and retiring the certificate?
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Gloria’s comment:
• An economy can be perfectly (Pareto) efficient and perfectly disgusting.