A P.O. Is a C.E.

© 1998, 2007 by Peter Berck

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.

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.

The First Welfare Theorem

• A Competitive Equilibrium is a Pareto Optimum

• But first an example to introduce the machinery

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.

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

Who Got What?

Picture of a P.O.

The “Lens” of Pareto Preferred

A Possible Trade to a P.O.

Which Are P.O.?

All Possible P.O.’S

A

SDoes Endowment Matter Now???? Is there a Coase Theorem?

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.

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.

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.

Wrong Price

Pw = 1; Consumer starts with (10,40)

Other Consumer

Starts with (20,50)

A Price Change

CE is a PO

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.

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?

Gloria’s comment:

• An economy can be perfectly (Pareto) efficient and perfectly disgusting.