A P.O. Is a C.E.

© 1998 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

The Point

When all goods are traded in a competitive market, the outcome is Pareto optimal. This is the justification for “letting the market

work” or non-interference by government. It is not true when goods like “clean air

services” are not traded freely. It does not imply that income is distributed in

an even fashion.

Does Ownership of the Air Matter?

The Coase theorem: it does not matter whether the polluter or pollutee owns the rights to clean air, the amount of clean air will be the same.

Two FirmsA

dditi

onal

Pro

fits F

rom

One

Mor

e U

nit o

f C

AS Clean Air ServicesFirm 1 Firm 2

No matter who owns theCAS to begin with, the firmsalways trade to the intersectionof their bid curves.

Two FirmsA

dditi

onal

Pro

fits F

rom

One

Mor

e U

nit o

f C

AS Clean Air ServicesFirm 1 Firm 2

Dead weight loss is greatest,with no trade, if the Red firmis prohibited from polluting.If the red firm were liable for thedamages of its pollution, it wouldpollute and pay the damages.

Smoker and AsthmaticIn 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?

0102030405060708090100

0 1 2 3 4 5

CAS

Chocolate

A

S

Picture of a P.O.

0102030405060708090100

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

CAS

Chocolate

A

S

The “Lens” of Pareto Preferred

A Possible Trade to a P.O.

0102030405060708090100

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

CAS

Chocolate

A

S

Which Are P.O.?

0102030405060708090100

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

CAS

Chocolate

A

S

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 TheoremWhen 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.

Gloria’s comment:

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

Free Rider Problem

When I buy a candy bar, who benefits?When I buy an SO2 certificate, who

benefits? Do all the beneficiaries contribute to the cost of

buying and retiring the certificate? Nother example: 6 of us go out to dinner and

split the bill. What happens to the size of our tab?

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.