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
S
– Asthmatic uses CAS
to breathe
– Smoker, to smoke
• The height is the
amount of
chocolate
Chocolate
• The width is the
amount of CAS
A
CAS
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
Does Endowment Matter Now???? Is there a Coase Theorem?
S
A
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.