L24
Public Goods
Public Goods -- Definition

Some goods are:
– Nonexcludable (NE): property rights
cannot be enforced.
– Nonrival (NR): all consumers can
simultaneously consume the good.
E
NE
R
NR

A good is public if it is NE and NR
Examples of public goods
 National
defense
 Mathematical formula (Research)
 Broadcast radio and TV programs
 National parks
Park Size: Market Outcome
 Two
agents: A and B
 Pubic good: Park
 A:
Regular consumer
 B:
Park lover
Plan for today
 1.
Free Markets (Nash Equilibrium)
 2.
Socially optimal outcome
 3.
Implementation
A: best response to
A: best response to
B: best response
Equilibrium
 Nash
x1A * , x1B *
Equilibrium:
A*
B*
x
x
- 1 best response to 1
A*
B*
x
- x1 best response to 1
Free riding by A
Nash Equilibrium: x , x  (0, 4)
B: Creates a park of size 4
A: Does not contribute at all and
uses the park created by B
 Free riding by A
 Size of the park (General rule)
 In
A*
1
B*
1
Free Market Supply
Pareto efficient outcome
 Mayor
maximizes welfare of both A and B
U U A U
B
Underprovision of public
 Efficient
size of Park: 6
 Underprovision of public good
 Public good: positive externality
 (Pareto) optimal size (General Rule)
Socially optimal supply
Implementation of efficient outcome
 How
to implement efficient outcome?
 Tax agents and provide Public Good
 Problem: Information about valuation
 Mechanism
design: How to extract
information in the least costly way