Public Goods
© 1999, 2007 by Peter Berck
Definition
• A good is a pure public good if one person’s
consumption of the good does not diminish
another person’s consumption of the good.
• Examples: National defense, TV Programs, Clean Air,
Views, Existence of Wild Creatures
Market Doesn’t Work
• Let P = a – bQ be a typical person’s
marginal willingness to pay for the public
good.
• Suppose there are N people
• Since EACH of the N people consume’s
(enjoys? loathes?) Q
• Total marginal willingness is
• N P = N (a- bQ)
Social Welfare Max
• Demand=Total Marginal Willingness=
• N P = N (a- bQ)
• So Social optimum
• mc(Q) = NP = N (a-bQ)
• or a – bQ = mc(Q) / N
• in social optimum each person should bear only 1/N
of marginal cost
Market Outcome
• No person will buy any more Q when
• P = a –b Q = mc(Q)
The Picture
The public good is
underprovided by
the free market
N( a –bQ)
mc
a -bQ
DWL
Triangle is DWL.
Area under N(a-bQ)
is lost willingness.
N( a –bQ)
mc
a -bQ
Area under mc
avoided cost.
Conclusion
• Although the Market will properly allocate
private goods, like candy bars
• It will not provide a outcome with public
goods that
• Maximizes surplus plus profits
Therefore
• With Public Goods, the government is
needed to
• either produce them
• or stop them from being destroyed
• It can accomplish these aims with
• Command and Control (standards)
• or Incentives (taxes)