Chapter 4 Public Goods

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Chapter 4 Public Goods
A. Definition and Fundamentals - A public good
satisfies the following two conditions. - Nonrival
ry Once provided to some, the good can be
provided to an additional person without any
additional costs, and, - Non-excludability
Nobody can be denied the consumption of the
good. - Consumption of a public good need not be
valued equally. - Some goods may be rival but
non-excludable (i.e. common resources) or
non-rival but excludable. - Classification as
public good depends on the market condition.
(Examples?) - Public goods may be provided
privately and vice-versa. B. Efficient Provision
of Private Goods Revisited - Consider again the
Adam Eve example with production of apples and
fig leaves. - Let DfA and DfE denote Adam and
Eves demand curves for fig leaves, equivalent to
each persons willingness to pay for a particular
quantity. - For convenience, assume that Pa
1. - The price of fig-leaves, Pf , varies with
market (aggregate) demand, DfAE, which is found
by horizontal summation. - Since Pa 1, utility
maximization leads to
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- Then, the two demand curves, DfA and DfE , also
depict each individuals MRSfa schedule for each
quantity. - Similarly, the supply curve, Sf ,
gives MRTfa . - Then, at the market equilibrium
where DfAE and Sf intersect C. Efficient
Provision of Public Goods - With public goods,
market demand is not found by horizontal
summation, simply because each person gets the
same quantity of the (non-excludable and
non-rival) good. - The publics willingness to
pay, instead, is found by vertical summation. -
Instead of fig leaves, assume that the second
good was rockets in a public fireworks display.
- Suppose that for the first three rockets, Adam
and Eve are willing to pay (6,3,2) and
(3,2,1), respectively. Suppose also that each
rocket costs 5. What is the efficient number of
rockets? - The intuition above is clear With
public goods, efficiency dictates that the good
be provided until the summation of all
individuals marginal valuations be equivalent to
the marginal cost of the last unit. - In our
framework, efficiency requires that D.
Free-Rider Problem - Assume that to finance the
display, the govt asked Adam and Eve for their
valuation of the first rocket. How much value
would Adam reveal? Eve? Would there be a firework
display at all?
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- It is easy to see that efficiency will almost
never be reached. - Even if the good is
excludable, non-rivalry will render the voluntary
provision of the good inefficient. Why? - Is
there a way out? A. Perfect price discrimination
is one way out but usually impossible. B.
Perhaps some people care for others, in which
cases free-riding may be reduced. C. Government
may need to control the provision of public
goods. D. Where bargaining costs are minimal and
the group is small, the government may assign the
right of producing to one person. Then,
bargaining may lead to optimal production. - The
following argument makes the last point
explicit. - Let DrA DrE Dr be the unique
demand schedule for both Adam and Eve. Let the
supply Sr be perfectly inelastic, i.e. constant
MCr. - Individually, no one can afford the
fireworks. But if Adam or Eve was allowed to
provide the good, bargaining would lead to
efficient provision.