Assume that the indirect utility function is now

Consider the model of fiscal competition discussed in class. Assume that the indirect
utility function is now given by:
V ( g, p, y ) = -{ αg
ρ
+ [ y p
- B
]
ρ
} (5)
where ρ < 0, α > 0 and 1 > B > 0. Remember households differ in income y which
is distributed with density f ( y ).
a) Using Roy’s identity derive the housing demand for each household type. What
are the price and income elasticities of housing demand?
b) Derive the condition which characterizes boundary indifference between two adja-
cent communities.
c) Suppose households not only differ in income, but also tastes for public goods
denoted by α . Derive the new condition which characterizes boundary indifference
between two adjacent communities.
d) Consider a model with 2 communities. Provide a graph that illustrates household
sorting for the model in (c) (Hint: graph the boundary indifference condition in the
( α, y ) space and explain who lives in which community.)

Problem 4: Externalities and Global Warming
The newly elected mayor of an city has pledged to reduce air pollution. The city
has no close neighbors. The only source of air pollution are the two domestic plants
run by firm A and firm B. Firm A has pollution abatement (=reduction) costs of x 3 ,
where x is a unit of pollution. Firm B has a pollution abatement cost of x
2
. Assume
that neither firm is initially engaging in pollution abatement. The per unit benefit to
a unit of pollution abatement experienced by the island’s citizen is constant at $300.
a) What is the socially optimal level of pollution abatement? How is the socially
optimal level of abatement split between the two firms?
b) The mayor considers engaging in command and control style quantity regulation
and declares that each firm must engage in 80 units of pollution abatement. Is this
optimal? Why or why not?
c) Alternatively the mayor considers providing a subsidy of $300 per unit of pollution
abatement. What is the per firm and total level of pollution abatement? Is this
socially optimal?
d) The mayor also considers issuing pollution permits and establishing a market for
these permits. For reasons associated with the relative generosity of the firms to his
recent election campaign, firm A is given permits such that is must engage in 100
units of pollution abatement if it fails to enter the market. Firm B is given permits
such that it must engage in 60 units of pollution abatement if it fails to enter the
market. Each unit allows the firm holding the unit to produce one unit of pollution.