2/19/2009
ProblemSetsW09.doc
5:28 PM
1
Robert Deacon
Econ. 210C
Winter 2009
Problem Set #1
(Where the problem setup is one of partial equilibrium, you may assume that the
underlying preferences make it legitimate to use partial equilibrium analysis.)
1.
An economy consists of two consumers,
2
,
1
=
i
, who have preferences given
by
i
i
i
m
x
U
+
=
2
1
2
where
i
x
is
i
'’s consumption of an ordinary consumption good
and
i
m
is
i
'’s consumption of the numeraire. The economy’s production technology
requires that producing
q
units of the consumption good requires using 2
q
units of
numeraire as input. Consumers are endowed with
i
ϖ
units of the numeraire and their
consumptions of the two goods must satisfy
0
,
0
≥
≥
i
i
m
x
.
a.
Find the utility possibility frontier (
)
(
2
1
U
F
U
=
) for this economy.
b.
Suppose a tax of
t
per unit is imposed on consumption of
x
and the economy
reaches a competitive equilibrium. What is the Marshallian surplus for this
economy and what is the deadweight loss from the tax?
2.
A city-owned golf course charges different prices for residents and nonresidents, with
the nonresident price being exactly twice as high as the resident price. The golf
course operates at zero marginal cost and has a fixed capacity of
Q
rounds of golf per
day. The mayor, who does not play golf, keeps any profits from golf course operation.
All golfers, residents and nonresidents, have identical quasilinear utility functions, all
demand functions are linear over the relevant range, and there are equal numbers of
golfers in each group.
a.
Characterize the prices the city will charge if it wishes to have zero excess
demand.
a.
Do golfers (residents and nonresidents), considered as a group, gain or lose from
this pricing policy, relative to a policy of charging the same (competitive
equilibrium) price to all? How does the mayor fare under the discriminatory
pricing policy, relative to charging a homogeneous price.
3. A perfectly competitive industry
is
composed of numerous identical firms, each of
which has the cost function
2
1
)
(
j
j
q
q
c
α
+
=
, where
q
j
is the output of the
j
th
firm.
Aggregate demand is perfectly inelastic in the relevant range, at
X=
200.
a.
What is the long run (allowing for entry) equilibrium price and number of firms?
(Don’t worry if the number of firms is not an integer.)
b.
Suppose the industry is in long run equilibrium with
α
=
1. If
α
increases to 2, how
will industry profits be affected in the short run situation where the number of
firms cannot adjust?
c.
What number of firms will operate in the new long run equilibrium?

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