Econ 6202, Fall 2009
Dmitry Shapiro
Problem Set 10
Optional
1. A monopolist faces a market demand curve given by
q
(
p
) = 70

p.
(a) If the monopolist can produce at constant average and marginal costs of
AC
=
MC
= 6, what
output level will the monopolist choose to maximize profits?
What is the price at this output
level? What are the monopolist’s profits?
(b) Assume instead that the monopolist has a cost structure where the total costs are described by
TC
(
q
) =
1
4
q
2

5
q
+ 300
.
Find the pricequantity combination that maximize the monopolist’s profit. What will profits be?
2.
Firstdegree price discrimination
Consider the following economy. There are two consumers, 1 and 2, who derive utility from a certain
good (
x
) and from money (
m
). The consumers’ utility functions are
u
1
(
x, m
) = 40
√
x
+
m,
u
2
(
x, m
) = 60
√
x
+
m.
A monopolist produces the good at constant average and marginal costs
c
= 5.
Suppose that the
monopolist observes the consumers’ utility and makes takeitorleaveit offers (
r
i
, x
i
)),
i
= 1
,
2 (
r
i
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 Fall '09
 SHAPIRO
 Economics, monopolist, marginal costs, Dmitry Shapiro, Assume interior solutions

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