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Answer Key: Problem Set 2
February 2, 2005
Problem 1
(a) Under leasing, the monopolist chooses monopoly pricing each period.
The pro
f
t of the monopolist in each period is:
π
t
=
P
t
Q
t
Demand in each period is:
P
t
= 1000
−
Q
t
where
t
=1
,
2
.The
f
rst order conditions w.r.t
Q
t
is:
1000
−
2
Q
t
=0
where
t
=1
,
2
. Solving them gives us
Q
1
=
Q
2
= 500
,thepro
f
tmaximizing
rental rate
P
1
=
P
2
= 500
,p
ro
f
t per period $250,000, and total pro
f
ts $
250
,
000(1 +
δ
)
.
(b) The monopolist knows that her
f
rstperiod sales are irreversible, so
in the secondperiod, she faces a residual demand:
Q
2
(
P
2
)=
Q
(
P
2
)
−
Q
1
= 1000
−
P
2
−
Q
1
So the inverse demand function for the second period is:
P
2
= 1000
−
Q
1
−
Q
2
The monopolist’s pro
f
t in the second period (given
Q
1
units sold in the
f
rst period) is:
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View Full Document π
2
=
Q
2
(1000
−
Q
1
−
Q
2
)
The
f
rst order condition is:
1000
−
Q
1
2
=
Q
2
.
Price in the second period
is:
P
2
=
1000
−
Q
1
2
,
and the pro
f
t in the second period is
π
2
=
(1000
−
Q
1
)
2
4
.
In the
f
rst period, consumers who buy the durable good this period can
consume it for two periods. They are willing to pay:
P
1
= 1000
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This note was uploaded on 07/18/2008 for the course ECON 200 taught by Professor Philiphaile during the Spring '08 term at Yale.
 Spring '08
 PHILIPHAILE
 Monopoly

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