BPUB250
Problem Set5
Due: April 4-5, 2012 in Class
Question 1
Hugh is planning to open a Shabu Shabu restaurant in Philadelphia. It is the only restaurant in
Philly specialized in Shabu Shabu, so it has a monopoly (in at least a narrowly defined market).
Demand is predicted to be
q=100-2p
, and Hugh’s total cost function is given by
C(q) = q
2
+5q
.
(a)
Hugh stopped attending BPUB250 class before the midterm, and he insisted that a firm
should always produce where price equals marginal cost. Compute Hugh’s quantity
choice, price, and profits under this assumption.
(b)
Now compute the profit-maximizing quantity, price and profits. Why do the values you
calculated in (a) and (b) differ?
(c)
Hugh has the option to build a second kitchen with a onetime construction cost of
F.
The
second kitchen, which is equipped with state-of-the-art cooking utensils, will operate at a
constant marginal cost of $25. With this option, Hugh can serve the Shabu Shabu demand,
q=100-2p,
with two kitchens. What is the maximum cost
F
you would advise Hugh to
pay for building the second kitchen?
Question 2
Steve Jobs has been very successful in selling the
iPad3
. He has two manufacturing plants, one
in the US (
U
) and the other in China (
C
). The phones produced by each plant are identical, and
Steve is a monopolist in both countries. The demand curve in each country is given by
(respectively):
Q
c
= 100 – P
c
Q
u
= 200 – 2P
u
The total cost function of each plant is given by (respectively):
C
c
(Q
c
) = 2Q
c
2
C
u
(Q
u
) = F +10Q
u
+ Q
u
2
where
F
is a fixed cost. Unless suggested otherwise, assume
F
is such that Steve chooses to
manufacture at the US plant.
(a)
Initially Steve is only permitted to sell an
iPad3
manufactured in one country to
consumers in that country. How many units does each plant produce? What price does
Steve charge in each country? What are Steve’s total profits ( as a function of
F
)?

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