Homework 3 – Eco 431
Due: Wednesday April 10.
1. The maker of the printer BlackInk, faces an important product design
dilemma: deciding the speed of its popular laser printer. There are two
market segments: Professionals are willing to pay up to $800 (a − .5)
for the printer, where a is printer speed. Students, in turn, are willing
to pay up to $100 a. Maximum printer speed corresponds to a = 1,
whereas a = 0 corresponds to a worthless printer. There are one million
professionals and one million students. It is equally costly to produce a
printer with any level of a. In fact, other than the initial development
costs, production costs are zero. How many versions of the BlackInk
should Printing Solutions sell? Which versions? What are the optimal
prices of each version?
2. Sony’s engineers have just finished work on the new marvel in video
games: the PlayStation 5! Originally planned for a 2014 release, the
product is available to Sony as of 2013. The question is, should Sony
launch it now or should it keep the early development a secret.
Sony’s market research team produced the following numbers regarding
willingness to pay (WTP) for PS4 and PS5:
User type
Low-end user
High-end user
Number users
80 million
20 million
WTP for PS4 WTP for PS5
800
1100
1200
2200
The estimated production cost of a PS5 is $400, while that of a PS4 is
$200.
(a) Determine the optimal solution if Sony is to sell one version only.
(b) Determine if Sony is better off by selling the PS3 and PS4 simultaneously.
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(c) Suppose that Sony’s market research team is confident about the
values of willingness to pay, but not about the fraction of highend users. Specifically, suppose there is a total of 100 million consumers, a fraction α of which are high-end users. (For questions
(a) and (b) we considered α = .2.),
Determine the optimal policy as a function of α.
3. You are the sole US producer of the generic antidepressant Sensitrum.
Your marginal cost is $2 per dose. Demand is given by Q = 400 − 50 p
(Q in millions of doses, p in $). There is a second producer in India
whose marginal cost is INR 145 (including transportation cost to the
US). Firms set prices simultaneously.
(a) What is your equilibrium profit at the current exchange rate of
INR 48 / US$?
(b) An advertising and retailing campaign costing $80m is expected
to increase demand by 40%. Should your firm go ahead with it?
(c) One macroeconomics expert tells you that “it is likely that the
rupee will appreciate in the near future.” How would this influence
your decision?
4. Two firms produce a specialized microchip (Trium X406) used in certain home appliances. Demand is given by Q = 100 − 2 p (Q in thousands of units, p in $). Whichever firm sets the lowest price gets all
of the demand, and there are no capacity constraints. Both producers
have a marginal cost of $30. A cost-reducing innovation would allow
Firm 1 to decrease its cost down to $20. The cost of the innovation is
$520 k per period.
(a) Should Firm 1 go ahead and acquire the innovation?
(b) Macroeconomic conditions indicate that demand is expected to
increase by up to 40% in the future? Would this change your
answer?
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