- Firms A and B make up a cartel that monopolizes the market for a scarce
natural resource. The firms’ marginal costs are MCA 6 2QAand
MCB 18 QB, respectively. The firms seek to maximize the cartel’s
total profit.
a. The firms have decided to limit their total output to Q 18. What
outputs should the firms produce to achieve this level of output at
minimum total cost? What is each firm’s marginal cost?
b. The market demand curve is P 86 Q, where Q is the total output
of the cartel. Show that the cartel can increase its profit by expanding
its total output. (Hint:Compare MR to MC at Q 18.)
c. Find the cartel’s optimal outputs and optimal price. (Hint:At the
optimum, MR MCAMCB.) - A single buyer who wields monopoly power in its purchase of an item is
called a monopsonist.Suppose that a large firm is the sole buyer of parts
from 10 small suppliers. The cost of a typical supplier is given by C 20
4Q Q^2.
a. Suppose that the large firm sets the market price at some level P. Each
supplier acts competitively (i.e., sets output to maximize profit, given
P). What is the supply curve of the typical supplier? Of the industry?
b. The monopsonist values the part at $10. This is the firm’s break-even
price, but it intends to offer a price much less than this and purchase
all parts offered. If it sets price P, its profit is simply:
where Qsis the industry supply curve found in part (a). (Of course,
Qsis a function of P.) Write down the profit expression and maximize
profit with respect to P. Find the firm’s optimal price. Give a brief
explanation for this price.- a. When a best-selling book was first released in paperback, the Hercules
Bookstore chain seized a profit opportunity by setting a selling price
of $9 per book (well above Hercules’ $5 average cost per book). With
paperback demand given by P 15 .5Q, the chain enjoyed sales of
Q 12 thousand books per week. (Note:Q is measured in thousands
of books.) Draw the demand curve and compute the bookstore’s
profit and the total consumer surplus.
b. For the first time, Hercules has begun selling books online—in
response to competition from other online sellers and in its quest for
new profit sources. The average cost per book sold online is only $4.
As part of its online selling strategy, it sends weekly e-mails to
(10P)Qs,344 Chapter 8 Monopoly*
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