2. Two firms produce luxury sheepskin auto seat covers, Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by C(q) = 30q+1.5q² The market demand for these seat covers is represented by the inverse demand equation P=300-30 where Q=q1 + 92, total output. a. If each firm acts to maximize its profits, taking its rival's output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm?

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Chapter12: Price And Output Determination: Oligopoly
Section: Chapter Questions
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2. Two firms produce luxury sheepskin auto seat covers, Western Where (WW) and
B.B.B. Sheep (BBBS). Each firm has a cost function given by
C(q) = 30q+1.5q²
The market demand for these seat covers is represented by the inverse demand
equation
P=300-30
where Q=q1 + q2, total output.
a. If each firm acts to maximize its profits, taking its rival's output as given (i.e.,
the firms behave as Cournot oligopolists), what will be the equilibrium quantities
selected by each firm? What is total output, and what is the market price? What
are the profits for each firm?
b. It occurs to the managers of WW and BBBS that they could do a lot better by
colluding. If the two firms collude, what will be the profit-maximizing choice of
output? The industry price? The output and the profit for each firm in this case?
c. The managers of these firms realize that explicit agreements to collude are
illegal. Each firm must decide on its own whether to produce the Cournot
quantity or the cartel quantity. To aid in making the decision, the manager of
WW constructs a payoff matrix like the one below. Fill in each box with the
profit of WW and the profit of BBBS. Given this payoff matrix, what output
strategy is each firm likely to pursue?
Round off profits to whole dollars, the payoff matrix is as follows:
BBBS
Profit Payoff Matrix
(WW profit, BBBS profit)
WW Produce Cournot q
WW Produce Cartel 9
Produce
Cournot q
Produce
Cartel q
d. Suppose WW can set its output level before BBBS does. How much will WW
choose to produce in this case? How much will BBBS produce? What is the
market price, and what is the profit for each firm? Is WW better off by choosing
its output first? Explain why or why not.
Transcribed Image Text:2. Two firms produce luxury sheepskin auto seat covers, Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by C(q) = 30q+1.5q² The market demand for these seat covers is represented by the inverse demand equation P=300-30 where Q=q1 + q2, total output. a. If each firm acts to maximize its profits, taking its rival's output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm? b. It occurs to the managers of WW and BBBS that they could do a lot better by colluding. If the two firms collude, what will be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case? c. The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. To aid in making the decision, the manager of WW constructs a payoff matrix like the one below. Fill in each box with the profit of WW and the profit of BBBS. Given this payoff matrix, what output strategy is each firm likely to pursue? Round off profits to whole dollars, the payoff matrix is as follows: BBBS Profit Payoff Matrix (WW profit, BBBS profit) WW Produce Cournot q WW Produce Cartel 9 Produce Cournot q Produce Cartel q d. Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much will BBBS produce? What is the market price, and what is the profit for each firm? Is WW better off by choosing its output first? Explain why or why not.
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