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北大光华微观经济学作业 Problem Set-4.pdf
Intermediate Microeconomics
Fall 2008
Problem Set 4
1.Two firms A and B produce luxury sheepskin auto seat covers. Each firm has a
cost function given by C(q) 20q +q2 . The market demand for these seat covers
is represented by the inverse demand curve P 200 −2Q , where Q qA =+qB .
1) If each firm acts to maximize its profits, taking its rival’s output as given, what
will be Cournot equilibrium output level for each firm? What are the profits for
each firm?
2) It occurs to the managers of firm A and B that they could do a lot better by
colluding. If the two firms collude, what will be the profit-maximizing choice of
output? What is the output and the profit for each firm?
3) 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. What output strategy is each firm likely to purse? Why?
2. Two firms compete by choosing price. Their demand functions are
Q 20 =−P +P ; Q 20 =−P +P
1 1 2 2 2 1
where P and P are the prices charged by each firm, respectively, and Q and Q are
1 2 1 2
the resulting demands. Marginal costs are zero.
1) Suppose the two firms set their prices at the same time. Find the resulting Nash
equilibrium prices.
2) Suppose Firm 1 sets its pricefirst , and then Firm 2 sets its price. What price will
each firm charge, how much will it sell, and what will its profit be? Does the first
mover have a first-mover advantage?
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