Two firms, A and B, compete as duopolists in an industry. The firms produce a homogeneous good. Each firm has a cost function given by:

C(q) = 30q + 1.5q 2

The (inverse) market demand for the product can be written as:

P = 300 3Q , 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 Firm A and Firm B that they could do better by colluding. If the two firms collude, what would 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 Firm A constructs a payoff matrix like the real one below. Fill in each box with the (profit of Firm A, profit of Firm B). Given this payoff matrix, what output strategy is each firm likely to pursue?

(d) Suppose Firm A (leader) can set its output level before Firm B (follower) does. Use backward induction method to determine how much will Firm A choose to produce in this case? How much will Firm B produce? What is the market price, and what is the profit for each firm? Is firm A better off by choosing its output first? Explain why or why not.