Cournot with three firms. Three firms are producing identical products, and the marginal cost is fixed at MC = 20. The demand curve for the product is given by Q = 70 P/2. Firms 1 can choose any quantity q1 0. Firm 2 can choose any quantity q2 0. Firm 3 can choose any quantity q3 0. For example, if q1 = 10,q2 = 10,q3 = 20, then the total quantity produced is Q = q1 + q2 + q3 = 40 and price is P = 140 2Q = 60. 1

(a) What quantity q1 maximizes firm 1's profit if firm 2 chooses to produce q2 = 10 units and firm 3 chooses to produce q3 = 20 units? (b) Find the best reply formula for firm 1. That is, specify a formula for firm 1's profit maximizing quantity for any given quantities q2 and q3 produced by firms 2 and 3. (c) What is the Nash equiblirium of the game? (You can use symmetry to obtain best reply formulas for firms 2 and 3 given your answer to part b). That is, find q1,q2,q3 such that q1 is a best reply to q2,q3, and similarly q2 and q3 are best replies to quantities chosen by other firms. (d) Does each firm have a dominant strategy?