Question

Consider firms facing the demand curve P=90-5Q 17 where Q- Q1 +Q2 The firms' cost functions are Cl (Q1) = 15 + 5Q1 12 and (2)-+1002 Suppose that both firms have entered the industry. What is the joint profit-maximizing level of output? How much will each firm produce? Combined, the firms will produce units of output, of which Firm 1 will produceunits and Firm 2 will produce units. (Enter a numeric response using a real number rounded to two decimal places.) 0 1 2 3 4567 8 9 10 11 12 1314 15 16 17 18 Firm 2's output What is each firm's equilibrium output and profit if they behave noncooperatively? Use the Cournot model If the firms comnete then Firm 1 will nroduce units of outnut and

Answer 1

Demand curve: P = 90 -5Q_1 Q = Q_1 + Q_2 (given) cost function of firm 1: c_1 (Q_1) = 15 + 5Q_1 cost function of firm 2: C_2 (Q_2) = 5 + 10Q_2 marginal cost curve for firm 1: d(c_1)/dQ_1 = 5 marginal cost curve for firm 2: d(c_2)/dQ_2 = 10 total Me for industry = 5 + 10 = 15 now, we know from economic theory that p = Mc therefore 90 -5Q = 15 implies 5Q = 75 implies Q* = 15 therefore 15 is the joint profit maximizing level of output similarly, for firm 2: R_2 = PQ_2 = (90- 5Q_1 -5Q_2)Q_2 = 90Q_2 -5Q_1 Q_2 -5Q^2_2 MR_2 = 90 -5Q_1 -10Q_2 now, MR_2 = Me_2 implies 90- 5Q_1 -10Q_2 = 10 implies 80 = 5Q_1 + 10Q_2 implies Q_2 = 80- 5Q_1 /10 = 8- 0.5Q_1 this is reaction curve of firm 2 now, since this is coronet model, replacing Q_2 in firm 1's reaction curve Q_1 = 17- (8- 0.5Q_1)/20 implies 2Q_1 = 9 + 0.5Q_1 implies 1.5Q_1 = 9 implies Q*_1 = 6 therefore Q*_2