Question

5. Cournot Competition Consider a Coumot duopoly model. Suppose that market demand is P-a-qi Also suppose that the cost functions of the two firms are TG (q) = q, and T( (a) Write the profit function, and the first order condition. (b) Find out the profit maximizing output for each firm. (c) Find the pofit earned by each firm, total profit eamed by the two fims to (d) Now assume that the two firms collude and act as a monopoly. Find q by the new monopoly firm and the profit eamed. Compare the profite monopoly with the total profit eamed by the two firms in (c).

Answer 1

Answer. P-a-ql-q2 Date: ----9/5/2019 a) Profit function for firm I: (a ql- q2)q1 q12 For the first order condition differentiating the above function with respect to ql and setting equal to zero. a 2q1- q2 2q1 Profit function for firm 2: (a-q1-92)q2 = q22 For the first order condition differentiating the above function with respect to q2 and setting equal to zero. a 2q2 - ql 2q2 4q2-a - q1 q2 (a ql)/4 b)

Put the value of q2 in qlwe get, q2 (a ql)/4 q2 = (a-((a-q2)/4))/4 q2 a/5 Put the value in ql (a q2)/4 Profit of firm 1: 3a/5*a/5 - (a/52 2a2/25 Total Profit = 4a2/25 d) Now the firm collude Profit of firm 2 Profit = (a-Q)Q-Q2 Differentiating the function with respect to Q and setting equal to zero, a-2Q-2Q = 0

a = 4Q Q a/4 2_.2 Thus the total profit earned by two firms (4a2/25) is less than the profit of monopoly (a2/8)