Question

Please be descriptive.

The market demand curve in a commodity chemical industry is given by Q 600 - 3P, where Q is the quantity demanded per month and P is the market price in dollars. Firms in this industry supply quantities every month, and the resulting market price occurs at the point at which the quantity demanded equals the total quantity supplied. Suppose there are two firms in this industry, Firm 1 and Firm 2. Each firm has an identical constant marginal cost of $80 per unit. (a) (20 points) Find the Cournot equilibrium quantities for each firm. What is the Cournot equilibrium market price? librium quantities for each firm. What is the Stackelberg equilibrium price? elberg equilibria. Under which equilibrium is overall industry profit the greatest? (b) (20 points) Assuming that Firm 1 is the Stackelberg leader, find the Stackelberg equi- (c) (10 points) Calculate and compare the profit of each firm under the Cournot and Stack-

Answer 1

Given data: Q = 600 - 3p let the stockelborg model: pi_2 = q_! + q_2 + q_2 = 360 q_1 + 2q_2 = 360 q_2 = 360/2 - 4/2 = 180 - q_1/2 pi_1 = profit = T_R - T_C = p_1q_1 - 80 q_1 = [200 - q^2_1/3 - q_2/3] q_! - 80q_1 = 200q_1 - q^2_1/3 - q_1q_2/3 - 80q_! = 120q_1 - q^2/3 - q_1q_2/3 = 120q_1 - q^2_1/3 - 60q_1 + q^2_!/6 partial differential pi/ partial differential q_1 = 120 - 2q_1/2 - 60 + q_1/3 = 0 60 = partial differential q_1/3 - q_1/3 60 = q_1/3 q_1 = 180 q_2 = 180 - 180/2 = 180 - 90 q_2 = 90 p = 600 - Q/3 = 600 - (180 + 90)/3 p = $110 \r\n pi_1 = p_1q_1 - 80 q_1 = q_1(p - 80) = 120(120 - 80) = 120(40) = 4800 pi_2 = p_1q_2 - 80q_2 = q_2(p - 80) 120(120 - 80) = 4800 by the stackelberg: pi_1 = p_1q_1 - 80 q_1 = q_1(p - 80) = 180(110 - 80) = 180(30) = 5400 pi_2 = pq_2 - 80 q_2 = q_2(p - 80) = 90 time 30 = 2700 total = pi_1 + pi_2 = 5400 + 2700 = 8100 Q = 600 - 3p 3p = 600 - Q p = 200 - (q_1 + q_2/3) from the firm - 1 TR = p_1q_1 = 200q_1 - q^2_i/3 - q_1q_2/3 MR = 200 - 2q_i/3 - q_2/3