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An industry consists of two firms, firm I and firm 2. The demand function for the product of each firms is given by q, = 720 - 3p, + 2p2 and q2 = 720 - 3p2 + 2p. We assume for simplicity that the total cost of production is zero: 70, = 7C. =0 (a) (8 points) Are these two products substitutes or complements? Assuming that firms compete over prices, find the price best-response functions for firm 1 and firm 2. Draw a diagram that shows the BRFs and the equilibrium. Are prices strategic substitutes or complements? Find the Bertrand Nash equilibrium in prices and outputs. Obtain the profits of each firm. (b) (8 points) Show that the duopolists have incentives to collude. Find their joint profit-maximizing price, output, and profit: find each firm's price. output and profit. Is collusion a Nash equilibrium? If not. what is the optimal defection for each firm Show this game in a 2X2 matrix form. What does this imply about the Nash equilibrium or the stability of their collusive agreement? Is it a Prisoner's Dilemma Type? (c) (8 points) Suppose now that firms move sequentially in setting their prices: firm I moves first and set its price and then firm 2 moves after observing firm I's price. Find the Nash equilibrium prices and profits. Do firms have first moving advantage? Why or why not