Consider a market for two differentiated products. Demand for good 1 is given by

and demand for product 2 is

D1(p1,p2)=1304/3p1 +2/3p2

D2(p1,p2)=1304/3p2 +2/3p1

where p1 and p2 are the prices of good 1 and 2. The cost function for both products and any firm producing them is C(q) = 15q.

(a)Are the two goods complements or substitutes? Briefly explain why. What is the diversion ratio of this demand schedule?

(b) Suppose the two goods are produced by one firm. What are the optimal prices for the two goods? What is total profit for the firm? [Hint: Make sure the demand of each good enters the monopolist's profit function!]

(c) Suppose firm 1 produces good 1 and firm 2 produces good 2. Assume that the two firms compete in prices. Derive the reaction function of each firm and give the Nash equilibrium prices and profits.

(d) Finally, assume the two firms from (c) play the price game with an infinite horizon and a common discount rate of . Construct a subgame perfect equilibrium with trigger strategies in which both firms charge the prices you found in (b) and punish devia- tions by reverting forever to the Nash equilibrium prices in (c). Under which condition can the firms sustain this equilibrium?