Consider a market for two differentiated products.

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

D1(p1,p2)= 130− 4/3p1 + 2/3p2

and demand for product 2 is

D2(p1,p2)= 130− 4/3p2 + 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) [8 marks] Are the two goods complements or substitutes? Explain why.

(b) [10 marks] Suppose the two goods are produced by one firm. What are the optimal prices for the two goods? What is the total profit for the firm? [Hint: Make sure the demand of each good enters the monopolist’s profit function!]

(c) [10 marks] 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) [12 marks] Finally, assume the two firms from (c) play the price game with an infinite horizon and a common discount rate of δ. 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?

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