Consider a market for two differentiated products. Demand for good 1 is given by 1 Di(P1, P2) 1 P₁+ 4P2 and demand for product 2 is D2(P1, P2)=1-P2+ P1 where p₁ and p2 are the prices of good 1 and 2. Suppose firm 1 produces good 1 and firm 2 produces good 2. All production costs are sunk, that is, firms supply at zero production cost. Assume that firms compete in prices. (a) [4 marks] Calculate the diversion ratio and explain its meaning (in two to four sen- tences). (b) [6 marks] Derive the reaction function of each firm and calculate the Nash equilibrium in prices. (c) [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!] Compare the prices with your solution to subquestion (b) and explain in two to four sentences. (d) [10 marks] Now suppose again that the products are produced by two different firms. Furthermore, the firms play the price game with an infinite horizon and a discount rate of 8. Construct a subgame perfect equilibrium with trigger strategies in which both firms charge the prices you found in (c) and punish deviations by reverting forever to the Nash equilibrium prices in (b). Under which condition can firms sustain this equilibrium?

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