In a market, there are two firms, firm A and firm B, producing differentiated products. Denoting the prices with pA and pB, firm A faces a demand given by qA(pA,pB) = 3802pA +4 pB, where 0 < 1, and firm B faces a demand given by qB(pA,pB) = 180 2pB + pA. Each firm has a constant marginal cost, cA =cB =10andnofixedcosts.

1. (a)(12 pts) Suppose that the firms compete in prices simultaneously. Find the Nash equilibrium prices in terms of . Provide intuition on the effect of on the equilibrium prices.
2. (b)(14 pts) Now suppose that = 1/4 and that firm A can affect , through an investment that costs exactly K > 0. If firm A spends amount K on this investment, then becomes 2/3, otherwise does not change and stays at 1/4. The timing of the game is now as follows: Firm A chooses to invest the amount K or not, then is observed by both firms, and then firms compete in prices simultaneously. For which values of K, does the firm choose to invest?