Question

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) = 380−2pA +4 α pB, where 0 ≤ α < 1, and firm B faces a demand given by qB(pA,pB) = 180 − 2pB + pA. Each firm has a constant marginal cost, cA =cB =10and no fixed costs.

1. (a)   Suppose that the firms compete in prices simultaneously. Find the Nash equilibrium prices in terms of α. Provide intuition on the effect of α on the equilibrium prices.

2. (b)   Now suppose that α = 1/4 and that firm A can affect α, through an investment that costs exactly K > 0. If firm A spends amount K on this investment, then α becomes 2/3, otherwise α 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 α is observed by both firms, and then firms compete in prices simultaneously. For which values of K, does the firm choose to invest?

Answer 1

substituting reaction function for firm B in reaction function for firm A

Part (B)

the maximum value of "K" that firm A would be willing to invest is