Question 4

Two firms engage in a game that lasts two periods. At the beginning of period 1 either firm can exit. If a firm exits, it cannot reenter in period 2. If both firms stay in the market they set prices simultaneously to maximize their respective profits (i.e., they play a Bertrand game). Consumers buy from the firm that charges the lowest price; if prices are exactly the same, all consumers buy from firm 1. If only one firm stays in the market, it sets a price to maximize its monopoly profit. The interaction between the two firms repeats itself in period 2: first the two firms decide whether to stay or exit and then given their decision the firms that stay (firm 1, firm 2, or both) choose prices. The demand in every period is P = 80-Q, where P is the price and Q is the aggregate quantity, firm 1 has a marginal cost 20 3 per unit, firm 2 has a marginal cost 30 per unit, and both firms have a fixed cost of 300 per period if they are in the market. If a firm exits, its profit is 0.

(a) What is the price that firm 1 will set if it operates alone in the market? What will be its profit?

(b) What is the price that firm 2 will set if it operates alone in the market? What will be its profit?

(c) Suppose both firms are in the market in period 2. What are the Nash equilibrium prices that they will set? What are their profits?

(d) Suppose both firms are in the market at the start of period 2. What will they decide regarding staying in the market or exiting at the start of period 2?

(e) Given your answer to (d), what will the two firms decide regarding staying in the market or exiting at the start of period 1?