Q3 (70 points) Suppose three firms compete in a market for a single product with industry inverse demand curve p = A - Q. All three firms have constant marginal cost 2 c. Firm 1 moves first and selects output level q. Firm 2 moves secondly and select 92. Firm 3 moves lastly and select q3. Total output is Q = 9 +92 +93. (a) (30 points) Determine the subgame perfect Nash equilibrium of this game by giving the equilibrium quantities of each firm q1, 92 and q3, the equilibrium price p* as well as the equilibrium profits , and 3. All these equilibrium values should be expressed in terms of only c. 2 (b) (10 points) Which firm produces the most and which firm produces the least in equilibrium? Which firm has the highest profit and which firm has the lowest profit in equilibrium? Explain why. (c) (10 points) How each firm's profit varies with c? (d) (10 points) Assume now that the firm 1 is a potential entrant whereas firms 2 and 3 are incumbents. If firm 1 enters the market, the sequence of actions is as before, that is firm 1 first chooses q, then firm 2 chooses q2 and finally firm 3 chooses 93. . The entry cost for firm 1 is F > 0. If firm 1 chooses to not enter, then its profit is zero. We assume that if firm 1 has profit equals to zero whether it enters or not enters in the market, it always prefers enter in the market. For which value of F the firm will decide to enter in this market? c (e) (10 points) Assume now that F = 16* Does firm 1 enter in the market? Discuss the results in terms of entry versus not entry for different values of c. Calculate firm 1's profit in all possible cases.