1. (12pts) (Stackelberg Duopoly) Two firms produce identical products. Each has the same constant average cost of $10 per unit of output. Market price P = 90 2(q1 + q2). Both firms choose outputs to compete. (a) (5pts) Find the subgame perfect equilibrium outcome of the Stackelberg Duopoly game with Firm 1 moving first. First, solve for the follower's (Firm 2's) best response function. Then solve for the leader's optimal strategy. (b) (4pts) Find the Nash equilibrium of the Cournot duopoly under the same assumptions on costs and demand. (c) (3pts) Compare the two equilibria. Discuss the differences as to which firm earns more profit in which case. 2. (6pts) Again consider the same firms as in Question 2 above. Each has the same constant average cost of 10. Market price P = 90 2(q1 + q2). Both firms choose outputs to compete. (a) (2pts) Suppose the two firms start off in the Stackelberg equilibrium. Then suppose after Firm 2 made its equilibrium choice q2, Firm 1 is unexpectedly given a chance to adjust its output level q1. Given Firm 2's output, should Firm 1 change its output? to what level? (b) (4pts) Suppose now Firm 2 claims it would produce the Cournot equilibrium output regardless of what q1 Firm 1 would choose. If Firm 2 can commit to such an output level, then what is the best output choice for Firm 1? Compared with Stackelberge equilibrium in Problem 1 part (a), verify if Firm 2 will earn more profit in this case. What is the difficulty that may prevent Firm 2 from achieving this outcome?