Question

Two firms, A and B, produce complementary products. That is, rather than competing for the same customers, demand for each firm’s output increases if the other firm produces more. Specifically, the inverse demand for Firm A’s product is given by pA = 110 − qA + qB. The inverse demand for Firm B’s product is given by pB = 50 − qB + qA. Both firms have marginal cost of 10 and choose quantities to maximize their profit. 5. If the firms make their decisions simultaneously (Cournot), what are the Nash Equilibrium quantities (q N A , q N B ) that the firms will choose to maximize profits? (a) q N A = 60 and q N B = 60 (b) q N A = 80 and q N B = 60 2 (c) q N A = 60 and q N B = 80 (d) q N A = 80 and q N B = 80 6. Again assume that the firms make their decisions simultaneously (Cournot). Denote by p N A and p N B the prices for firms A and B, respectively, assuming that the firms set their quantities as in the correct answer to the previous question. What are the values of p N A and p N B ? (a) p N A = 80, p N B = 60 (b) p N A = 100, p N B = 40 (c) p N A = 60, p N B = 80 (d) p N A = 90, p N B = 70 7. Suppose now that the firms make their decision sequentially (Stackelberg). Specifically Firm A is the first to make a decision and choose the quantity that maximizes its profits. After observing Firm A’s decision, firm B chooses the quantity to maximize its own profits. Solving the game by backwards induction, find the quantities set by firms A and B (q S A and q S B, respectively) in the Subgame Perfect Nash Equilibrium of this game. Also, find the prices that hold for each firm (p S A and p S B for firms A and B, respectively) in this equilibrium. (a) q S A = 120, p S A = 70, q S B = 80, p S B = 90 (b) q S A = 100, p S A = 80, q S B = 90, p S B = 70 (c) q S A = 95, p S A = 105, q S B = 90, p S B = 55 (d) q S A = 90, p S A = 100, q S B = 70, p S B = 60 8. Suppose instead that the order of the Stackelberg game changes, so that Firm B is the first to make a decision and choose the quantity that maximizes its profits. After observing firm B’s decision, Firm A will choose the quantity to maximize its profits. Find the quantities set by firms A and B (q S A and q S B, respectively) in the Subgame Perfect Nash Equilibrium of this game. Also, find the prices that hold for each firm (p S A and p S B for firms A and B, respectively) in this equilibrium. (a) q S A = 120, p S A = 70, q S B = 80, p S B = 90 (b) q S A = 100, p S A = 80, q S B = 90, p S B = 70 (c) q S A = 95, p S A = 105, q S B = 90, p S B = 55 3 (d) q S A = 90, p S A = 100, q S B = 70, p S B = 60 9. Which of the following statements is true when comparing the Cournot (simultaneous) case in questions 5 and 6 with the the Stackelberg (sequential) cases in questions 7 and 8? (a) Firm A’s profit is higher in the Stackelberg case than in the Cournot case, regardless of the order the firms move. (b) Firm A’s profit is higher in the Stackelberg case than in the Cournot case, but only if it is the second mover. (c) Firm A’s profit is always higher in the Cournot case than in the Stackelberg case. (d) Firm A’s profit is higher in the Stackelberg case than in the Cournot case, but only if it is the first mover.

Answer 1