2. Stackelberg Firms 1, 2 and 3 compete in quantities. The inverse market demand is given by p= 400 (91 +92 +93), where 91, 92 and q3 are the quantities produced by firms 1, 2 and 3, respectively. The marginal cost for firm 1 is c₁= 20, and the marginal cost for both firm 2 and firm 3 is 40. The order of play is as follows: Firm 1 first sets a quantity q₁. Then, firms 2 and 3 observe qı and simultaneously set q2 and 93. Each firm sets its quantity to maximize its own profits. (a) Let us first consider the optimal action of firm 2. Given a value q₁ initially set by firm 1 and a value of q3 set by firm 3, what is the value of q2 that maximizes the profits of firm 2? Hint: Your answer should provide q2 in terms of 91 and 93. (b) Notice that, after firm 1 sets q1, a subgame starts, in which firms 2 and 3 simultaneously set 92 and 93. Given 9₁, find the values of q2 and q3 that firms 2 and 3 must set in a Subgame Perfect Nash Equilibrium. Hint: Your answer should provide 92 and q3 in terms of q₁. (c) Find the value of q₁ that firm 1 sets in the Subgame Perfect Nash Equilibrium of this game. What is the equilibrium price? And what are the equilibrium profits of each firm?

2. Stackelberg Firms 1, 2 and 3 compete in quantities. The inverse market demand is given by p= 400 (91 +92 +93), where 91, 92 and q3 are the quantities produced by firms 1, 2 and 3, respectively. The marginal cost for firm 1 is c₁= 20, and the marginal cost for both firm 2 and firm 3 is 40. The order of play is as follows: Firm 1 first sets a quantity q₁. Then, firms 2 and 3 observe qı and simultaneously set q2 and 93. Each firm sets its quantity to maximize its own profits. (a) Let us first consider the optimal action of firm 2. Given a value q₁ initially set by firm 1 and a value of q3 set by firm 3, what is the value of q2 that maximizes the profits of firm 2? Hint: Your answer should provide q2 in terms of 91 and 93. (b) Notice that, after firm 1 sets q1, a subgame starts, in which firms 2 and 3 simultaneously set 92 and 93. Given 9₁, find the values of q2 and q3 that firms 2 and 3 must set in a Subgame Perfect Nash Equilibrium. Hint: Your answer should provide 92 and q3 in terms of q₁. (c) Find the value of q₁ that firm 1 sets in the Subgame Perfect Nash Equilibrium of this game. What is the equilibrium price? And what are the equilibrium profits of each firm?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.4P

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