8. Suppose there are two identical firms in an industry who compete by settingquantities. The output of firm 1 is denoted by q1 and that of firm 2 is denotedby 92. Each firm faces a constant marginal cost of 3. Let Q denote total output,1.e. Q-91 +42. The inverse demand curve in the market is given byP-15-Q(a) Find the Cournot-Nash equilibrium quantity produced by each firm andthe market price."//(b) If the firms could collude, what would be the total output inket? Assuming each firm produces half of the collusive output,the profit of each firm?the mar-what is(c) Suppose each firm produces half of the collusive output identified in part(b). Firm 1 considers a deviation from this arrangement. What would bethe best deviating output of firm 1 and its deviation profit?(d) Suppose firms interact repeatedly over an infinite horizon, and firms havea common discount factor & € (0,1). Specify a trigger strategy for eachfirm to sustain the collusive arrangement as an equilibrium outcome. Cal-culate the minimum value of & for which such a trigger strategyaincollusion as an equilibrium in the repeated interaction.

The market demand function: P=15-Q There are only two firms in the market, firm 1 produces…

8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 42. Each firm faces a constant marginal cost of 3. Let Q denote total output, L.e. Q-91 +92. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar- ket? Assuming each firm produces half of the collusive output, what is the profit of each firm? (c) Suppose each firm produces half of the collusive output identified in part (b). Firm 1 considers a deviation from this arrangement. What would be the best deviating output of firm 1 and its deviation profit? (d) Suppose firms interact repeatedly over an infinite horizon, and firms have a common discount factor & € (0,1). Specify a trigger strategy for each firm to sustain the collusive arrangement as an equilibrium outcome. Cal- culate the minimum value of & for which such a trigger strategy collusion as an equilibrium in the repeated interaction. nin

8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 42. Each firm faces a constant marginal cost of 3. Let Q denote total output, L.e. Q-91 +92. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar- ket? Assuming each firm produces half of the collusive output, what is the profit of each firm? (c) Suppose each firm produces half of the collusive output identified in part (b). Firm 1 considers a deviation from this arrangement. What would be the best deviating output of firm 1 and its deviation profit? (d) Suppose firms interact repeatedly over an infinite horizon, and firms have a common discount factor & € (0,1). Specify a trigger strategy for each firm to sustain the collusive arrangement as an equilibrium outcome. Cal- culate the minimum value of & for which such a trigger strategy collusion as an equilibrium in the repeated interaction. nin

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

8. Suppose there are two identical firms in an industry who compete by setting
quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted
by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output,
1.e. Q-91 +42. The inverse demand curve in the market is given by
P-15-Q
(a) Find the Cournot-Nash equilibrium quantity produced by each firm and
the market price.
"//
(b) If the firms could collude, what would be the total output in
ket? Assuming each firm produces half of the collusive output,
the profit of each firm?
the mar-
what is
(c) Suppose each firm produces half of the collusive output identified in part
(b). Firm 1 considers a deviation from this arrangement. What would be
the best deviating output of firm 1 and its deviation profit?
(d) Suppose firms interact repeatedly over an infinite horizon, and firms have
a common discount factor & € (0,1). Specify a trigger strategy for each
firm to sustain the collusive arrangement as an equilibrium outcome. Cal-
culate the minimum value of & for which such a trigger strategy
ain
collusion as an equilibrium in the repeated interaction.

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