Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by if Q< 400 400-Q, P(Q) {40 " otherwise = 40q1, and firm 2 has a cost function where Q = 91 +92. Firm 1 has a cost function C₁ (91) C2 (92) = 5092. Answer the following questions. =

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.7P
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Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given
by
400-Q, if Q< 400
P(Q)
=
"
otherwise
where Q = 91 +92. Firm 1 has a cost function C₁ (91) = 40q1, and firm 2 has a cost function
C2 (92) = 5092. Answer the following questions.
1) Assume the game lasts only one period. Compute the approximate equilibrium profits for
both firms.
2) If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce?
Denote this quantity as QM.
3) One possible strategy is that each firm produces. This gives a more Pareto efficient
outcome. But given that firm 2 produces this quantity, how much does firm 1 want to
produce?
4) Assume this game is infinitely repeated and the interest rate in this economy is r. For what
values of r the strategy in (3) is sustainable by using a "Grim Trigger" strategy?
Transcribed Image Text:Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by 400-Q, if Q< 400 P(Q) = " otherwise where Q = 91 +92. Firm 1 has a cost function C₁ (91) = 40q1, and firm 2 has a cost function C2 (92) = 5092. Answer the following questions. 1) Assume the game lasts only one period. Compute the approximate equilibrium profits for both firms. 2) If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce? Denote this quantity as QM. 3) One possible strategy is that each firm produces. This gives a more Pareto efficient outcome. But given that firm 2 produces this quantity, how much does firm 1 want to produce? 4) Assume this game is infinitely repeated and the interest rate in this economy is r. For what values of r the strategy in (3) is sustainable by using a "Grim Trigger" strategy?
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