Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 15, Problem 15.12P

a

To determine

To find:

The Nash equilibrium.

b)

To determine

To find:

Nash equilibrium of firm 1 and 2.

c)

To determine

To find:

Bayesian Nash equilibrium.

d)

To determine

To find:

Type of firm’s which gain from incomplete information and complete information and whether firm 2 earn more profit on an average.

e)

To determine

To find:

Seperating equilibrium and whether thr loss to the low type from trying to pool in the first period exceeds the second period gain from having convinced firm 2 that it is the high type.

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Exercise 6.6. Consider a duopoly in which companies compete according to Cournot's model. The inverse market demand curve is: P(Q)=100-Q , where Q=Q1+Q2 and the average and marginal costs of firms are constant and equal to 40 Calculate profits would each company make? How much would company 1 be willing to invest to reduce its CM from 40 to 25, assuming company 2 does not support it? Graphically show and comment on all results.
Cournot model: linear demand; identical firms. Q(P)=D-P TC(C)=cQ, where D>c a) Suppose that there are 2 firms. They can either choose to produce the Cournot quantity, or choose to produce one half of the monopoly quantity. Write down the 2X2 “payoff matrix” for this game. b) If D= 6 and c = 2, suppose that the game is repeated infinitely often with a discount factor of beta. For what values of beta will it be possible to sustain collusion? c)  Now consider the same game with 3 firms. Compute the profits in the static Cournot- Nash equilibrium, and the profits when the 3 firms each produce one third of the monopoly quantity. For what values of beta will it be possible to sustain collusion in this case?
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