Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
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?
the question is in the image attached
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