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?
Consider a duopoly market, where two firms sell differentiated prod-
ucts, which are imperfect substitutes. The market can be modelled
as a static price competition game, similar to a linear city model.
The two firms choose prices p1 and p2 simultaneously. The derived
demand functions for the two firms are: D1 (P1, P2) = ; +
and D2 (P1, P2) =+ 2, where S > 0 and the parameter t > 0
measures the degree of product differentiation. Both firms have
constant marginal cost c > 0 for production.
S
P2-P1
2t
S
(a) Derive the Nash equilibrium of this game, including the prices,
outputs and profits of the two firms.
Pj-Pi derive
(b) From the demand functions, q; = D; (pi, Pj) =
the residual inverse demand functions: p; = P;(qi, Pi) (work out
P:(qi, Pi)). Show that for t > 0, P:(q;, P;) is downward-sloping,
aP:(gi-Pj)
+
2t
i.e.,
0 as given, firm i
is like a monopolist facing a residual inverse demand, and the
optimal q; (which equates marginal revenue and marginal cost)
or pi makes P;(qi, P¡) =…
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