Let's consider an k-firm repeated game over an infinite discrete-time horizon t = 0, 1, ... with discount factor o≤ 1. The goods that firms produce are perfect substitutes. Firms are in Bertrand competition. Each firm has constant marginal cost m. The demand at time t is q(t)= D(pt), where ẞ is an expectation of future expansion or contraction and ẞ8 < 1. (i) ẞ and k are fixed, for what values of 8 is full collusion at the monopoly price a sustainable equilibrium of the repeated game? (ii) How does the ease of sustaining collusion change as the rate of expansion or contraction of the industry changes?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.8P
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Let's consider an k-firm repeated game over an infinite discrete-time
horizon t = 0, 1, .. with discount factor os 1. The goods that firms
produce are perfect substitutes. Firms are in Bertrand competition.
Each firm has constant marginal cost m. The demand at time t is
q(t)=6'D(pt), where B is an expectation of future expansion or
contraction and B8 < 1.
B and k are fixed , for what values of 8 is full collusion at the
(i)
monopoly price a sustainable equilibrium of the repeated game?
(ii)
How does the ease of sustaining collusion change as the rate
of expansion or contraction of the industry changes?
Transcribed Image Text:Let's consider an k-firm repeated game over an infinite discrete-time horizon t = 0, 1, .. with discount factor os 1. The goods that firms produce are perfect substitutes. Firms are in Bertrand competition. Each firm has constant marginal cost m. The demand at time t is q(t)=6'D(pt), where B is an expectation of future expansion or contraction and B8 < 1. B and k are fixed , for what values of 8 is full collusion at the (i) monopoly price a sustainable equilibrium of the repeated game? (ii) How does the ease of sustaining collusion change as the rate of expansion or contraction of the industry changes?
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