Consider a homogeneous-product duopoly. The two firms in the mar- ket are assumed to have constant marginal costs of production equal to c. The two firms compete possibly over an infinite time horizon. In each period they simultaneously set price pi, i = 1;2. After each period the market is closed down with probability 1 - 8. 1. Market demand Q(p) is decreasing, where p = min {p₁; P2}. Sup- pose, furthermore, that the monopoly problem is well defined, i.e. there is a solution p arg max, (p - c) Q(p). If firms set the same price, they share total demand with weight X for firm 1 and 1-X for firm 2. Suppose that A € [1/2; 1]. Suppose that firms use trigger strategies and Nash punishment. 2. Suppose that 8 = 0. Derive the equilibrium of the game. 3. Suppose that 8 > 0 and X = 1/2. Derive the condition according to which firm 1 and firm 2 do not find it profitable to deviate from the collusive price pM. = 4. Suppose that 6 > 0 and X > 1/2. Derive the condition according according to which pM is played along the equilibrium path. Show that the condition is the more stringent the higher X.

Consider a homogeneous-product duopoly. The two firms in the mar- ket are assumed to have constant marginal costs of production equal to c. The two firms compete possibly over an infinite time horizon. In each period they simultaneously set price pi, i = 1;2. After each period the market is closed down with probability 1 - 8. 1. Market demand Q(p) is decreasing, where p = min {p₁; P2}. Sup- pose, furthermore, that the monopoly problem is well defined, i.e. there is a solution p arg max, (p - c) Q(p). If firms set the same price, they share total demand with weight X for firm 1 and 1-X for firm 2. Suppose that A € [1/2; 1]. Suppose that firms use trigger strategies and Nash punishment. 2. Suppose that 8 = 0. Derive the equilibrium of the game. 3. Suppose that 8 > 0 and X = 1/2. Derive the condition according to which firm 1 and firm 2 do not find it profitable to deviate from the collusive price pM. = 4. Suppose that 6 > 0 and X > 1/2. Derive the condition according according to which pM is played along the equilibrium path. Show that the condition is the more stringent the higher X.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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