Consider the following inverse demand function, p(Q) = 5-7Q, Q = 91 + 92, where q, denotes firm i's output, i = 1,2. Assume that the total cost of firm i is cq₁/2, with e > 0. Firms choose quantities simultaneously and non cooperatively. The game described above is infinitely repeated. Firms use grim trigger strategies (infinite Nash reversion). Firms discount future profits at a rate r > 0. a) b) Compute the cartel profits. Derive the critical discount factor above which full cartelization (joint profit maximization) is sustainable as a Subgame Perfect Nash Equilibrium (SPNE) of the infinitely repeated game.

Consider the following inverse demand function, p(Q) = 5-7Q, Q = 91 + 92, where q, denotes firm i's output, i = 1,2. Assume that the total cost of firm i is cq₁/2, with e > 0. Firms choose quantities simultaneously and non cooperatively. The game described above is infinitely repeated. Firms use grim trigger strategies (infinite Nash reversion). Firms discount future profits at a rate r > 0. a) b) Compute the cartel profits. Derive the critical discount factor above which full cartelization (joint profit maximization) is sustainable as a Subgame Perfect Nash Equilibrium (SPNE) of the infinitely repeated game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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