Consider a two-firm industry producing two differentiated products indexed by i = 1,2. For simplicity, we assume that production is costless. Suppose that the demand functions for the two products are given by q1 = 168 2p1 + p2 and q2 = 168 - 2p2 + p1. a Suppose that the two firms set their price independently and simultaneously. Find the Bertrand-Nash equilibrium. b Suppose that the two firms move sequentially rather than simultaneously. In particular, suppose that firm 1 sets its price first. After observing firm 1' selection, firm 2 chooses its price. Find the Subgame Perfect Nash Equilibrium.

Consider a two-firm industry producing two differentiated products indexed by i = 1,2. For simplicity, we assume that production is costless. Suppose that the demand functions for the two products are given by q1 = 168 2p1 + p2 and q2 = 168 - 2p2 + p1. a Suppose that the two firms set their price independently and simultaneously. Find the Bertrand-Nash equilibrium. b Suppose that the two firms move sequentially rather than simultaneously. In particular, suppose that firm 1 sets its price first. After observing firm 1' selection, firm 2 chooses its price. Find the Subgame Perfect Nash Equilibrium.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.1P

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