Suppose that there are two firms and they each have MC=2. No fixed costs. They each produce a slightly differentiated product; that is, consumers substitute imperfectly between products. This means demand for firm 1's product is decreasing in their price and increasing in their competitor's price. Demand functions are as follows: Firm 1: Q1 = 10 - 2P1 + P2 Firm 2: Q2 = 10- 2P2+ Pi %3! Firm 1 chooses their Pi first, then Firm 2 observes their choice and selects P2. Solve backwards, i.e., start by setting up Firm 2's profit maximization problem and solving it for their best response function. Plug this into Firm l's maximization problem. Once you have each firm's best response functions, solve for the SPNE prices. Calculate equilibrium profits to see whether there is a first mover advantage or a second mover advantage.

Suppose that there are two firms and they each have MC=2. No fixed costs. They each produce a slightly differentiated product; that is, consumers substitute imperfectly between products. This means demand for firm 1's product is decreasing in their price and increasing in their competitor's price. Demand functions are as follows: Firm 1: Q1 = 10 - 2P1 + P2 Firm 2: Q2 = 10- 2P2+ Pi %3! Firm 1 chooses their Pi first, then Firm 2 observes their choice and selects P2. Solve backwards, i.e., start by setting up Firm 2's profit maximization problem and solving it for their best response function. Plug this into Firm l's maximization problem. Once you have each firm's best response functions, solve for the SPNE prices. Calculate equilibrium profits to see whether there is a first mover advantage or a second mover advantage.

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 9PA

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