3. Consider the Hotelling problem we discussed in class. Assume consumers are uniformly distributed on the [0, 1] interval, that Firm 1 is at 0, and Firm 2 is at 1. A consumer at x is distance from Firm 1 and distance 1-2 from Firm 2. Consumers purchase from the firm which has lower costs td+p where dis the distance and p is the price and t is a travel cost. (a) Define the indifferent consumer and write out the profit function for each firm. Using the first order conditions, show that the Nash equilibrium prices are p₁ P2=c+t. (b) Suppose instead that Firm 1 is located at y which is close to 0. Find the Nash equilibrium for any y and show that Firm 1 is better off choosing = ย 0 and show that the direct effect of choosing y > 0 is positive (the direct effect is a derivative evaluated at y = 0 and is calculated holding P2 fixed). This is harder because the prices are not symmetric.

3. Consider the Hotelling problem we discussed in class. Assume consumers are uniformly distributed on the [0, 1] interval, that Firm 1 is at 0, and Firm 2 is at 1. A consumer at x is distance from Firm 1 and distance 1-2 from Firm 2. Consumers purchase from the firm which has lower costs td+p where dis the distance and p is the price and t is a travel cost. (a) Define the indifferent consumer and write out the profit function for each firm. Using the first order conditions, show that the Nash equilibrium prices are p₁ P2=c+t. (b) Suppose instead that Firm 1 is located at y which is close to 0. Find the Nash equilibrium for any y and show that Firm 1 is better off choosing = ย 0 and show that the direct effect of choosing y > 0 is positive (the direct effect is a derivative evaluated at y = 0 and is calculated holding P2 fixed). This is harder because the prices are not symmetric.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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