Question

1. Two firms compete in a linear city of length 1 unit. Consumers are uniformly located along the city. Consumer i's utility derived from buying firm j's product is given by jj-(-x)2-Pj where j 1,2 indicate the two firms, t is the per unit cost of travelling along the city, is the location of consumer i, x is the location of firm j, and pj is the price of product j. Product one contains some intrinsically superior features and 22, while 20. Each consumer buys a single unit of the good. Firms compete with each other by simultaneously choosing prices. Each firm has constant marginal costs of c and no fixed costs. (a) Assume that the two firms are located at each end of the city. That is, x 0 and x2 i. Calculate the demand for each firm in terms market prices and transport costs. [3 marks] ii. Find the reaction function for each firm i. Find the Nash equilibrium prices for each firm [4 marks [3 marks (b) Assume instead that both firms are located in the same spot with xx2 0.4. Identify Nash equilibrium in prices. Explain. [You may suppose that if consumers are indifferent they buy from Firm 1. 5 marks

Answer 1

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