Discuss the relationship between the equilibrium prices and the marginal cost of production.

Consider an industry consisting of three firms located respectively at points 0, 1/4 and 1 on a linear city of length 1. Firms face marginal cost of production $2 and no fixed costs. There are 10 consumers uniformly distributed on this linear city. Consumers have unit demands and derive the same value of consuming the products of all firms. The travel cost is t > 0. 1. Suppose that the market is covered all consumers consume. What is the demand that each firm faces? How does it depend on own and rival price? Why? 2. Suppose that firms simultaneously choose prices and t = $1. What is the Nash equilibrium of this game? Discuss the relationship between the equilibrium prices and the marginal cost of production.

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