Suppose that there is a unit mass of consumers who are uniformly distributed on the segment[0,1]. Two firms are located on the line and sell identical products. Consumers obtain K utility from consuming a product; assume that K is large enough that all consumers purchase from at least one of the firms despite the costs of transportation, which are linear in distance with a constant marginal cost of t. For each of the following cases, what is 1) the symmetric demand function, and 2) the symmetric equilibrium price? (in terms of the parameters of the model)
a) maximum differentiation: firms locate at 0 and 1
b) Moderate case: firms locate at 1/4 and 3/4
c) No differentiation: firms both locate at 1/2