Exercise 1: Horizontal Differentiation Consider a two firm differentiated product environment where firms choose their price but not their product type. The product is differentiated in one dimension: in particular, the good can take on types ranging from zero to one. As we saw in class, consumers derive an inherent utility from consuming one unit of the good {:3}, pay a price pi for it (where i can be either 1 or 2, depending which firm they are buying from) and incur in a linear adjustment cost [disutility) of t = 1 when deviating from their favorite type. Consumer types are identied with the parameter 6 which is distributed uniformly in the [0,1] interval. Suppose firms' cost functions are as follows: C101\") = mm + F and fth) = %ttq2 + F. Suppose firm 1 is forced to locate at point D and firm 2 is forced to locate at point 1. a) - ' What is the optimal price that each firm will set? b) ' ' . Assume now that a; = 1 and P = 0.2. What are the prots for each firm