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 (27), 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 (dis-utility) of t = 1 when deviating from their favorite type. Consumer types are identified with the parameter 6 which is distributed uniformly in the [0,1] interval. Suppose firms' cost functions are as follows: C1(q1) = 0:611 + P and C2(q2) = 0q2 + P. Suppose firm 1 is forced to locate at point 0 and firm 2 is forced to locate at point 1. a) (8 points) What is the optimal price that each firm will set? b) (8 points) Assume now that 0c 2 1 and F = 0.2. What are the profits for each firm