Consider a linear city on which consumers are uniformly distributed with density one. Each consumer has unit demand and can choose between two rms 1' and j, located at points i,- and F}- respectively, where 0 0. The value of consumption of any good is 1' > 0. The two rms have constant marginal costs C > 0 and set prices p; and pf, respectively. The game is played in two stages as follows: At the first stage, the rms simultaneously and noncooperatively choose locations (L, If). At the second stage, they simultaneously and non cooperatively set prices (pi, P1)- (1) Consider the subgame at stage two where the locations (If, G) are given. Solve for the Bertrand Nash equilibrium (pH/g, 1}), pl} Us 6-)) of this subgame, assuming that there is full market coverage. (2) Given the equilibrium values (pi*(ff, @103 (ff, 5-)), write down expressions for J? :- *(ff, 1;) and 76*\"; If)- (3) Discuss the rms' incentive to differentiate their products by locating far away from their rival