Exercise 5: Horizontal Differentiation Part 1 Consider a two rm differentiated product environment where rms 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 {a}, pay a price p; for it (where i can be either 1 or 2,. depending which rm 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 9 which is distributed uniformly in the [Ill] interval. Suppose firms' cost functions are as follows: Cllqu] = sup +F and Cqz} = gag: +F. Suppose firm 1 is forced to locate at point i] and rm 2 is forced to locate at point 1. a] [3 points] What is the optimal price that each rm will set? b] [3 points] Assume now that a = 1 and F = 0.2. What are the prots for each firm? Part 2 Suppose now a differentiated product environment where there are N firms, located equidistantly one from the other and sharing the same cost function: C(qi} = it].- + Iii: Consumers in this market are assumed to behave in the exact same way as before. a] [3 points] What is the demand mction that a rm 1' is facing in this market? Provide a clear expression Econ 4631Indusu-ial Organization HW 3 b] [3 points] Set up rm E's maximization problem and nd the optimal price. Use this to obtain rm's prots c] [3 poo-its] Find the equilibrium number of firms in the market [if you obtain a non-integer number, then consider only the integer part of your number to answer this question). Suppose xed cost drops to 311. What is the new number of firms? Provide an explanation to your results