Consider n profit-maximizing firms that compete in location. They can choose to locate on the interval [0, 2]. Each consumer buys a unit from the firm that is located the closest, and, if firms choose the same location. the closest consumers are equally split between these firms. For simplicity assume that the price ofthe product is 1, the cost is D {so the profit is the length of the attracted line segment). 1) [5 points] Find Nash equilibriumla) when n = 2 and firms can locate anywhere m for the elmd interval [2!3, 43] which is already occupied by some commercial buildings (and n_ot consumers. so the consumers live only on [[1,2]3) U (hi3.2]). In other words. [213. 113] interval is a \"d ead zone" for the firms. 2) [5 points] Find Nash equilibrium(a) when n = 3 and firms can locate anywhere on [I], 2] and consumers also populate the whole interval without any exceptions (i.e., you should disregard the information from the previous point)