4. Consider the following product differentiation model. Suppose that the consumers are uniformly distributed on a circle with perimeter d > 0. Firms are also located on the circle, each selling a homogenous product. Each firm has marginal cost c > 0 and faces a fixed entry cost F. Firm i's profit is: 1 = J (pi - c) yi - F if it enters 0 otherwise where y is the demand for firm i. Consumers want to buy one unit of the good and have a quadratic transport cost. There are two stages: in the first, all firms simultaneously choose whether or not to enter. Let n denote the number of entrants. The firms do not choose the location on the circle, but are automatically located equidistant from each other. In the second stage, the n entrants compete in prices. (a) Find the best-reply for firm i. (b) Use the best-reply for firm i to find the symmetric Nash equilibrium. (c) How many firms n* will there be in this market? Assume a firm enters if it is indifferent between entering and staying out