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5. Consider the following variant of Hotelling's product differentiation model. Suppose that the consumers are uniformly distributed on a circle with perimeter d 1. Firms are also located on the circle, each selling a homogenous product. Each firm has marginal cost c and also faces a fixed entry cost F. Firm i's profit is: (pi c) yi F if it enters 0 otherwise where yi is the demand it faces. Consumers want to buy one unit of the good and have a transport cost of t. Hence, the price facing a consumer who purchases from firm i is pi ta, where pi is the price charged by firm i and where is the distance between the consumer and firm i. 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) Derive the profit function of firm i (b) Find the (symmetric) equilibrium price in the market (c) How many firms n" will there be in this market? 5. Consider the following variant of Hotelling's product differentiation model. Suppose that the consumers are uniformly distributed on a circle with perimeter d 1. Firms are also located on the circle, each selling a homogenous product. Each firm has marginal cost c and also faces a fixed entry cost F. Firm i's profit is: (pi c) yi F if it enters 0 otherwise where yi is the demand it faces. Consumers want to buy one unit of the good and have a transport cost of t. Hence, the price facing a consumer who purchases from firm i is pi ta, where pi is the price charged by firm i and where is the distance between the consumer and firm i. 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) Derive the profit function of firm i (b) Find the (symmetric) equilibrium price in the market (c) How many firms n" will there be in this market