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Cournot with Entry In an industry there are N firms producing a homogeneous product. Let qi denote the output level of firm i, i = 1, 2, ..., N, and let Q denote the aggregate industry production level. That is, Q = Em qi. Assume that the demand curve facing the industry is p = 270 -Q. Suppose that the cost function of each firm i is given by TCi(qi) = 100 if qi > 0 0 if qi = 0 In other words, the firms only incur a fixed cost if they decide to produce (qi > 0). (a) Suppose that the number of firms in the industry N is sufficiently small so that all firms make positive profits. Calculate the output and profit levels of each firm in a Cournot equilibrium. (b) Now, assume that firms are allowed to enter to or exit from the industry. Find the equilib rium number of firms in the industry. Hint: Equate a firm's profit level that you found cearlier to zero and solve for N. (c) (challenging!) What number of firms maximizes total surplus (Consumer surplus + in- dustry profits (do not forget the fixed cost!) in? What do you notice? Is there too little or too much entry from a social point of view? Explain