The monopolistic competition model of Chapter 6 determines the number of firms that optimally serve markets in each country given autarky and the number of firms serving the two countries if there is trade. Let total costs of production for a firm be given by C = cq+ fwhere q is firm output, c is marginal cost, and f is fixed cost. Suppose firm output is related to total market demand, Q, the average price of its competitors Pavg, it own price P, and a responsiveness parameter, z, in the following way q = Q[1/N + z(Pavg - P)] i) Solve for the number of firms N. Show your work. Take it slowly and try and be neat. (Hint: Rewrite firm demand in the form q = a - bp ) Average costs are equal to (C = cq + f)/q = AC = c + f/q and marginal costs are MC = C Assuming that all firms share in the market equally q = Q/N and so AC = c + Nf/Q Write demand as q = Q/N + z QPavg - ZQP or P = 1/(zN) + Pavg - q/(zQ) Total revenue is TR = q/(zN) + qPavg - q2/(zQ) and MR = 1/(zN) + Pavg - 2q/(zQ) = P - q/(zQ) Again assuming all firms share in the market equally q = Q/N and MR = P - 1/(zN) A profit maximizing firm equates MR to MC so that P - 1/(zN) = c Since in the long run there are zero economic profits P = c + 1/(zN) = c + Nf/Q = AC And so solving for N we find that N = (Q/zf) 1/2