Suppose automobiles are produced by a monopolistically competitive industry. The demand curve facing any given producer described by the following equation is

Q = S [1/n - b (P - P*)]

where: Q is the number of automobiles sold per firm, S is the total number sold for the industry, n is the number of firms, P is the price that a firm charges and P* is the average price of other firms and b is 1/30,000.

Suppose there are two countries Home and Foreign and the total cost function faced by both countries is

C = 750,000,000 + 5000 Q

Home has annual sales of 900,000 automobiles and the Foreign has annual sales of 1.6 million.

Find the number of firms Home would have if the per-unit sale price is 10,000 in absence of free trade. (Hint: since all firms are identical, they charge the same price i-e in equilibrium P = P*)