Monopolistic competition problem

Consider two countries that are freely trading in differentiated products. Each producer in the industry is subject to increasing returns to scale, derived from fixed costs of production. In particular, the cost function of a firm in the industry is linear with respect to output, with fixed costs of 150 and variable costs of 25 per unit of output. The demand function for each differentiated product is equal to

Q = S [ (1/n) - (1/2)(P - P* ) ]

Where S is size of the market, P is the price charged by producer and P* is the average price in the industry. There is free entry in the industry. Assume that the size of the market is 2,050 in the Home country and 4,025 in the foreign country.

a) Compute the equilibrium price that any producer will charge, as a function of the number of firms in the industry and the size of the market

b) Write down the average costs faced by any firm, as a function of the number of firms in the industry and the size of the market.

c) Compute the number of firms (in the long run), the price charged for each product, and the quantity produced by each firm in the industry in the free trade equilibrium. Show it in a graph.

d) Assume now that entry in the market is not free: each firm has to pay a license fee of 336 to its own government, to be renewed every year, in order to participate in the market. Compute the number of firms (in the long run) in the free trade equilibrium under this new situation.

e) What happens to the consumers' welfare? Explain.