Suppose a monopolistic firm produces a good Q in two different plants. Plant A located in a rural area and plant B in the city. The total cost at each plant is as follows: CTa = 50 + 2(Qa)^2 ; CTb = 30 + (Qb)^2 The firm sells its product in a market where it faces the following demand function: Q = 60 - P

A. Calculate the price, the total quantity traded in the market, and what it produces at each plant to maximize its profit.

B. The above analyses are based on the assumption of a market in a closed economy. Suppose now that the economy is opened up and this monopolist faces a domestic and a foreign market.

In the former the demand function (QN = 60 - P) holds. For the foreign market he is also a monopolist and faces the following demand function: QE = 100 - (2.5)P.

On the other hand, the monopolist changes the production system by converting the plants into a single one, thus managing to decrease its fixed costs from 80 that it had with two plants (50 in A and 30 in B) to only 10 with the new single plant. Given this new situation, suppose that the monopolist can price discriminate in the two markets. If his objective is to maximize profit, calculate the total quantity he must produce and sell, the prices he charges and the quantity he sells in each market, and the profit he makes.

C. Suppose that, because of international agreements, this monopolist must charge the same price in the domestic market as in the foreign market. Calculate the new quantity produced and sold, the price he charges and the quantities he sells in each market, and the profit he makes.