A monopolist operates in two markets. One market is the domestic market, described by the demand function Qd=100-Pd, where Qd is the quantity sold to domestic consumers and Pd is the price paid by domestic consumers, and the other market is the word market, which has a constant price elasticity of demand equal to 3.
The cost of production of the monopoly is given by C(Q)=100+Q2 where Q is the total quantity sold by the monopolist. For each unit sold on the world market, the monopolist has to pay an additional shipping cost of $5 per shipped unit.

a. Assume the monopolist wants to produce 50 units. How many units should be sold domestically? on the world market? What price would the domestic buyers be charged? international consumers? Are the two types of customers charged different prices? Does this monopolist practice price discrimination?

b. Find the quantity that maximizes the profit of the monopolist, the profit of the monopolist and the corresponding domestic and international price.