Question

A monopolist has marginal costs MC=Q and a home market demand P=30-Q. The monopolist can also sell to a foreign market at a constant price of Pf=12. Find and graph the quantity produced, quantity sold in the home market, quantity sold in the foreign market, and price charged in the home market. Explain why the monopolist's profits would fall if it were to produce the same quantity but sell more in the home market.

Answer 1

As mention in the question,the demand curve P=30-Q has been related with marginal revenue MR=30-2Q. The profit-maximizing level of production for a monopolist trading to different markets appears where ∑ MR= MC. The marginal revenue of foreign markets is equals to the home marginal revenue function means, and the foreign marginal revenue function is 12 for any units.
The marginal revenue equivalent to marginal cost at MRf=MC, so where Q=12. Marginal cost for this level of production equivalent to home marginal revenue at
30 - 2Qh = 12
30 - 12 = 2Qh
18 = 2Qh
18/2 = Qh
9 = Qh,
with remaining units sold abroad;
Qf = Q - Qh
= 12 - 9
= 3
In the home market monopolist charges,
Ph = 30 - Qh
= 30 - 9
= 21
The monopolist's profits would decrease if it were to produce the same quantity but sell more in the home market, because the marginal cost in the home market was greater than foreign market.

Diagram:1

In the above diagram, the quantity produced, quantity sold in the foreign market, and price charged in the home market is presented.