Question

A monopolist has a marginal cost curve MC=Q and a home market demand P=30-Q. The monopolist can also sell in a foreign market at a price pf Pf=12. Find the quantity produced, quantity sold at home, and quantity sold in the foreign market, as well as the price charged at home.

Answer 1

P=30-Q

MR=30-2Q

Profit maximization for a monopolist which sells to segmented markets is where MR=MC

Across the markets, the marginal revenue for foreign = marginal revenue for home and the foreign marginal revenue function, MR=12 for additional units.

As MR=MC,Q=12

MC=MR for home:

30-2Q =12

Q(H) = 18/2 = 9 which is sold in the home market and the remaining will be sold to the foreign market

Q(F) = 12-9 = 3 units

Price charged at Home: = 30-quantity sold in home

=30-9 = 21