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 and graph the quantity produced, quantity sold at home, and quantity sold in the foreign market, as well as the price charged at-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

This is an example of price discrimation in home and foreign markets on the basis of demand elasticity.

To find out the quantity sold in both markets and the prices charged here, we will use MC-MR equilbrium approach of profit maximising equilibrium for both markets.

First, lets consider home market. Let quantity here be denoted by Qh.

MC = Qh

ARh = Ph = 30 - Qh

TRh = (ARh) x Qh = 30Qh - Qh²

MRh = 30 - 2Qh

Equilibrium when MC = MRh or Qh = 30 - 2Qh which gives Qh = 10. This gives Ph = 20

Next, lets consider foreign market. Let quantity here be denoted by Qf.

MC = Qf

ARf = Pf = 12

TRf = (ARf) x Qf = 12Qf

MRf = 12

Equilibrium when MC = MRh or Qf = 12. This gives Pf = 12.

So total quantity produced by monopolist is Q such that

Q = Qh + Qf = 10 + 12 = 22.

To calculate profits or PR,

PR = (TRh + TRf) - TC = (30Qh - Qh² + 12Qf) - Q = 30(10) - (10)(10) + 12(12) - 22 = 300 - 100 + 144 - 22 = 322

This is the classic case of dumping; a monopolist sells more of his good's quantity in the foreign market than the home market as demand is more inelastic in the latter than former. So at home he can charge a higher price than abroad.

Graphically, following is shown.

If the monopolist were to produce the same quantity as before that is 22, but sell more of it in home market where demand is more inelastic, he cannot change the price much even when the quantity changes. This was his price will continue to be somewhat unchanged but quantity sold would rise. This way his profits will not rise as much as when he is selling more qunatity in foreign market. Hence dumping helps him maximize his profits.