Question: Third degree price discrimination

Suppose that a monopolist faces two markets with demand curves given by

D(p₁) = 100 - p₁
D(p₂) = 100 - 2p₂

Assume that the marginal cost is constant at 20.

Suppose the monopolist can price discriminate.

(a) What is the maximization problem of the monopolist?

(b) What price should it charge in each market in order to maximize pro?ts?

Suppose now that the monopolist can't price discriminate.

(c) What is the maximization problem of the monopolist?

(d) What price should it charge?

(e) Compare the pro?ts of price discrimation versus uniform pricing. Compare the consumer surplus with price discrimation and uniform pricing