Suppose a monopolist faces the constant price elasticity demand curve:

Suppose a monopolist faces the constant price elasticity demand curve:

p = Qε
where ε < 0. The monopolist has a constant marginal cost of c. a. If ε < -1, can you determine what price and quantity will the monopolist set? Explain. b. If 0 > ε > -1, what is the price and quantity the monopolist will set?

ANSWER

a. The necessary condition is:
(1 + ε)Qε = c
For ε < -1, the condition cannot be met — the monopolist can always raise the price and increase total revenue (and reduce total cost). b. The optimal quantity is (c/(1 + ε))1/ε and price is c/(1 + ε).