Suppose a monopolist faces the constant price elasticity demand curve:

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


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).

Economics

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