It is possible that a profit-maximizing monopolist who is able to practice first-degree (perfect)price discrimination would sell a quantity x such that the demand curve for his product is inelastic when the quantity sold is x.

First-Degree (Perfect) Price Discrimination

A pricing strategy where a seller charges the maximum possible price for each unit consumed that the consumer is willing to pay.

Profit-Maximizing Monopolist

A monopolist's strategy of setting a level of production and price that maximizes its profits.

Inelastic

A characteristic of goods whose demand or supply is not significantly altered when the price changes.