A monopolist faces the following demand curve: The monopolist has fixed costs of $1,000 and has a constant marginal cost of $2 per unit.If the monopolist were able to perfectly price discriminate,how many units would it sell?

Question

A monopolist faces the following demand curve:  The monopolist has fixed costs of $1,000 and has a constant marginal cost of $2 per unit.If the monopolist were able to perfectly price discriminate,how many units would it sell?

Quizplus · Accepted Answer

Under perfect price discrimination, the monopolist charges each consumer their willingness to pay and captures the entire consumer surplus. Therefore, the monopolist produces until marginal cost equals the highest willingness to pay in the market.

In this case, the highest willingness to pay is represented by the first consumer, who is willing to pay $10 for the first unit. The marginal cost is $2 per unit, so the monopolist will continue producing and selling units until the marginal revenue from the last unit produced equals $2.

The marginal revenue is given by the inverse of the demand curve, which is MR = 10 - Q/100. Setting MR equal to $2 and solving for Q yields Q = 880. However, the monopolist can also charge the first consumer their full willingness to pay of $10 for the first unit, and still capture all of the consumer surplus. Therefore, the monopolist will produce and sell 900 units in total.

A Monopolist Faces the Following Demand Curve: the Monopolist