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 maximum willingness to pay, which decreases as more units are sold. In this case, the marginal revenue curve is the same as the demand curve: MR = 110 – 0.1Q. Setting MR equal to marginal cost of $2, we can solve for the profit-maximizing quantity:
110 – 0.1Q = 2
108 = 0.1Q
Q = 1,080
However, since the monopolist has fixed costs of $1,000, the actual profit-maximizing quantity would be:
Q = 1,080 – 1,000 = 80
Therefore, the monopolist would sell 80 units under perfect price discrimination, generating total revenue of:
TR = 110(80) – 0.05(80)^2 = $6,400

A Monopolist Faces the Following Demand Curve