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 the maximum price they are willing to pay. In this case, the maximum price each consumer is willing to pay is indicated by the demand curve. 
Thus, the monopolist can sell 100 units at a price of $10, 200 units at a price of $8, 300 units at a price of $6, 400 units at a price of $4, and 500 units at a price of $2. 
Total revenue would be $10*100 + $8*100 + $6*100 + $4*100 + $2*100 = $2,800. 
At $2 marginal cost, total profit would be $2,800 - $1,000 - $2*q, where q is the total quantity sold. 
To maximize profit, we need to find the quantity that maximizes 2,800 -1000 -2*q or 1,800 - 2*q. This occurs when q = 900. Thus, the monopolist would sell 900 units under perfect price discrimination.

A Monopolist Faces the Following Demand Curve: the Monopolist