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?
A)400
B)500
C)900
D)4,200

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?
A)400 
B)500 
C)900 
D)4,200

Quizplus · Accepted Answer

Perfect price discrimination means that the monopolist is able to charge each individual customer a price equal to their maximum willingness to pay. Therefore, the monopolist can sell every unit it produces up to the point where the marginal cost equals the price. 
The marginal revenue curve for a monopolist is twice as steep as the demand curve, so we can find the profit-maximizing quantity by setting marginal cost equal to half of the demand price, or MC = (1/2)P. From the demand curve, we can see that at a price of $25, the quantity demanded is 900. So, we have:
(1/2)P = $2
P = $4
Q = (1,150 - 4)/2 = 573
However, the monopolist has fixed costs of $1,000, so the total profit-maximizing quantity is:
Q = (1,150 - 4)/4 = 286.5
Since we cannot sell a fractional number of units, we round up to get 287, for a total revenue of:
TR = $25 x 287 = $7,175
This is higher than the profit the monopolist would earn by charging a uniform price, which would be TR - TC = ($25 x 500) - ($2 x 500 + $1,000) = $11,500 - $2,500 = $9,000.

A Monopolist Faces the Following Demand Curve: the Monopolist