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

Under perfect price discrimination, the monopolist is able to charge each consumer their maximum willingness to pay, resulting in capturing the entire consumer surplus. The monopolist will produce at the point where marginal cost equals marginal revenue for each individual consumer. In this case, the marginal revenue for each additional unit sold is given by the inverse demand function: MR = 500 - 0.2Q. Setting this equal to the constant marginal cost of $2 gives the equilibrium quantity for each individual consumer: 
500 - 0.2Q = 2 
0.2Q = 498 
Q = 2490 units at $498 each 
Multiplying by the number of consumers in the market (1000) gives the total quantity sold under perfect price discrimination: 
Qtotal = 1000 x 2490 = 2,490,000 
Therefore, the monopolist would sell 900 units to each individual consumer for a total of 900 x 1000 = 900,000 units sold.

A Monopolist Faces the Following Demand Curve: the Monopolist