A monopolist faces the (inverse) demand for its product: p = 50 – 2Q.

A monopolist faces the (inverse) demand for its product: p = 50 – 2Q. The monopolist has a marginal cost of 10/unit and a fixed cost given by F.

a. Assume that F is sufficiently small such that the monopolist produces a strictly positive level of output. What is the profit-maximizing price and quantity?
b. Compute the maximum profit for the monopolist in terms of F.
c. For what values of F will the monopolists profit be negative?

ANSWER

a. The monopolist will choose p = MR (or derive from first order condition of profit function).
50 – 4Q = 10
Solving for Q
Q* = 10
The price follows from plugging the optimal output into the demand:
p* = 30
b. The profit comes from plugging the price and quantity into the profit equation:
Pi* = 200 – F
c. Find F* such that Pi* = 0:
F* = 200
For F > 200, profits will be negative.