Question

A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Q = 200 - 2P MR = 100 - Q TC = 5Q MC = 5 a. What is the profit maximizing level of output? (10 pts.) b. What is the profit maximizing price? (8 pts.) c. How much profit does the monopolist earn? (10 pts.)Immersive Reader (28 Points)  

Answer 1

The demand curve an marginal revenue curve of the monopolist is gven as

Q = 200 - 2P or P = 100 - (Q/2)

MR = 100 - Q

The total costs and marginal costs costs are:

TC = 5Q

MC = 5

(a) The equilibrium for a monopolist occurs at a point where

MR = MC

100 - Q = 5

Q* = 95

Thus, the profit-maximising level of output is 95 units.

(b) The profit-maximising price at the profit-maximising quantity Q* = 95 is given by:

P = 100 - (Q*/2)

P = 100 - (95/2) = 100 - 47.5 = 52.5

P* = 52.5

Thus, profit-maximising price is 52.5 units.

(c) The profits are given by:

π = TR - TC

Here,

TR = P*Q = [100-(Q/2)]*Q = 100Q - (Q²/2) and TC = 5Q

At, Q* = 95,

TR = (100*95) - (95²/2) = 9500 - 4512.5 = 4987.5

TC = 5*95 = 475

Thus,

π = TR - TC = 4987.5 - 475 = 4512.5

Thus, the monopolist earns 4,512.5 units of profit.