Question

41. A monopolist has a constant marginal and average cost of $10 and faces a demand curve of QD = 1000 – 10P.
Marginal revenue is given by MR = 100 – 1/5Q.
a. Calculate the monopolist’s profit-maximizing quantity, price, and profit.
b. Now suppose that the monopolist fears entry, but thinks that other firms could produce the product at a cost of $14
per unit (constant marginal and average cost) and that many firms could potentially enter. How could the monopolist
attempt to deter entry and what would the monopolist’s quantity and profit be now?
c. Should the monopolist try to deter entry by setting a limit price?

Answer 1

A. Monopolist profit maximizing quantity is decided by MC=MR

10=100-1/5Q

1/5Q=90

Q*= 450

450=1000-10*P

P= 550/10

P*= $55

Proft= TR-TC= (450*55)-(10*450)= $20250

B. Monopolist can deter the entry by setting price slightly below $14. The other firms will will not be able to enter the market with negative profit as this price is below their Average cost. But Monopolist can still earn positive profits.

P= $13

Q= 1000-10*13= 870

Profit= TR-TC= P*Q-AC*Q= (13*870)-(10*870)= $ 2610

C. Yes the monopolist should set a limit price below the price at which other firms can produce. If the monopolist doesn't set limit price, other firms will enter the market and monopolist would lose the monopoly power.