Question

Consider a monopoly firm that faces the following demand curve, total cost curve, and marginal cost: P(Q) = 120 – 4Q; TC(Q) = 400 + 4Q; MC = 4

a. What is the marginal revenue (MR) equation?

b. Determine the profit maximizing level of production for this monopolist.

c. What is the price that the monopolist will charge at the profit maximizing level of production?

d. What is the monopolists’ profit at the profit maximizing level of output?

e. Suppose the government regulates the industry and forces the monopolist to produce at the socially optimal level, what will be the production level and price?

f. Suppose instead, the government decides to force the monopolist to charge a price equal to their average total cost, and the monopolist will produce 25 supply at this price, then what will be the monopolists profit?

Answer 1

Answer : a) TR (Total Revenue) = P*Q = (120 - 4Q) * Q = 120Q - 4Q^2

MR = TR / Q = 120 - 8Q

Therefore, here the MR function is, MR = 120 - 8Q.

b) For monopolist the profit maximizing condition is MR = MC. So,

120 - 8Q = 4

=> 120 - 4 = 8Q

=> 116 = 8Q

=> Q = 116 / 8

=> Q = 14.5

Therefore, here the monopolist's profit maximizing output level is, Q = 14.5 .

c) From demand function we get,

P = 120 - (4 * 14.5)

=> P = 62

Therefore, here the monopolist's profit maximizing price level is, P = 62.

d) Now by putting Q = 14.5 in TC we get,

TC = 400 + (4 * 14.5) = 458.

TR = P*Q = 62 * 14.5 = 899

Profit = TR - TC = 899 - 458 = 441

Therefore, here the monopolist's profit level is, Profit = 441.

e) At socially optiomal output level P = MC occur. So,

120 - 4Q = 4

=> 120 - 4 = 4Q

=> 116 = 4Q

=> Q = 116 / 4

=> Q = 29

From demand function we get,

P = 120 - (4 * 29)

=> P = 4

Therefore, at socially optimal level the output is, Q = 29 and price is, P = 4.

f) Now if Q = 25 then from demand function we get,

P = 120 - (4 * 25)

=> P = 20

TR = P*Q = 20 * 25 = 500.

TC = 400 + (4 * 25) = 500

Profit = TR - TC = 500 - 500 = 0.

Therefore, here the monopolist's profit level is zero (0).