Question

Suppose a monopolist faces the following demand curve:

Q = 200 – 5P

Also, the long run total cost of the monopolist is given by

TC = 20 + 2Q - .5Q²

a. What the monopolist’s MC function? (1/2 Point)

                        

b. What is the monopolist’s MR function? (1/2 Point)

c. What is the monopolist’s profit maximizing level of output? (1/2 Point)

d. What is monopolist’s profit maximizing level of price? (1/2 Point)

e. How much profit is this monopoly firm is earning? (1/2 Point)

f. What is the value of consumer surplus under monopoly? (1 Point)

g. What is the value of the deadweight loss when the market is a monopoly? (1 Point)

h. What is the value of the Lerner Index? (1/2 Point)

Answer 1

Q = 200 – 5P (It must be P = 200 - 5Q). I am taking it as P = 200 - 5Q because when we draw MR curve of Q = 200 - 5P, it is never negative.

P = 200 - 5Q

Total Revenue = P * Q = 200Q - 5Q^²

TC = 20 + 2Q - .5Q²

a) MC (first derivative of total cost with respect to Q) = 2 + Q

b) Marginal Revenue (First derivative of total revenue with respect to Q) = 200 - 10Q

c) Monopolist profit maximizing situation occurs when MR = MC

200 - 10Q = 2 + Q

198 = 11Q

Q = 18

d) At this quantity, Price monopolits charge is 36.4

e) Profit = (Price - Average Total Cost) * Quantity sold

Average total cost = (20 / Q) + 2 - 0.5Q

Average total cost at Q = 18 is -5.88

Profit = (36.4 + 5.88) * 18 = 761.04

e) Consumer surplus is the area of portion A + B whose sum is (1/2) * (200 - 36.4) * (18 - 0) = 1,472.4

f) Deadweight loss is the area of triangle C whose sum is (1/2) * (33 - 18) * (36.4 - 20) = 123

g) Learner Index = [(P - MC) / P] = [(36.4 - 20) / 36.4] = 0.45