In: Economics
Question 3B. (5 Point) CLO3 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)
justify your answer please with steps and by comments or word not by hand please
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 - 0.5Q2
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 monopolist 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
f) Consumer surplus is the area of portion A + B whose sum is (1/2) * (200 - 36.4) * (18 - 0) = 1,472.4
g) Deadweight loss is the area of triangle C whose sum is (1/2) * (33 - 18) * (36.4 - 20) = 123
h) Learner Index = [(P - MC) / P] = [(36.4 - 20) / 36.4] = 0.45