Suppose a monopoly faces the inverse market demand p = 100 – 2Q such that MR = 1
ID: 1202074 • Letter: S
Question
Suppose a monopoly faces the inverse market demand p = 100 – 2Q such that MR = 100 – 4Q. The monopoly has a constant marginal cost of $12 (variable cost = 12Q) and a fixed cost of $600. Answer the following questions:
A) Find the maximum profit for the monopoly firm.
B )Find the Lerner Index for the monopoly firm.
C) Find the size of the monopoly deadweight loss. [Hint: competitive equilibrium is MC = inverse market demand.]
D) If the government imposes optimal price regulation on this monopoly firm, calculate the profit the firm makes under the price regulation.
Explanation / Answer
Monopolist produces where MR cuts MC and charges price where thsi quantity cuts the demand curve
(A) MR = MC
100-4Q = 12
88= 4Q
Q = 22
P = 100-2x22 = $56
Profit = PQ-TC
Profit = 56 x22 - 12x22-600
Profit = $368
(b) lerner index = (P-MC) /P = (56-12) / 56= 0.78
(c) MC =P competitve
12 = 100-2Q
88 = 2Q
Q= 44
P = 12
dead weight loss = (44-22) x (56-12) =968
(d) Profit at competitive price = (P-AC) Q
As MC = AC = P profits = 0
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