Consider a monopolist that has a total cost curve of TC = 110Q - (0.25)Q 2 . The market demand equation is Q d = 155 - P.
(A) What are the total revenue, marginal revenue, marginal cost, equilibrium quantity,
equilibrium price, and profits for the monopolist in this market?
(B) Suppose the government instructs the firm to produce using average cost pricing. What
are the equilibrium quantity, equilibrium price, and profits?
(C) Suppose further that the government wants the firm to produce where supply equals
demand. What will be the equilibrium quantity, equilibrium price, and profits?
Price can be written as P = 155 - Q.
(A) TR is price multiplied by quantity for TR = P × Q = 155 × Q - (0.25) × Q 2 .
Marginal revenue is MR = 155 - 2 × Q d .
Marginal costs are MC = 110 - 0.5 × Q.
MC = MB for monopolist
Q* = 30,
P* = 125,
TR = P × Q = 125 × 30 = 3,750
Profits = TR - TC = 3,750 - [110 × 30 - (0.25) 30 2 ] = 675.
(B) AC = TC/Q = 110 + (0.25) × Q.
AC = D if the government intervenes,
110 - (0.25) × Q = 155 - Q so Q* = 60 and P* = 95
TR = P × Q = 60 × 95 = 5,700
Profits = TR - TC = 5,700 - [110 × 60 - (0.25) × 60 2 ] = 0
(C) Now the monopolist produces at perfectly competitive market quantity,
S = D so MC = D thus 110 + (0.5) × Q = 155 - Q
Q* = 90 and P* = 65
TR = P × Q = 65 × 90 = 5,850
Profits = TR - TC = 5,850 - [110 × 90 - (0.25) × 90 2 ] = - 2,025
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