A monopolist faces a demand curve given by Q = 70 - P. The monopolist\'s margina

Question

A monopolist faces a demand curve given by Q = 70 - P. The monopolist's marginal revenue function is given by MR = 70 - 2Q. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, what output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits? Assume instead that the monopolist has a cost structure where total costs are described by TC = 0.25Q2 - 5Q + 300 and marginal cost is given by MC = 0.5Q - 5. With monopolist facing the same market demand and marginal revenue, what price - quantity combination will be chosen now to maximize profits? What will profits be?

Explanation / Answer

a. Monopolist would choose Q such that MC = MR

70 - 2Q = 6

=> 2Q = 64

=> Q = 32

P = 70 - Q = 70 - 32 = 38

Profits = P * Q - AC * Q = (P - AC) * Q = (38 -6) * 32 = 32 * 32 = 1024

b.

Monopolist would choose Q such that MC = MR

0.5Q - 5 = 70 - 2Q

=> 2.5Q = 75

=> Q = 30

Price = 70 - Q = 70 - 30 = 40

Profits = P * Q - TC

TC = 0.25Q^2 - 5Q + 300 = 0.25 * (30)^2 - 5 * 30 + 300 = 225 - 150 + 300 = 375

Profits = P*Q - TC = 40 * 30 - 375 = 1200 - 375 = 825

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