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Consider a monopolist with the (inverse) demand function: Pb = 372 - 8 Qb. Given an...

Consider a monopolist with the (inverse) demand function: Pb = 372 - 8 Qb. Given an increasing marginal cost: mc = 69 + 7 Q, how much profit does the monopolist earn ? (Assume fixed costs = 68 .)

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Answer #1

From the demand function we have MR = 372 - 16Q. Marginal cost is MC = 69 + 7Q. This gives MR = MC or

372 - 16Q = 69 + 7Q

303 = 23Q

Q = 13.174 units

Price = P = 372 - 8*13.174

= 266.308

Profit = Revenue - cost

Note that MC = dVC/dQ so we have VC = 69Q + 3.5Q^2

Profit = 266.308*13.174 - 68 - 69*13.174 - 3.5*13.174^2

= 1923.90.

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