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A monopolist faces the inverse demand function p = 300 – Q. Their cost function is...

A monopolist faces the inverse demand function p = 300 – Q. Their cost function is c (Q) = 25 + 50Q. Calculate the profit maximizing price output combination

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Answer #1

Profit is maximized where marginal revenue and marginal cost both are equal.

Demand Function

P = 300 - Q

Marginal revenue function is the same as demand function the only difference is, the coefficient of Q is double.

Marginal Revenue Function

MR = 300 - 2Q

Total Cost Function

TC = 25 + 50Q

Marginal cost can be calculated from the total cost function by differentiation.

MC = dTC / dQ

MC = 50

Equating both MR and MC

300 - 2Q = 50

2Q = 250

Q = 125

The profit-maximizing quantity is 125 units

To find the profit-maximizing price we will use this quantity in demand function.

P = 300 - Q

P = 300 - (125)

P = 175

The profit-maximizing price is $175

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