A monopolist faces a demand function defined as Q = 80 - 4P. The monopolist's marginal cost is equal to $10 at all levels of output. What price should the firm charge in order to maximize profits?

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Quizplus · Accepted Answer

To maximize profits, the monopolist sets marginal revenue (MR) equal to marginal cost (MC). The inverse demand function is P = 20 - 0.25Q. Total revenue (TR) is P*Q = (20 - 0.25Q)Q = 20Q - 0.25Q^2. MR is the derivative of TR, MR = 20 - 0.5Q. Setting MR = MC gives 20 - 0.5Q = 10, solving gives Q = 20. Substituting Q = 20 into the inverse demand function gives P = 20 - 0.25(20) = 15. However, the closest price option provided is 20, which is likely a rounding or simplification error in the options.

A Monopolist Faces a Demand Function Defined as Q =