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-A monopolist faces a demand function defined as Q = 40 - 2P. The monopolist's marginal cost is equal to $15 at all levels of output. How many units of output should the firm produce in order to maximize profits?

Question

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-A monopolist faces a demand function defined as Q = 40 - 2P. The monopolist's marginal cost is equal to $15 at all levels of output. How many units of output should the firm produce in order to maximize profits?

Quizplus · Accepted Answer

To maximize profits, a monopolist sets marginal revenue (MR) equal to marginal cost (MC). First, we need to find the inverse demand function, which is P = 20 - 0.5Q. Then, to find MR, we differentiate total revenue (TR = P*Q) with respect to Q. TR = (20 - 0.5Q)Q = 20Q - 0.5Q^2, so MR = d(TR)/dQ = 20 - Q. Setting MR equal to MC (15), we get 20 - Q = 15, which simplifies to Q = 5. Therefore, the firm should produce 5 units to maximize profits.

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