(Scenario: A Monopolist) A monopolist faces a demand curve given by P = 20 - Q and has total costs given by TC = Q². By using a bit of calculus, you should be able to determine that the firm's marginal revenue is MR = 20 - 2Q and its marginal cost is MC = 2Q. If the firm's profit-maximizing output level is 5 and its profit-maximizing price is $15, what are its monopoly profits at this price and quantity?

Question

Quizplus · Accepted Answer

To find the monopolist's profits, we need to first calculate its total revenue and total cost at the profit-maximizing output level of 5. Total revenue (TR) = Price x Quantity = $15 x 5 = $75 Total cost (TC) can be calculated by plugging in Q=5 into the given TC equation: TC = Q² = (5)^(1/2) x 15^(1/2) x 20^(1/2) = $50 Therefore, the monopolist's profits are: Profit = TR - TC = $75 - $50 = $25 So the answer is B, $50.

(Scenario: a Monopolist) a Monopolist Faces a Demand Curve Given