A firm with market power faces the demand function q = 1,000 - P. The firm's total cost function is TC(q) = 5q + q² + 500. If the firm behaves as a single-price monopoly, the firm's optimal price is $____. A) 751.25 B) 510.45 C) 326.75 D) 248.75

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To maximize profits, the firm sets marginal revenue equal to marginal cost. Marginal revenue is the derivative of total revenue with respect to quantity, and marginal cost is the derivative of total cost with respect to quantity.Total revenue is equal to price times quantity, so marginal revenue is equal to the derivative of price times quantity with respect to quantity. In this case, price is a constant, so marginal revenue is equal to price.Total cost is equal to 5q + q^2 + 500, so marginal cost is equal to the derivative of 5q + q^2 + 500 with respect to quantity. In this case, marginal cost is equal to 5 + 2q.Setting marginal revenue equal to marginal cost, we get:Price = 5 + 2q1,000 - P = 5 + 2qP = 1,000 - 5 - 2qP = 995 - 2qTo find the firm's optimal price, we substitute the firm's demand function into the equation for price:P = 995 - 2qP = 995 - 2(1,000 - P)P = 995 - 2,000 + 2PP = -1,005 + 2PP = 751.25Therefore, the firm's optimal price is $751.25.

A Firm with Market Power Faces the Demand Function Q