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. Use calculus for the following:
a. If the firm behaves as a single-price monopoly, what are the firm's optimal price and output level?
b. Demonstrate that the single-price monopolist's profit-maximizing choice of price and output also maximize producer surplus.
c. Identify the output level that would maximize total surplus.
d. Identify the output level that a perfect-price discriminating monopolist would produce.

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The Answer of 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. Use calculus for the following: a. If the firm behaves as a single-price monopoly, what are the firm's optimal price and output level? b. Demonstrate that the single-price monopolist's profit-maximizing choice of price and output also maximize producer surplus. c. Identify the output level that would maximize total surplus. d. Identify the output level that a perfect-price discriminating monopolist would produce.

A Firm with Market Power Faces the Demand Function Q