A firm with market power faces the demand function q = 4,000 - 40P. The firm's total cost function is TC(q) = 10q + 0.001q2 + 1,000.
a. If the firm behaves as a single-price monopoly, identify the firm's optimal price and output level.
b. Demonstrate that the single-price monopolist's profit-maximizing choice of price and output also maximizes 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.