A firm with market power faces the demand functionq= 2,000 - 20P. The firm's total cost function isTC(q) = 20q+ 0.02q²+ 2,000.

a. If the firm behaves as a single-price monopoly, what are its 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 perfectly price-discriminating monopolist would produce.