A firm with market power faces the demand function q=4000-40p. The firm's total cost function is TC(q)=10q+.001q^2+1000.
a. If the firm behaves as a single price monopoly, identify the firm's optional price and output level.
b. Demonstrate that the single price monopolist's profit maximizing choice of price and ouput also maximizes producer surpulus.
c. Identify the output level that would maximize total surplus.
d. Identify the output level that a perfect price discriminating monopolist would produce.