A monopolist has total cost function C(Q) = K + 10Q, where K is the fixed cost. There are 10 consumers in the market, and each consumer has demand function P = 20 - Q.

a) Suppose that the firm can use two-part tariffs with a per-unit price P and a fixed fee F. Denote the profit-maximizing P and F by P* and F*. What is the value of P*? Without further calculation, explain how to set F*?

b) Compared to the situation where the firm can only set a unit price P to the consumer, how does the two-part tariff pricing affect the firm, the consumer, and the total surplus?