2. (Church & Ware, page 181, problem 6) Consider the market for a product with two types of potential users: those in proportion A have inverse demand schedule P = 5 - Q, while the remaining 1 - A have inverse demand P = 10 - Q. Normalize the total number of consumers to 1, and let e = 2 be the constant marginal cost. (a) What is the optimal (profit-maximizing) two-part tariff (as a function of A) that induces both types of consumer to buy? (Hint: Use the fact that for an inverse demand curve of the form P = a - bQ, consumer surplus at price P is given by CS = #(a - P)2. ) (b) What is the optimal two-part tariff when only high-demand consumers purchase the good? (c) If A = , which of the pricing schemes [(a) or (b)] yields a higher total profit? What about when A =