Consider the market for a product with two types of potential users: those in proportion f have inverse demand schedule P = 5 - 0.5 Q, while the remaining 1 - f have inverse demand P = 10 - Q. Normalize the total number of consumers to 1, and let c = 2 be the constant marginal cost of the monopolist.
a) What is the optimal (profit-maximizing) two-part tariff (as a function of f) that induces both types of consumers 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 =
(1/2b)(a - P)^2)
b) What is the optimal two-part tariff when only high-demand consumers purchase the good?
c) If f = 0.5, which of the pricing schemes [(a) or (b)] yields a higher total profit? What about when f = 0.75?