Consider an airline selling tickets to two types of consumers, both of whom want to buy exactly one ticket (q {0, 1}). Leisure travelers have a valuation uniformly distributed on [1, 2], and business travelers have a valuation uniformly distributed on [0, 1] [2, 3]. Formally, if a traveler with valuation v flies and pays a total of T to the airline, her utility is v T. If she does not fly and pays T to the airline, her utility is T. Intuitively, business travelers face greater valuation uncertainty than leisure travelers: they really need to travel if they have something to do in another city, and they cannot travel easily if they have something to do in their own city. The proportion of leisure travelers is one-third, and both types' outside option is zero. The cost of flying a passenger is 1, and all seats are the same.

Travelers learn their valuation over time. At the beginning of period 1, consumers know whether they are a leisure or business travelers, but know nothing about their actual valuation other than that it is distributed as outlined above. At the beginning of period 2, consumers learn their actual valuations. A traveler's type, as well as her valuation for a ticket, is private information. Travelers want to fly at the end of period 2. The interest rate is zero.

(a) What is the highest expected profit the airline can achieve if it waits until period 2 to sell tickets? Specify both the airline's maximization problem in the above situation and the solution to it.

(b) Show that the firm can do strictly better by selling tickets in period 1 instead. [Hint: consider tickets specifying (a) the ticket's price; and (b) a refund amount if the buyer does not travel in period 2.] Explain the intuition behind the firm's pricing scheme.