Consider an airline trying to sell plane tickets to business travellers and tourists. The airline cannot distinguish between the two at the point of sale, but knows that in general, business travelers have higher willingness to pay for better seats. Let Pf and Pc be the price of first class and coach tickets respectively. Suppose that business travelers are willing to pay $1000 for a first class seat and $400 for a coach seat, whereas tourists are willing to pay $500 for a first class seat and $300 for a coach seat.

(a) If the airline wants to implement second-degree price discrimination so that business travelers buy first class seats and tourists buy coach seats, what are the incentive compatibility constraints they face?

(b) Using your incentive compatibility constraints, find the price that the airline will charge for a coach seat.

(c) What are the information rents that the airline must leave to business travelers? What is the price of a first class seat?