AA and BB are the only airlines competing on the France Spain route. Every day there are 900 potential travelers, each with a preferred departure time. These preferred times are distributed uniformly between 09:00 and 19:00. Customers value a trip at their preferred departure time at $450, but every hour of deviation reduces the value by $40. It is not possible for two flights to depart at the same time.

Departure slots are available at quarter-hour intervals, the first slot at 09:00 and the last at 19:00. A plane can carry up to 500 passengers at a fixed cost of a $40k per flight, while the marginal cost of adding passengers is negligible. The airfare is fixed by regulators at $250 (discounts are not allowed either).

Everything works the same in both flight directions, so consider just one direction.

(a) Both airlines have the capacity to serve this route for at most one flight per day. AA gets to choose its departure time first having been the first to enter this market in the past. Describe the flight departure times and profits in equilibrium?

(b) In the long run the companies can adjust their number of flights per day. Describe the flight departure times and profits in a long-run equilibrium where no two consecutive departures are operated by the same company. In equilibrium neither company can profit from adding or discontinuing one flight.

(c) Describe a flight schedule that would maximize industry profits.

(d) Describe a flight schedule that would maximize total surplus