American Airlines and United Airlines compete for customers on flights between

Chicago and Los Angeles. The total number of passengers flown by these two firms (per quarter), q, is the sum of the passengers flown on American, qA, and those flown on United, qU. Assume no other companies can enter. The flight Chicago-Los Angeles costs each airline $147 per passenger. Let p be the price per passenger in dollars. Suppose that the demand function is q(p) = 339-p

1) If American were a monopoly, what would its optimal quantity and price be? What would its profit be?

2) In the duopoly described above, what is the Cournot equilibrium price for this industry? What is each airline's profits?

3) If American were to move first, and United second, what would be the stackelberg equilibrium quantities? Price? Profits?

4) Consider a situation where American and United would form an alliance, called AUA, which behaves as a monopolist on this market. What would AUA's optimal quantity be? What would be the resulting price? What would its profit be? Assuming each airline gets half of AUA's profits, what would each airline's profit be? Are those profits greater than their profits in the duopoly (both cournot and stackelberg)?