Two identical risk-neutral airlines have applied for the exclusive right to operate an airline route during the coming year. The marginal cost is $100, and the demand curve for its services is P = 1000 - Q, where P is the price per passenger and Q is the expected number of passengers. The exclusive right to operate the airline route is assigned for only one year, and it allows the airline with the right to charge the monopoly price for the airline ticket. The airline awarded the right cannot price discriminate across different passengers.
a. If the government chooses the firm that spends the most money lobbying the government members and firms cannot collude, what is the equilibrium strategy for each firm? For that equilibrium strategy, what is the expected amount each firm will devote to lobbying? Provide a detailed explanation and a graphical illustration.
b. Now suppose that a higher lobbying activity increases the probability of getting the rent but does not ensure a win. If firm i spends the amount xi on lobbying activity, it will get the franchise with probability pi = xi / (xi + x-i), where x-i stands for the lobbying activity of all other firms. How much will each firm spend on lobbying in a symmetric equilibrium? How much do all firms spend in total? Provide a detailed proof.
c. Identify and discuss the differences in results between parts (a) and (b).