A real estate agency owns a land close to an airport. Due to noise pollution, the price of houses is a effected by the airport activity. Let X be the number of planes (landings and take-offs) and Y the number of houses built on this land. The airport profit is A(X) = 48X - X^2. The real estate agency profit is E(Y, X) = 60Y - Y^2 - XY.

a. How many planes land and take-off at the airport and how many houses are built on the land assuming that each firm maximizes its own profit taking the choices of the other firm as given?

b. How many planes and houses if the two firms merge? Why does the answer change if the firms merge?

c. Show that "no pollution" is not an efficient outcome.

d. Find the number of planes, houses and the profits if the airport is obliged to compensate the real estate agency for the damage XY it causes.

e. Find the optimal Pigouvian tax.

f. Assume that a regulator assigns property rights on the externality, i.e. right to make noise or to enjoy an environment free of noise. Show that by agreeing on the airport traffic and on compensations, the two firms reaches the efficient outcome (i.e. number of planes and houses). What are the compensations that are accepted by the two bargaining parties?