4. (2 marks for each part) An airport is located next to a large tract of land owned by a housing developer. Noise from the airport reduces the value of the developer's land. Let X be the number of planes using the airport and Y be the number of houses the developer builds. Assume:

Airport profits = 2aX ? X 2

Developer profits = bY ? Y 2 ? XY, where 4a > b > a > 0.

Put your answers for parts (i) and (ii) into a table like the one below. In row (i) each firm acts to maximize its own profits and there is no communication between the firms.

In row (ii) the airport and the developer merge their firms and maximize their joints profits. Label the optimal level of X in row (ii) X? .

(iii) Now suppose there is no merger, but the developer offers to pay the airport A dollars to get the airport to set X = X? . What are the bounds on A such that both the airport and the developer have at least as much profit as each has in (i)?