An airport is located on a tract of land owned by a housing developer. The developer would like to build houses but noise from the airport reduces the value of the land. The airport’s total profits are ΠA(x) = 48x − x^2 where x is the number of airport landings. The developer’s total profits are ΠD (x, y) = 60y − y^2 − xy where y is the number of houses built. Consider the following institutional rules about bargaining between the airport and the developer.
(a) Suppose no bargains can be made between the two and each must decide its own level of activity. Calculate the number landings that maximizes the airport’s profits for any level of housing development. Given that level of landings, what is the developer’s profits maximizing number of houses? Calculate the sum of total profits.
(b) Suppose the town council is lobbied into enacting an ordinance making it illegal to land planes at the airport because they impose an externality on the developer. Given that no planes will fly, calculate the developer’s profit maximizing number of houses. Calculate the sum of total profits.
(c) Suppose a law is passed making the airport liable for any damages the developer experiences due to reduced housing values. Note that comparing the two profit functions for the developer calculated above, the amount of damages experienced by the developer will be DD(x,y) = xy for all levels of landings and houses. Therefore, the airport’s profits will be ΠA(x, y) = 48x − x^2 − xy where the last term is the level of damages. Calculate the profit maximizing level of houses and landings and the sum of total profits.
(d) Suppose a single firm bought both the land and the airport. Write out the total profit function for this firm. Calculate the profit maximizing levels of landings and houses. Calculate the sum of total profits.
(e) Suppose the airport and developer are independent. If the first situation was one of “free to choose,” could the developer increase her net profits by paying the airport to reduce its number of landings? If the developer agrees to compensate the airport for all lost profits due to reductions in flights, how many flights per day would she be willing to pay to eliminate? Calculate the sum of total profits at this level of landings and houses.