An airport is located on a tract of land owned by a housing developer. The devel
ID: 2494343 • Letter: A
Question
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 A(x) = 48x x^2 where x is the number of airport landings. The developer’s total profits are D (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 A(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.
Explanation / Answer
A)
airport’s total profits are maximum when derivative of (48x x^2 ) = 0.
we get, 48 - 2x = 0 or X=24
Profit = 576
Similarly,
60 2y x = 0
we get, Y = 18
Profit of developer = 324
Sum of profits = 324+576 = 900
B)
If X=0
The developer will maximize profits when 60 2y x = 0
Y= 30
Total profits = 900
C)
The developer’s profits including the amount he receives in payment of damages will be 60Y Y ^2XY +XY = 60Y Y ^2. To maximize his net profits, the developer will choose to build 30 houses no matter how many planes are flown. To maximize its profits, net of damages, the airport will choose to land 9 planes. Total profits of the developer will be 900 and total profits of the airport will be 81. The sum of their profits will be 981.
(note :calculations are similar to part A and B)
D)
Total profits, expressed as a function of X and Y would be 48X X2 + 60Y Y 2 XY Total profits are maximized when X = 12 and Y = 24. Total profits are then equal to 1,008.
(note :calculations are similar to part A and B)
E)
Yes and 12.
(calculate profits as done above)
Hope this answer is helpful.
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