Farmer Hoglund has discovered that on his farm, he can get 30 bushels of corn per acre if he applies no fertilizer. When he applies N pounds of fertilizer to an acre of land, the marginal product of fertilizer is 1 − N/200 bushels of corn per pound of fertilizer.
(a) If the price of corn is $3 a bushel and the price of fertilizer is $p per pound (where p < 3), how many pounds of fertilizer should he use per acre in order to maximize profits?
b) (Only for those who remember a bit of easy integral calculus.) Write down a function that states Farmer Hoglund’s yield per acre as a function of the amount of fertilizer he uses.
(c) Hoglund’s neighbor, Skoglund, has better land than Hoglund. In fact, for any amount of fertilizer that he applies, he gets exactly twice as much corn per acre as Hoglund would get with the same amount of fertilizer. How much fertilizer will Skoglund use per acre when the price of corn is $3 a bushel and the price of fertilizer is $p a pound?
(d) When Hoglund and Skoglund are both maximizing profits, will Skoglund’s output be more than twice as much, less than twice as much or exactly twice as much as Hoglund’s? Explain.
(e) Explain how someone who looked at Hoglund’s and Skoglund’s corn yields and their fertilizer inputs but couldn’t observe the quality of their land, would get a misleading idea of the productivity of fertilizer.