When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 -N/200 bushels of corn.If the price of corn is $1 per bushel and the price of fertilizer is $.20 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?
A)84
B)328
C)320
D)160
E)200

Question

Quizplus · Accepted Answer

To maximize profits, Farmer Hoglund should equate the marginal cost of fertilizer to the marginal product of fertilizer times the price of corn. The marginal product of fertilizer is given as $1 - \frac{N}{200}$ bushels of corn per pound of fertilizer. The price of corn is $1 per bushel, making the value of the marginal product $1 - \frac{N}{200}$. The cost of one pound of fertilizer is $0.20. Setting the value of the marginal product equal to the cost of fertilizer gives $1 - \frac{N}{200} = 0.20$. Solving for $N$ gives $N = 160$ pounds of fertilizer per acre.

When Farmer Hoglund Applies N Pounds of Fertilizer Per Acre