Question

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 $4 per bushel and the price of fertilizer is $1.20 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

 

Answer 1

Substitute the given values in the following identity to calculate the value of \(\mathrm{N}\) as follows:

$$ \frac{M P_{F}}{M P_{C}}=\frac{P_{F}}{P_{C}} $$

This can be done as follows:

$$ \begin{aligned} \frac{M P_{F}}{M P_{C}} &=\frac{P_{F}}{P_{c}} \\ \frac{(1-N / 200) M P}{M P_{C}} &=\frac{1.20}{4} \\ 1-N / 200 &=0.3 \\ 1-0.3 &=N / 200 \\ 0.7 &=N / 200 \\ & N=140 \end{aligned} $$

Thus, the farmer should use 140 pounds of fertilizer per acre in order to maximize his profits.