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In: Economics

When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is...

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?

 

Solutions

Expert Solution

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.

Rahul Sunny answered 2 years ago
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