The farmer's "allocation problem" is: How much labor to commit to the north field, and how much to the south field? One "common sense" approach might be to abandon the infertile north field and allocate the whole 1000 hours of labor to the south field. But a little arithmetic shows that this won't work. Here is a table that shows the correlated quantities of labor on the two fields, and the total output of corn from both fields taken together.
| Labor on North Field |
Labor on South Field |
total output in bushels of corn |
|---|---|---|
| 0 | 1000 | 85000 |
| 100 | 900 | 89600 |
| 200 | 800 | 92400 |
| 300 | 700 | 93400 |
| 400 | 600 | 92600 |
| 500 | 500 | 90000 |
| 600 | 400 | 85600 |
| 700 | 300 | 79400 |
| 800 | 200 | 71400 |
| 900 | 100 | 61600 |
| 1000 | 0 | 50000 |
We see that the farmer gets his largest output by allocating most, but not all, of his labor to the south field. Because of the principle of diminishing returns, however, he shouldn't put all his resources into the one field, but divide the labor resource (unevenly!) between the two.
But how much should go to the north plot, and how much to the south plot?
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