Figure 6 shows the most efficient allocation of resources in this case. It is to allocate 300 hours of labor to the north field, and 700 hours to the south field, as shown by the vertical red-orange line. For maximum output, labor is allocated so that the marginal productivity of labor on the north field is equal to the marginal productivity of labor on the south field.
To see why this works, think it through in reverse: what happens if the allocation of labor is not 300 to the north field and 700 to the south field? For example, suppose 200 hours are allocated to the south field and 800 to the north field. This puts us to the left of the orange line -- and we read off the diagram that the marginal productivity of labor on the north field is 80 bushels of corn, while the marginal productivity on the south field is about 62. Remembering the definition of marginal productivity, that means: if the farmer spends one additional hour on the north field, he will gain 80 bushels, while spending one less on the south field will cost him 62 bushels, leaving a net gain of 18 bushels. What has happened is that spending 800 hours of labor on the south field has pushed the "diminishing returns" on that field so far that it is less productive at the margin than the north field. and that will be true anywhere to the left of the orange line, since, in that range, the marginal productivity on the north field is always greater than the marginal productivity on the south field.
Now let's see what happens if the allocation is to the right of the most efficient one -- for example, suppose the farmer were to allocate 600 hours to the north field and 400 to the south field. Looking at the diagram, we see that the marginal productivity on the north field is 40 while the marginal productivity on the south field is 90. Thus, moving an hour of labor from the north field to the south field will yield a gain of 90-40=fifty bushels of corn. And the farmer will continue to gain as he moves toward the efficient allocation from the right, because, in that range, the marginal product on the south field is always bigger than the marginal product on the north field.
We have seen that the farmer can gain by reallocating his labor from either side toward the efficient output. Once he has 300 hours of labor on the north field and 700 on the south, the farmer cannot increase his output any further. That is why we think of it as the "efficient" allocation of resources.
Copyright