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The Law of Diminishing Marginal Product
Maximizing this expression with respect to labor yields ∂APL 0.5(25K 0.5L-0.5 )L - 25K 0.5L.5 = ∂L L2 Since L > 0, this implies that 0.5(25K 0.5L-0.5 )L - 25K 0.5L0.5 = 0 0.5(25K 0.5L-0.5 ) =
25K 0.5L0.5 L
As demonstrated earlier, the term on the left-hand side of the expression is the marginal product of labor, while the term on the right is the average product of labor. Thus, this expression may be rewritten as MPL = APL
THE LAW OF DIMINISHING MARGINAL PRODUCT It was noted earlier that the Cobb–Douglas production function exhibits a number of useful mathematical properties. One of these properties is the important technological relationship known as the law of diminishing marginal product (law of diminishing returns). This concept can be described with the use of a simple illustration. Consider a tomato farmer who has a 10-acre farm and as much fertilizer, capital equipment, water, labor, and other productive resources as is necessary to grow tomatoes. The only input that is fixed in supply is farm acreage. The farmer decides that to maximize output, additional workers will have to be hired. With the exception of farm acreage, each worker has as many productive resources to work with as necessary. Initially, as one might expect, output expands rapidly. At least in the early stages of production, as more workers are assigned to the cultivation of tomatoes, the additional output per worker might be expected to increase. This is because in the beginning land is relatively abundant and labor is relatively scarce. While each worker has as much land and other resources to work with as is necessary for efficient production, at least some land initially stands fallow. Labor can be said to be fully utilized while land can be said to be underutilized. As more laborers are added to the production process, total output rises; beyond some level of labor usage, however, incremental additions to output from the addition of more workers, while positive, will begin to decline. That is, while each additional worker contributes positively to total output, beyond some point the amount of land allocated to each worker will decline. No matter how much water, fertilizer, and other inputs are made available to each worker, the amount of output per
