## Diminishing Returns to a Factor Concept

The law of diminishing returns states that the marginal product of a variable factor must eventually decline as more of the variable factor is combined with other fixed resources. The law of diminishing returns is sometimes called the law of diminishing marginal returns to emphasize the fact that it deals with the diminishing marginal product of a variable input factor. The law of diminishing returns cannot be derived deductively. It is a generalization of an empirical regularity associated with every known production system.

For example, consider an assembly line for the production of refrigerators. If only one employee is put to work, that individual must perform each of the activities necessary to assemble refrigerators. Output from such a combination of labor and capital is likely to be small. In fact, it may be less than could be achieved with a smaller amount of capital, given the inefficiency of having one employee accompany a refrigerator down an assembly line rather than building it at a single station. As additional units of labor are added to this production system—holding capital input constant—output is likely to expand rapidly. The intensity with which the capital resource is used increases with additional labor, and increasingly efficient input combinations result. The improved use of capital resulting from the increase in labor could cause the marginal product, or rise in output associated with each successive employee, to actually increase over some range of additional labor. This increasing marginal productivity might reflect the benefits of worker specialization.

An example in which the marginal product of an input increases over some range is presented in Table 7.2. The first unit of labor (input X) results in 15 units of production. With two units of labor, 31 units can be produced. The marginal product of the second unit of labor MPx=2 = 16 exceeds that of the MPX=1 = 15. Similarly, the addition of another unit of labor results in output increasing to 48 units, indicating a marginal product of MPX=3 = 17 for the third unit of labor.

Eventually, sufficient labor is combined with the fixed capital input so that the benefits of further labor additions will not be as large as the benefits achieved earlier. When this occurs, the rate of increase in output per additional unit of labor, the marginal product of labor, will drop. Although the marginal product of labor is positive and total output increases as more units of labor are employed, the rate of increase in output eventually declines. This diminishing marginal productivity of labor is exhibited by the fourth, fifth, sixth, and seventh units of input X in Table 7.2.

Conceivably, a point might be reached where the quantity of a variable input factor is so large that total output actually begins to decline with additional employment of that factor. In the refrigerator assembly example, this might occur when the labor force became so large that additional employees actually got in each other's way and hindered the manufacturing process. This happens in Table 7.2 when more than seven units of input X are combined with two units of input Y. The eighth unit of X results in a one-unit reduction in total output, MPx=8 = -1; units 9 and 10 cause output to fall by two and three units, respectively. In Figure 7.3(b), regions where the variable input factor X exhibits increasing, diminishing, and negative returns have been labeled. 