Marginal Productivity

Productivity, by definition, is a ratio of output to labor input. In most statistical discussions of productivity, we refer to the average productivity of labor:

Average labor productivity is an important concept, especially in macroeconomics. In microeconomics, however, we will focus more on the marginal productivity. We can think of the

marginal productivity of labor as: the additional output as a result of adding one unit of labor, with all other inputs held steady and ceteris paribus.

In algebraic terms, an equally correct definition is:

Let's have a numerical example to illustrate the application of the theory. Suppose that:

When 300 labor-days per week are employed the firm produces 2505 units of output per week.
When 400 labor-days per week are employed the firm produces 3120 units of output per week.
It follows that the change in labor input, Labor, is 100.
It also follows that the change in output, Output, is 615.
Applying the formula above, we approximate the marginal productivity of labor by the quotient 615/100 = 6.15.
We can interpret this result as follows: over the range of 300 to 400 man-days of labor per week, each additional worker adds approximately 6.15 units to output.

Of course, if we had more information, we could get a closer approximation. For example, if we had the outputs for 310, 320, ... 390 man-days of labor, we could see how MP varies within the range 300-400.

But we can be sure that the values will be in the neighborhood of 6.15.

Now let's think a little further about the Law of Diminishing Returns.