Table 19-2 calculates the value of the marginal product of labor on George and Martha’s farm, on the assumption that the price of wheat is $20 per bushel. In Figure 19-3 the horizontal axis shows the number of workers employed; the vertical axis measures the value of the marginal product of labor and the wage rate. The curve shown is the value of the marginal product curve of labor. This curve, like the marginal product of labor curve, slopes downward because of diminishing returns to labor in production. That is, the value of the marginal product of each worker is less than that of the preceding worker, because the marginal product of each worker is less than that of the preceding worker.

We have just seen that to maximize profit, George and Martha must hire workers up to the point at which the wage rate is equal to the value of the marginal product of the last worker employed. Let’s use the example to see how this principle really works.

Assume that George and Martha currently employ 3 workers and that workers must be paid the market wage rate of $200. Should they employ an additional worker?

Looking at Table 19-2, we see that if George and Martha currently employ 3 workers, the value of the marginal product of an additional worker is $260. So if they employ an additional worker, they will increase the value of their production by $260 but increase their cost by only $200, yielding an increased profit of $60. In fact, a producer can always increase total profit by employing one more unit of a factor of production as long as the value of the marginal product produced by that unit exceeds its factor price.

Alternatively, suppose that George and Martha employ 8 workers. By reducing the number of workers to 7, they can save $200 in wages. In addition, the value of the marginal product of the last one, the 8th worker, was only $100. So, by reducing employment by one worker, they can increase profit by $200 − $100 = $100. In other words, a producer can always increase total profit by employing one less unit of a factor of production as long as the value of the marginal product produced by that unit is less than the factor price.

Using this method, we can see from Table 19-2 that the profit-maximizing employment level is 5 workers given a wage rate of $200. The value of the marginal product of the 5th worker is $220, so adding the 5th worker results in $20 of additional profit. But George and Martha should not hire more than 5 workers: the value of the marginal product of the 6th worker is only $180, $20 less than the cost of that worker. So, to maximize total profit, George and Martha should employ workers up to but not beyond the point at which the value of the marginal product of the last worker employed is equal to the wage rate.

Now look again at the value of the marginal product curve in Figure 19-3. To determine the profit-maximizing level of employment, we set the value of the marginal product of labor equal to the price of labor—a wage rate of $200 per worker. This means that the profit-maximizing level of employment is at point A, corresponding to an employment level of 5 workers. If the wage rate were higher than $200, we would simply move up the curve and reduce the number of workers employed; if the wage rate were lower than $200, we would move down the curve and increase the number of workers employed.

In this example, George and Martha have a small farm in which the potential employment level varies from 0 to 8 workers, and they hire workers up to the point at which the value of the marginal product of the last worker is greater than or equal to the wage rate. (To go beyond this point and hire workers for which the wage exceeds the value of the marginal product would reduce George and Martha’s profit.)

Suppose, however, that the firm in question is large and has the potential of hiring many workers. When there are many employees, the value of the marginal product of labor falls only slightly when an additional worker is employed. As a result, there will be some worker whose value of the marginal product almost exactly equals the wage rate. (In keeping with the George and Martha example, this means that some worker generates a value of the marginal product of approximately $200.) In this case, the firm maximizes profit by choosing a level of employment at which the value of the marginal product of the last worker hired equals (to a very good approximation) the wage rate.

In the interest of simplicity, we will assume from now on that firms use this rule to determine the profit-maximizing level of employment. This means that the value of the marginal product of labor curve is the individual producer’s labor demand curve. And, in general, a producer’s value of the marginal product curve for any factor of production is that producer’s individual demand curve for that factor of production.