Marginal Product of Labor

Marginal Product of Labor Formula

The marginal product of labor (MPL) formula can be deduced from its definition. Since it refers to how much the output changes when the quantity of labor changes, we can write the marginal product of labor formula as:

\(MPL=\frac{\Delta\ Q}{\Delta\ L}\)

Where \(\Delta\ Q\) represents the change in the quantity of output, and \(\Delta\ L\) represents the change in the quantity of labor.

Let's try an example, so we can use the marginal product of labor formula.

Marginal Product of Labor Curve

The marginal product of labor curve can be illustrated by plotting the production function. It is the graphical illustration of the increase in the quantity of output as a result of adding an extra unit of labor. It is plotted with the quantity of output on the vertical axis and the quantity of labor on the horizontal axis. Let's use an example to draw the curve.

As initially indicated, the number of workers goes on the horizontal axis, whereas the quantity of output goes on the vertical axis. Following this, we have plotted Figure 1.

Fig. 1 - Production function

As Figure 1 shows, a single worker produces 200, 2 workers produce 280, 3 workers produce 340, 4 workers produce 380, and 5 workers produce 400 wine glasses. Simply put, the marginal product of labor represents the jump from one quantity of wine glasses (say, 200) to the next quantity of wine glasses (280) as the number of workers increases from 1 to 2, etc. In other words, the marginal product of labor is the slope of the total output curve represented by the production function.

Value of the Marginal Product of Labor

The value of the marginal product of labor (VMPL) is the value generated by each additional unit of labor employed. This is because a profit-maximizing firm looks particularly at the money it can make by selling its products. So, the objective here is not for the firm to determine how the output changes with each additional worker but rather how much money is generated from adding that extra worker.

Mathematically, it is written as:

\(VMPL=MPL\times\ P\)

To make sure you understand this easily, let's assume that all the firm's other inputs are fixed, and only labor can change. In this case, the value of the marginal product of labor is the marginal product of labor multiplied by how much the firm sells the product for.

You could look at it as shown in the following example.

In perfect competition, a profit-maximizing firm will continue to supply goods until its cost equals its benefit at the market equilibrium. Therefore, if the additional cost is the wage paid to the additional worker, then the wage rate is equal to the price of the product at the market equilibrium. As a result, the curve of the VMPL looks like Figure 2 below.

Fig. 2 - Value of marginal product of labor curve

As shown in Figure 2, the VMPL curve is also the labor demand curve in a competitive market. This is because the firm's wage rate equals the price of the product in a competitive market. Hence, while the curve shows the price and quantity of workers, at the same time, it also shows the wage rate the firm is willing to pay for different quantities of workers. The curve has a downward slope because the firm employs more labor as the wage rate reduces. You should note that the value of the marginal product of labor is only equal to labor demand for a competitive, profit-maximizing firm.

Diminishing Marginal Product of Labor

The law of diminishing marginal returns works on the marginal product of labor. Let's take a look at Table 4 to aid with the explanation of the diminishing marginal product of labor.

Table 4 - Diminishing marginal product of labor example

Notice how the quantity of wine glasses increases by a large margin from 1 worker to 2 workers, and the margin gets smaller as more and more workers are added? This is what diminishing marginal product of labor refers to. Diminishing marginal product of labor refers to the property of the marginal product of labor whereby it increases but at a decreasing rate.

The production function in Figure 3 below shows what the diminishing marginal product of labor looks like.

Fig. 3 - Production function

Notice how the curve begins with a sharp rise, then gets flatter at the top. This shows how the marginal product of labor increases at a decreasing rate. This happens because the more a firm adds employees, the more work gets done, and the less work remains. Eventually, there will be no extra work for an extra employee to do. So, each worker we add contributes less than the previous worker we added until there is eventually nothing to contribute, at which point we start wasting the salary on the extra employee. This can be understood better with an example.