Marginal Revenue Product of Labor

Marginal Revenue Product of Labor Formula

The formula for the marginal revenue product of labor (MRPL) looks at finding how much revenue is generated by an additional unit of labor. Economists equate it to the marginal product of labor (MPL) multiplied by the marginal revenue (MR).

Mathematically, this is written as:

\(MRPL=MPL\times\ MR\)

So, what are the marginal product of labor and marginal revenue? The marginal product of labor is the additional output produced by adding an extra unit of labor, whereas marginal revenue is the revenue from selling an extra unit of output.

Mathematically, these are written as:

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

\(MR=\frac{\Delta\ R}{\Delta\ Q}\)

Where Q represents a quantity of output, L represents a quantity of labor, and R represents revenue.

In a case where the labor market and goods market are both competitive, businesses will sell their products at the market price (P). This then means that the marginal revenue is equal to the market price since the business sells any additional product at the market price. Therefore, in the case where the labor market and goods market are both competitive, the marginal revenue product of labor is the marginal product of labor multiplied by the price of output.

Mathematically, this is:

\(MRPL=MPL\times\ P\)

• In the case where the labor market and goods market are both competitive, the marginal revenue product of labor is the marginal product of labor multiplied by the price of output.

Marginal Revenue Product of Labor Diagram

The marginal revenue product of labor diagram is referred to as the marginal revenue product of labor curve.

Let's take a look at it in a little more detail!

Marginal Revenue Product of Labor curve

The marginal revenue product of labor curve is the labor demand curve, which is plotted with the price of labor or wages (w) on the vertical axis and the quantity of labor, employment, or hours worked on the horizontal axis. It shows the price of labor at different quantities demanded. If the firm wants to profit from employing an extra worker, it must ensure that the price of adding this worker (the wage rate) is less than the revenue generated by the worker.

Figure 1 shows a simple marginal revenue product of labor curve.

Fig. 1 - Marginal revenue product of labor curve

As shown in Figure 1, the marginal revenue product of labor curve has a downward slope, and this is because the marginal product of labor decreases as the quantity of labor employed increases.

In a perfectly competitive market, the firm will hire as many workers at the market wage rate as it can until the marginal revenue is equal to the market wage rate. This means that as long as the marginal revenue product of labor (MRPL) is greater than the market wage rate, the firm will continue to hire workers until MRPL equals the market wage rate.

The profit-maximizing rule is, therefore:

\(MRPL=w\)

As wages are not affected by the activities of the firm, the supply of labor is a horizontal line.

Let's have a look at Figure 2.

Fig. 2 - Marginal revenue product of labor curve

As shown in Figure 2 above, point E is where the firm will stop employing more units of labor since the profit-maximizing rule will be satisfied at this point.

Marginal Revenue Product of Labor Differences

There are some differences between the marginal revenue product of labor in a competitive goods market and the marginal revenue product of labor in the case of a monopoly. In the case of perfect competition in the goods market, the marginal revenue product of labor is equal to the price of the good. However, in the case of a monopoly, the marginal revenue product of labor is lower than in perfect competition because the firm must reduce its output prices if it wants to sell more of the output. As a result, the marginal revenue product of labor curve in the case of a monopoly is below what we have in perfect competition, as shown in Figure 3.

Fig. 3 - Marginal revenue product of labor in a monopolistic vs. competitive output market

The MRPL formulas for perfect competition and monopoly power are written as follows.

• For perfect competition:\(MRPL=MPL\times P\)For a monopoly power:\(MRPL=MPL\times MR\)

In a perfectly competitive market, the firm will sell any quantity of products at the market price, and this means that the firm's marginal revenue is equal to the price. However, a monopoly power must reduce its prices to increase the number of products it sells. This means the marginal revenue is less than the price. Plotting the two on the same graph as shown in Figure 3, this is why the MRPL for the monopoly (MRPL₁) is below the MRPL for the competitive market (MRPL₂).

Marginal Revenue Product of Labor with Variable Capital

So, what about a case where both labor and capital are variable? In this case, a change in the price of either labor or capital affects the other. Let's look at the example below.

If the wage rate decreases, the firm will employ more labor even as capital remains unchanged. But as the wage rate decreases, it will cost less for the company to produce an extra unit of output. As this happens, the firm will want to increase its output to make more profits, and this means the firm will most likely buy extra machines to make more output. As capital increases, this means the marginal revenue product of labor will also increase.

This increase means the marginal revenue product of labor curve will shift to the right, increasing the quantity of labor demanded.

Let's look at an example.

Fig. 4 - Marginal revenue product of labor with variable capital

MRPL_L1 and MRPL_L2 represent the MRPL at different prices with fixed capital. At a wage rate of $20/hour, the firm demands 100 hours of labor (point A). The reduction of the wage rate to $15/hour makes the firm increase its hours of labor demanded to 120 (point B).

However, when capital is variable, the reduction in price will not just increase the quantity of labor, but it will also increase the marginal product of capital (additional output generated by an additional unit of capital). This will make the firm increase capital, which means it will also increase labor to make use of the additional capital. The hours of labor demanded increase to 140 as a result.

In summary, D_L represents the demand for labor with variable capital. Point A is for a wage rate of $20/hour with variable capital, and point B is for a wage rate of $15/hour with variable capital. In this case, MRPL_L1 and MRPL_L2 are not equal to D_L because they represent MRPL with fixed capital.