Marginal Revenue Product of Labor

If you were running a business, would you not want to know the value you would make from the workers you employ? A business wants to make sure anything added to its production processes adds value. Let's say you were using several inputs, among which there is labor, and you wanted to find out whether the labor was actually adding value; you would do this by applying the concept of the marginal revenue product of labor. It is about the value each additional unit of labor adds. Anyway, there's more to learn, so read on!

Marginal Revenue Product of Labor Marginal Revenue Product of Labor

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    Marginal Revenue Product of Labor Meaning

    The meaning of marginal revenue product of labor (MRPL) is the additional revenue acquired from adding an extra unit of labor. But first, let's show why it is important.

    The marginal revenue product of labor (MRPL) is the additional revenue acquired from employing an extra unit of labor.

    Labor is a factor of production which involves employing humans or manpower. And just like all other factors of production, it has a derived demand. This means that the demand for labor arises as the firm decides to supply a product that requires labor to produce. In other words, if there is a demand for a given good, then there is a demand for the labor required to make that good. Let's explain this with an example.

    A new directive in the USA makes it mandatory to wear face masks. This directive increases the demand for face masks, and the companies that manufacture face masks now need to employ more people to meet the increased demand.

    As shown in the example, the demand for more labor only emerged when the demand for face masks increased.

    Now, to understand how the marginal revenue product of labor works, we will make some assumptions. Let's assume that the business uses only capital and labor to make its products, and the capital (equipment) is fixed. This means the business only needs to decide how much labor it must employ.

    Now, let's assume that the firm already has some workers but wants to know whether it is worth it to add one more worker. It would only be profitable if the revenue generated by this extra worker (or the MRPL) is higher than the cost of employing that worker. This is why the marginal revenue product of labor is important. It allows economists to determine whether it is profitable to employ an additional unit of labor or not.

    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.

    The marginal product of labor is the additional output produced by adding an extra unit of labor.

    Marginal revenue is revenue generated from increasing output by an additional unit.

    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.

    Marginal Revenue Product of Labor Marginal Revenue Product of Labor Curve StudySmarterFig. 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.

    The more workers continue to be employed, the less the contribution of each additional worker.

    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.

    Marginal Revenue Product of Labor Marginal Revenue Product of Labor Curve StudySmarterFig. 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.

    Marginal Revenue Product of Labor  Marginal revenue product of labor in a monopolistic vs competitive output market StudySmarterFig. 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.

    Consider a company that wants to determine its marginal revenue product of labor when its machines and equipment (capital) can also change.

    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.

    The employees have more machines to work with, so each additional worker can now produce more.

    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.

    At a wage rate of $20/hour, the firm employs workers for 100 hours. As the wage rate reduces to $15/hour, the firm is able to add more machinery because it wants to produce more output, which then causes additional workers to have higher productivity than previously. The resulting marginal revenue product of labor curves is shown in Figure 4.

    Marginal Revenue Product of Labor Marginal revenue product of labor with variable capital StudySmarterFig. 4 - Marginal revenue product of labor with variable capital

    MRPLL1 and MRPLL2 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, DL 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, MRPLL1 and MRPLL2 are not equal to DL because they represent MRPL with fixed capital.

    Read our articles on Factor Markets and Labor Demand to learn more!

    Marginal Revenue Product of Labor - Key takeaways

    • The marginal revenue product of labor (MRPL) is the additional revenue acquired from employing an extra unit of labor.
    • The marginal product of labor is the additional output produced by adding an extra unit of labor.
    • Marginal revenue is the revenue generated from increasing output by an additional unit.
    • The formula for the marginal revenue product of labor is \(MRPL=MPL\times\ MR\)
    • 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.
    Frequently Asked Questions about Marginal Revenue Product of Labor

    How do you calculate marginal product of labor?

    Marginal product of labor (MPL) = ΔQ/ΔL

    Where Q represents quantity of output and L represents quantity of labor.

    What is the difference between the marginal product of labor and the marginal revenue product of labor for a firm?

    The marginal revenue product of labor (MRPL) is the additional revenue acquired from employing an extra unit of labor, whereas the marginal product of labor is the additional output produced by adding an extra unit of labor.

    What is the relationship between the marginal revenue product MRP and the demand curve for labor?

    The marginal revenue product of labor is a firm's demand curve for labor. The firm will employ labor until the marginal revenue equals the wage rate.

    What is the marginal cost of labor?

    The marginal cost of labor is the additional cost or employing an additional unit of labor.

    What does the expression marginal product of labor mean?

    The marginal product of labor is the additional output produced by adding an extra unit of labor.

    Test your knowledge with multiple choice flashcards

    The quantity of labor demanded is plotted on the vertical axis.

    The wage rate is the price of labor.

    The MRPL curve in the monopolistic output market is the same as the MRPL in the competitive output market.

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