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# Marginal Product of Labor

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Let's say you are running a bakery and need employees. Would you not want to know the contribution each employee makes to your output? We would! And this contribution is what economists call the marginal product of labor. Let's say you keep adding employees to a point where some of your employees are idle but take a salary at the end of the month. Would you not want to find out? Businesses want to know what each additional employee contributes to their overall output, and this is why they apply the marginal product of labor. But what is the marginal product of labor, and how do we figure it out? Read on to find out!

## Marginal Product of Labor Definition

To make the definition of the marginal product of labor easy to understand, let's first provide the reasoning behind it. Every firm that requires employees must look at how its number of employees influences its quantity of output. The question they ask here is, 'what contribution does each worker make to the firm's total output?' The answer to this lies in the marginal product of labor, which is the increase in the quantity of output as a result of adding an extra unit of labor. This tells the firm whether to keep adding employees or get rid of some employees.

Marginal product of labor is the increase in the quantity of output as a result of adding an extra unit of labor.

The concept can be understood with the simple example provided below.

Jason has just one employee in his wine glass manufacturing shop and can produce 10 wine glasses a day. Jason realizes that he has extra materials not being used and employs one more worker. This increases the number of wine glasses made each day to 20. The contribution made by the extra employee to the quantity of output is 10, which is the difference between the old output and the new output.

To learn why a firm needs employees, as well as the determinants of labor demand, check out our article:

- Labor Demand.

Economists sometimes find the average product of labor, which shows the ratio of total output to the number of workers. It is simply the average quantity of output that can be produced by each worker.

The average product of labor is the average quantity of output that can be produced by each worker.

The average product of labor is important because economists use it to measure productivity. In other words, the average product of labor tells us the contribution of each worker to the total output produced. It is different from the marginal product of labor, which is the additional output contributed by an extra worker.

## 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.

Jason's company manufactures wine glasses. Jason decided to increase the company's workforce from 1 to 3. However, Jason wants to know the contribution each employee made to the number of wine glasses produced. Assuming all other inputs are fixed and only labor is variable, fill in the missing cells in Table 1 below.

 Number of workers Quantity of wine glasses Marginal product of labor$$(MPL=\frac{\Delta\ Q}{\Delta\ L})$$ 1 10 10 2 20 ? 3 25 ?

Table 1 - Marginal product of labor example question

Solution:

We use the marginal product of labor formula:

$$MPL=\frac{\Delta\ Q}{\Delta\ L}$$

With the addition of the second worker, we have:

$$MPL_2=\frac{20-10}{2-1}$$

$$MPL_2=10$$

With the addition of the third worker, we have:

$$MPL_3=\frac{25-20}{3-2}$$

$$MPL_3=5$$

So, the table becomes:

 Number of workers Quantity of wine glasses Marginal product of labor$$(MPL=\frac{\Delta\ Q}{\Delta\ L})$$ 1 10 10 2 20 10 3 25 5

Table 2 - Marginal product of labor example answer

## 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.

The production function of Jason's wine glass factory is shown in Table 3 below.

 Number of workers Quantity of wine glasses 1 200 2 280 3 340 4 380 5 400

Table 3 - Production function example

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.

The value of the marginal product of labor is the value generated from the addition of an extra unit of labor.

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.

The firm added one more employee, who added 2 more products to the output. So, how much money did the new employee generate if 1 product was sold for $10? The answer is that the 2 more products added by the new employee sold for$10 each imply that the new employee just made \$20 for the firm. And that is the value of their marginal product of labor.

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.

 Number of workers Quantity of wine glasses 1 200 2 280 3 340 4 380 5 400

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.

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.

Let's say a company has 2 machines used to capacity by 4 employees. This means 2 employees can use 1 machine at a time without losing productivity. However, if the company continues to add workers without increasing the number of machines, the workers can begin to get in each other's way, and this means that there will be idle workers being paid to contribute nothing to the quantity of output.

Read our article on Labor Demand to understand why a competitive profit-maximizing firm hires more labor when the wage rate decreases!

## Marginal Product of Labor - Key takeaways

• Marginal product of labor is the increase in the quantity of output as a result of adding an extra unit of labor.
• The average product of labor is the average quantity of output that can be produced by each worker.
• The formula for the marginal product of labor is: $$MPL=\frac{\Delta\ Q}{\Delta\ L}$$
• The value of the marginal product of labor is the value generated from the addition of an extra unit of labor.
• Diminishing marginal product of labor refers to the property of the marginal product of labor whereby it increases but at a decreasing rate.

Marginal product of labor is the increase in the quantity of output as a result of adding an extra unit of labor.

The formula for the marginal product of labor is: MPL=ΔQ/ΔL

Marginal product of labor is the increase in the quantity of output as a result of adding an extra unit of labor. It diminishes because the more a firm adds employees, the less efficient they will become at producing a certain level of output.

Jason has just one employee in his wine glass manufacturing shop and can produce 10 wine glasses a day. Jason realizes that he has extra materials not being used and employs one more employee, and this increases the number of wine glasses made each day to 20. The contribution made by the extra employee to the quantity of output is 10, which is the difference between the old output and the new output.

The formula for the marginal product of labor is: MPL=ΔQ/ΔL

The formula for the average product of labor is: MPL=Q/L

## Marginal Product of Labor Quiz - Teste dein Wissen

Question

What is marginal product of labor?

Marginal product of labor is the increase in the quantity of output as a result of adding an extra unit of labor.

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Question

Marginal product of labor asks, "what contribution does each worker make to the firm's total output?"

True.

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Question

The average quantity of output that can be produced by each worker is known as _____.

The average product of labor

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Question

What is the formula for finding the marginal product of labor?

$$MPL=\frac{\Delta\ Q}{\Delta\ L}$$

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Question

In the formula for finding the marginal product of labor,  Δ Q represents ___.

The change in quantity of output

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Question

The marginal product of labor curve is the graphical illustration of the increase in the quantity of output as a result of adding an extra unit of labor.

True.

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Question

The value generated from the addition of an extra unit of labor is known as ____.

The value of the marginal product of labor.

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Question

The value of the marginal product of labor (VMPL) is the value that was generated by each unit of labor fired over time.

False.

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Question

What is the formula for finding the value of the marginal product of labor?

$$VMPL=MPL\times\ P$$

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Question

____ of labor refers to the property of the marginal product of labor where it increases, but at a decreasing rate.

Diminishing marginal product.

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Question

Diminishing marginal product is simply the average quantity of output that can be produced by each worker.

False.

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Question

The VMPL curve in perfect competition is also the labor demand curve.

True.

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