Marginal Product of Labor Formula

Marginal Product of Labor Formula (Table of Contents)

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What is the Marginal Product of Labor Formula?

The term “marginal product of labor” refers to the productivity measure that assesses the change in production output due to change in the production input, labor in this case. In other words, the marginal product of labor captures the incremental change in output resulting due to an added unit of labor. The formula for the marginal product of labor can be derived by dividing the change in production output (ΔY) by the change in input labor (ΔL). Mathematically, it is represented as,

or

Further, the formula for the marginal product of labor can be elaborated into

Where,

• Y₀ = Initial Production Output,
• Y₁ = Final Production Output,
• L₀ = Initial Labor Unit
• L₁ = Final Labor Unit

Examples of Marginal Product of Labor Formula (With Excel Template)

Let’s take an example to understand the calculation of the Marginal Product of Labor Formula in a better manner.

Marginal Product of Labor Formula – Example #1

Let us take the example of a company SDF Ltd which is engaged in the manufacturing automotive engine parts. Recently, the company’s management conducted a study to understand the impact of increasing workers on the production volume of the company. As per the study, the monthly production volume increased from 500,000 pieces in FY17 to 600,000 pieces in FY18 owing to a corresponding increase in a number of labors from 400 to 450. Calculate the marginal product of the labor of the company for the newly added labor force. Also, compare the productivity of the new labor force with the existing ones.

Solution:

Marginal Product of Labor is calculated using the formula given below

Marginal Product of Labor = (Y₁ – Y₀) / (L₁ – L₀)

• Marginal Product of Labor = (600,000 – 500,000) / (450 – 400)
• Marginal Product of Labor = 2,000 pieces per Labor

Existing Productivity is calculated using the formula given below

Existing Productivity = Y₀ / L₀

• Existing Productivity = 500,000 / 400
• Existing Productivity = 1,250 pieces per Labor

New Productivity is calculated using the formula given below

New Productivity = Y₁ / L₁

• New Productivity = 600,000 / 450
• New Productivity = 1,333 pieces per Labor

Therefore, SDF Ltd.’s marginal product of a labor of the new workforce is 2,000 pieces per labor that has resulted in an increase in the productivity of the entire team from 1,250 pieces per labor to 1,333 pieces per labor.

Marginal Product of Labor Formula – Example #2

Let us take the example of the above company again. Based on its successful recruitment of workers last year, the management has decided to further increase the workforce in a phased manner and track the change in productivity every month. During the first 6 months, the following production volume and workforce data are available, Calculate the marginal product of labor at the end of each month.

Solution:

Marginal Product of Labor is calculated as

February

• Marginal Product of Labor _Feb = (700,000 – 600,000) / (500 – 450)
• Marginal Product of Labor _Feb = 2,000 pieces per Labor

March

• Marginal Product of Labor _Mar  = (825,000 – 700,000) / (550 – 500)
•  Marginal Product of Labor _Mar = 2,500 pieces per Labor

April

• Marginal Product of Labor _Apr = (900,000 – 825,000) / (600 – 550)
•  Marginal Product of Labor _Apr = 1,500 pieces per Labor

May

• Marginal Product of Labor _May = (950,000 – 900,000) / (650 – 600)
• Marginal Product of Labor _May = 1,000 pieces per Labor

June

• Marginal Product of Labor _Jun = (975,000 – 950,000) / (700 – 650)
• Marginal Product of Labor _Jun = 500 pieces per Labor

Explanation

The formula for the marginal product of labor can be computed by using the following steps:

Step 1: Firstly, determine the initial production output and the required labor input for that which are represented by Y₀ and L₀ respectively.

Step 2: Next, determine the final production output and the corresponding labor input which are denoted by Y₁ and L₁ respectively.

Step 3: Next, calculate the change in production output by subtracting the initial production output (step 1) from the final output (step 2).

Change in Production Output, ΔY = Y₁ – Y₀

Step 4: Next, calculate the change in labor input by deducting the initial labor input (step 1) from the final one (step 2).

Change in Labor Input, ΔL = L₁ – L₀

Step 5: Finally, the formula for the marginal product of labor can be derived by dividing the change in production output (step 3) by the change in input labor (step 4) as shown below.

Marginal Product of Labor = Change in Production Output / Change in Input Labor

Marginal Product of Labor = (Y₁ – Y₀) / (L₁ – L₀)

Relevance and Use of Marginal Product of Labor Formula

The concept of the marginal product of labor is important as it can influence major decisions regarding the production level of any company. It is should be kept in mind that the marginal product of labor is governed by the law of diminishing marginal returns which means the marginal productivity will eventually be decreasing after a certain point due to various operational shortcomings. In fact, there can be occasions when the marginal productivity becomes negative which means that the total production level will fall with the addition of any new labor units.

Marginal Product of Labor Formula Calculator

You can use the following Marginal Product of Labor Formula Calculator

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