# How to calculate Marginal Product of Labor

The ability to calculate the Marginal Product of Labor is a crucial skill for every business owner and entrepreneur. Companies manage to grow and make a profit through meticulous planning and organization. They keep detailed financial statements, use various methods for profitable decision-making, and create future forecasts. All of this is done to make sure the company is being as efficient as possible and is not on the brink of bankruptcy or shutting down.

One method of keeping tabs on the production activity is through marginal analysis. Marginal analysis is used to examine the costs and benefits of an activity. It is a useful tool for evaluating if a strategy is profitable or not and it helps increase the efficiency and accuracy of decision-making. The majority of firms aim to increase their profitability by improving efficiency, productivity, and decision-making abilities.

Marginal analysis is also effective in keeping track of available resources and allocating them most efficiently. One of the key factors of production in companies is labor. Determining the optimal number of workers and employees is critical in maximizing profits and minimizing costs. This is where calculating the marginal product of labor comes into play- it helps business owners determine the costs and benefits of hiring/firing one employee. It also helps us understand why companies hire additional workers and what is the driving force behind the demand for labor.

This article will help you understand and learn the concept of marginal product, the marginal product of labor, how to calculate MPL, and all the additional theories connected to this concept.

## Marginal Product

Before jumping into what marginal product of labor is, it is important to understand what Marginal Product is. Anything called “Marginal” in economics refers to an added cost of benefit caused by the production of an additional unit. Marginal Product for example is the change in output as a result of using an additional unit of the variable input.

Marginal product is subject to the law of diminishing marginal returns. The Law of diminishing returns is a theory in economics that states that as more and more units of variable inputs are added to a given quantity of fixed inputs, the output from each additional unit will eventually diminish. This means that marginal product at first increases, reaches a maximum, and then starts decreasing as shown in the diagram below:

## Definition of MPL

To put it in simple terms, marginal product of labor measures the change in production output caused by an added unit of labor, aka an additional employee. It is calculated by dividing the change in the value of the total production output by a change in labor. The formula is as follows:

Marginal Product of Labor = Change in output/ Change in Labor

Marginal product of labor =

$\frac{\bigtriangleup&space;Q}{\bigtriangleup&space;L}&space;=&space;\frac{Q_{1}-Q_{0}}{L_{1}-L_{0}}$

Where Q1-Q2 and L1-L0 represent the difference between the current time period and the one before it.

Example 1

Slice of heaven” is a newly opened Pizzeria down the street. The pizza there is amazing and the restaurant has gathered quite a loyal group of customers that is growing day by day. The owner of the pizzeria realized that with an increase in popularity, the number of orders is growing rapidly, making it difficult to handle the 2 employees working there. He decided to expand and hire 3 more employees. Unfortunately, instead of the number of pizzas baked increasing they fell from an overall 44 pizzas per day to 35. The owner is puzzled and does not understand why.

### Calculations

To see what happened, we need to calculate the marginal product of labor to see how the change in units of labor impacted the overall output.

1. To do this, first, we need to calculate the change in total output.

∆Total output =

$Q_{1}&space;-&space;Q_{0}&space;=&space;35-44&space;=&space;-9$

2. After finding this out, we need to calculate the change in labor

∆Total output =

$L_{1}&space;-L_{0}&space;=&space;5-2&space;=&space;3$

3. Calculate the Marginal Product of labor.

Marginal Product of Labor =

A negative MPL means that hiring an additional worker is detrimental to the overall production of the pizzeria. Instead of helping the company and increasing output, it is disrupting the productivity of employees there. This is a clear example of the law of diminishing marginal returns and it has a clear explanation.

### Explanation of the results

In the beginning, when the pizzeria opened, they may have had a large kitchen with a lot of equipment and several ovens. When only two cooks were working there, they simply were not able to utilize all the fixed resources available at their hands to their full capacity- for example, they did not use all the ovens. On the other hand, if another cook was added to their group, the overall output would have increased. At this point MP would still be positive- another employee would be greatly productive, use up the available equipment, and bake a lot of pizzas.

However, the mistake that the owner made was hiring too many additional employees. At some point the MP starts decreasing until it eventually becomes negative, meaning any additional work is detrimental to the business. This is because the business has only so many fixed resources that the variable inputs can operate efficiently. Since the owner did not increase the kitchen space or add any new equipment there simply was not enought space or ovens for the five cooks to use. Thus, they just got into each other’s way and decreased the overall productivity of the group.

Example 2

A toy manufacturing company has seen a recent decline in its profit margins. The management is greatly concerned and has started looking at the cause. After investigating their accounts and financial statements the management realized that one of their biggest costs is labor costs. Thus, they decided to analyze the last 6 months of labor and output and determine if they need to decrease the number of workers to cut costs.

### Calculation

Step 1

First, we need to calculate the changes in Production volume. For this we just subtract the production volume of the previous month from the current month.

Step 2

Now, we need to calculate the change in number of workers by subtracting the previous month’s number from the current months number.

Step 3

Finally, we calculate the MPL = Change in production volume/Change in Number of workers.

As can be seen MPL increases until July after which it starts slowly declining. This means that after July the additional hired workers are not contributing to the increase in output as much. Considering labor costs are a significant portion of the overall expenses that the firm faces, the management will have to rethink their hiring decisions.

Point 1

The marginal product function is a derivative of the Total Product function. Additionally, the change in output/change in input is the same as rise/run, meaning, MP is also a slope of the TP curve.

Point 2

MPL is also associated with another concept that is known as the Cobb-Douglas production function. It is a view that believes, the amount of output produced is the result of the amount of capital and Labor used.

Point 3

The Marginal Product of Labor is used in various marginal analyses. One of the most important examples is when companies want to calculate the level of employment that will maximize profits. This is done by calculating the Value of the Marginal product of labor. VMPL shows the extra monetary value of output generated by an additional unit of labor and is calculated by multiplying MPL by the price of one unit of product.

VMPL = Price per unit sold x Marginal product of labor

Point 4

Calculating the Marginal Product of labor is important as it gives us an insight into calculating another measure: Marginal Revenue Product of Labor (aka MRPL). MRPL measures the change in total revenue generated by the company caused by hiring an additional employee (all other factors held constant). MRPL is calculated by:

MRPL = Marginal Revenue x Marginal product of labor

It helps companies evaluate the performance of their employees and showcases clearly when an employee does not contribute to earning enough revenue at the wage that they are being paid.

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