# How To Calculate Marginal Product in 6 Steps (With Examples)

Updated February 3, 2023

It is in a business's best interest to make sure the product supply matches customer demand. Calculating marginal product helps businesses make sure they are using their resources wisely. Understanding marginal product can give you a simple tool to keep production high and costs low for an organization.

In this article, we explain what marginal product is, discuss how to calculate marginal product, talk about what affects it and explore how to improve it before showing you examples you can use to learn more about using marginal product in your career.

## What is marginal product?

Marginal product is a formula used to determine how a change in one factor of production changes overall production. The factor in question may be labor, capital, land, machinery or any other aspect that directly affects the production of merchandise. When one of these elements increases, production increases, too. Businesses measure that production increase in revenue and costs to make sure the additional expense is adding value to its operations or goods and services.

Related: What is Strategic Planning? Definition, Techniques and Examples

## How to calculate marginal product

The following are the key steps for calculating marginal product:

### 1. Review the marginal product formula

Using the formula for marginal product is important for creating accurate calculations. The formula for calculating marginal product is:

Marginal product = (Q^n - Q^n-1) / (L^n - L^n-1)

Where:

• Q^n is the current total production time.

• Q^n-1 is the previous production time, prior to the marginal change.

• L^n is the total production units, whether machines or professionals at the time n.

• L^n-1 is the total production units at the time n-1, or the prior production time.

Related: How to Calculate Marginal Benefit

### 2. Identify Q^n

To use the marginal product formula, first, you identify what Q^n is. This can include determining the number of products an organization can produce during a specific period. This period can be as small as one hour or as much as one year. The size of the business and the total production cycle length can affect the length of the measurement period.

Example: Pizza Prince has two employees and can make 15 pizzas an hour. The company hires one more employee. Pizza output increases to 22 pizzas an hour. Q^n is 22, or the current number of pizzas made per hour.

Related: Guide To Diminishing Marginal Utility (With Examples)

### 3. Identify Q^n-1

Once you identify Q^n, it's important to identify Q^n-1, which is the previous output an organization has. This is useful because the marginal product of an organization is whether a change in production ability affects the output of an organization positively or negatively. A negative effect means the change in production was detrimental to the organization, while a positive effect is beneficial to the organization.

Example: For Pizza Prince, the Q^n-1 is 15, or the previous number of pizzas made per hour. Before you make the calculation, you can tell the organization increased its production rate from 15 to 22, which may show a positive inclination to the change in production.

Related: How To Calculate Marginal Revenue (With Formula and Examples)

### 4. Identify L^n

Once you find Q^n and Q^n-1, you can find L^n, which is the current number of production units or human resources the organization uses. For small organizations, this may be a single professional. Large organizations may use groups of professionals or teams to identify L^n.

Example: For Pizza Prince, the L^n is 3, which is their current number of professionals, after they hire one more. This value is important because it can determine how effective one additional unit of production is for the organization.

Related: Marginal Cost vs. Marginal Benefit: What's the Difference?

### 5. Identify L^n-1

The value of L^n-1 is how many production units an organization had at the time of production for Q^n-1. Often, this value subtracted from the value L^n comes out to be one because of the marginal nature of the calculation. Most organizations use this to determine if adding or removing one production unit affects the output of the organization significantly.

Example: For Pizza Prince, the L^n-1 is 2, or the previous number of employees. This value is important because it helps create the direct comparison of the previous production time and output to the current production time and output, which an organization can use to determine if the change to production was effective.

Related: Understanding the Marginal Revenue Formula

### 6. Calculate marginal product

To use the marginal product formula, it may be beneficial to write it out and substitute the value for each part of the equation with the numbers you find. For example, you can substitute the real values of Q^n, Q^n-1, L^n and L^n-1 with the values you found in the previous steps. This can help you create an accurate equation for the organization.

Example: Pizza Prince's marginal product equation is (22 - 15) / (3 - 2). Pizza Prince's marginal product, when going from two employees to three, is an increase of seven pizzas, which is significant for the organization because seven pizzas per hour is a lot more than they could make previously.

Related: Operations Management: Everything You Need to Know

## What affects marginal product output?

Several factors impact marginal product output. First, there is an increased production element. In the Pizza Prince example above, the increased production factor was labor. Any element of production can change and then you can measure it for the marginal product. Capital, or an increase in funding, is another moveable production factor. Some businesses purchase more land or workspace. Machinery is another factor that can affect marginal product output.

The goal of increasing production is to meet customer demand and eventually increase revenue. Thus, customer demand affects marginal product output. It makes sense for companies to hire more employees or purchase more machines to create merchandise if there is a higher demand for the product.

Related: How to Calculate Marginal Utility (With Example)

## Improving marginal product output

To make sure your business is getting the highest possible marginal product output, it is best to make minor adjustments to one element of production at a time. If you add more employees, purchase more warehouse space and invest more capital into merchandise all at once, it will be challenging to determine which of these elements had the most positive impact on revenue.

Increasing an element of production to an extreme can cause a loss of money. The increased profits from, say, an additional employee must be higher than or equal to the cost of paying the new employee. Hiring many new employees at once may cause spending more on wages than the company makes in revenue.

Related: Using Performance Management in the Workplace

## What is the law of diminishing returns?

The law of diminishing returns says that at a certain point increasing production elements will no longer lead to increased marginal product output. There are limits within a workplace that inhibit exponential production. Every business has an optimal level or a degree at which its production yields the highest profits with the lowest costs. Increasing production factors beyond that level will increase costs like wages without increasing revenue from merchandise.

Related: Diminishing Marginal Returns vs. Returns to Scale: What's the Difference?

## Examples of marginal product

Here are three examples of calculating marginal product:

### Example one

Below is an example of an organization that experiences the laws of diminishing returns for each professional it hires during the holiday season:

Toys Toys Toys has added several new employees for the holiday season to meet customer demand. 10 employees can make 20 toys a day. 11 employees can make 24 toys a day. 12 employees can make 25 toys a day. 13 employees can make 25 toys a day. As it hires more professionals, the organization wants to know what its optimal number of professionals is. After the changes, it calculates its marginal product as:

• From 10 to 11 employees: 24 - 20 = 4

• From 11 to 12 employees: 25 - 24 = 1

• From 12 to 13 employees: 25 - 25 = 0

The marginal product for 11 employees is four, for 12 employees is one and 13 employees is 0. The optimal number of employees for Toys Toys Toys is 12. Above 12, production does not increase.

### Example two

Below is an example of an organization that increases the machines it has to increase its production capabilities:

Shoe Emporium has added one machine to its production line. Previously, with three machines, Shoe Emporium could make 200 pairs of shoes a day. With the fourth machine, Shoe Emporium can make 280 pairs of shoes a day. After the change, it calculates its marginal product as:

• From three machines to four machines: 280 - 200 = 80

The marginal product output for Shoe Emporium is 80.

### Example three

Dairy Dudes have purchased an additional acre of land for their dairy cows. Before, Dairy Dudes had 10 acres of land. It produced 120 gallons of milk a week from its cows. Now, they are collecting 130 gallons of milk a week.  After the change, it calculates its marginal product as:

• 130 - 120 = 10

The marginal product output for Dairy Dudes is 10.

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