# How To Calculate Marginal Utility (With Examples)

- Jan. 11, 2021
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When consumers pay for a good or service, they place a certain value on what they provide for them. This value is known as a “utility.” It is the satisfaction or happiness a consumer gets from a good or service.

Utility plays a key role in consumer theory, which is the study of how a consumer decides to spend their money. This will be based on the amount of income a consumer has, their budgetary constraints, their needs, their wants, and their personal preferences.

A utility on a good or service shows a consumer’s certain willingness to spend. This is important for different types of people to know. Macroeconomists and business analysts will use utility to determine and predict market behaviors. As a consumer, you use utility, though you may not realize it, any time you decide whether or not to spend your money on something.

By understanding utility, you empower yourself to navigate the economy intelligently. It will guide you in the best choice possible, whether you are a market analyst or consultant determining prices and consumer behavior or whether you are a business owner buying goods and services for your company.

## Utility Quantified as Utils

Since utility is an arbitrary value of consumer satisfaction, it can be measured as a unit called “utils.” For example, imagine if you were at a restaurant, you could say the utility of one glass of soda is four utils, meaning that you derive this much value from one soda.

You can also place a currency value on utility. To do this, place something like a dollar amount on one unit of good or service. This would be the amount that the utility is worth to you, regardless of the actual price.

In fact, when your utility dollar amount is less than the actual price, then this is a situation where you would not pay for the goods or service because it would be beyond your determined value. This is partially how the demand curve works in establishing a price via supply and demand.

What is important is the consumer believes they will achieve some amount of satisfaction from the good or service and is therefore willing to pay a certain amount of money for it.

## What Is Total Utility?

Total utility is the sum of all utilities gained from a specific amount of a good or service. To continue with our soda example, imagine how you would feel drinking multiple sodas. If you said the first glass of soda was worth four utils, it means you enjoyed it. You enjoyed it so much you want a second one. To you, the satisfaction of drinking two sodas would be six utils.

Those two sodas were very delicious, so you decide to have three sodas. You still enjoy the experience, and your happiness with three sodas is seven utils. Now let’s say you feel bold and go for a fourth soda.

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However, you begin to feel full and a bit sick. You do not enjoy it as much as having just two or three sodas. At four sodas, we say you are at four utils again, which is back at where you started, which means you would be just as satisfied if you drank one or four sodas.

This can be visualized below as:

Number of Sodas Total Utility (Utils)
0 0
1 4
2 6
3 7
4 4

Notice that as you increase the number of sodas, the total utility increases less and less and then decreases. This change in total utility is called marginal utility.

## What Is Marginal Utility?

Marginal utility is the change in satisfaction a consumer gets when one or more new units of a good or service are added. In the example above, your satisfaction after your second soda is increased by two. Then after your third soda, your total utility increases by one util to bring you to a total of seven.

After the fourth soda, because you begin to feel sick, your satisfaction decreases, so much so that you are back where you started with one soda at four utils.

The marginal utility of this situation can be visualized as:

Number of Sodas Marginal Utility (Utils)
0 0
1 4
2 2
3 1
4 -3

Notice that, although your total utility has increased for the second and third sodas, your marginal utility slows down and then eventually begins to decrease. This is called the law of diminished utility, which says that marginal utility declines with every newly added unit of the good or service.

Essentially as a consumer, when your needs or wants are met with the first unit of the good or service, this creates the greatest amount of satisfaction. Though the following additions may increase your total satisfaction, each new unit itself cannot surpass the initial satisfaction of the previous one. Few goods or services are able to reverse this trend.

## How to Calculate Marginal Utility?

Since marginal utility is the change in utility after the addition of a new unit or units, you can break down marginal utility as the change in total utility divided by the change in the quantity of the units. It would look like this:

Marginal Utility = Change In Total Utility / Change In Units

The change in total utility can be calculated as the current total utility subtracted by a previous total utility.

The change in units can be calculated as the current unit amount subtracted by a previous unit amount.

“Current” here is defined as the most recent utility event you have to work with. Do not forget whatever previous total utility you use should match the previous unit amount.

Another way of looking at this is:

1. Define the total utility of the current event.

2. Define the total utility of a previous event.

3. Find the difference between the two.

4. Define the number of units of the current event.

5. Define the number of units of a previous event.

6. Find the difference between the two.

7. Divide the difference of total utility by the difference in units.

Using the soda example from above, the marginal utility was calculated as such:

Number of Sodas Total Utility (Utils) Current TU Minus Previous TU Current Number Of Sodas Minus Previous Marginal Utility
0 0 N/A N/A N/A
1 4 4 – 0 = 4 1- 0 = 1 4
2 6 6 – 4 = 2 2 – 1 = 1 2
3 7 7 – 6 = 1 3 – 2 = 1 1
4 4 4 – 7 = -3 4 – 3 = 1 -3

In this scenario, we examine the marginal utility between adjacent events; that is, we examine the change with each successive new soda added.

However, you can also examine the marginal utility between non-successive events. For example, the marginal utility between one soda and three sodas is 1.5. This is calculated by subtracting the total utility of three sodas (seven) by the total utility of one soda (four) and dividing it by the change in units (two).

Note that this is only an averaged marginal utility between the two soda amounts. This is because the marginal utility of one to two sodas is two, while the marginal utility from two to three units is one, making the average change in utility between one and three at 1.5.

## Types of Marginal Utility

Since it is based on rates of change, there are three main types of marginal utility. They are:

1. Positive marginal utility. This is when there is a positive rate of change in the total utility between unit amounts. In the soda example, we see positive marginal utility for the first three sodas.

2. Zero marginal utility. This is when there is no rate of change in the total utility between unit amounts. Imagine in the soda example, if the total utility for a third soda was six, just like it is for the second soda. This would be a hypothetical zero marginal utility.

3. Negative marginal utility. This is when there is a negative rate of change in the total utility between unit amounts. In the soda example, we see a negative marginal utility between the third and fourth sodas.

## Marginal Utility Per Dollar Spent

With marginal utility, you can calculate a dollar amount to know how efficient and effective you are with your money. This can help you compare one type of good or service to another and find the best deal for you.

To do this, you need to divide the marginal utility by the cost per unit. If in the soda example, we say that the soda costs two dollars, and so we discover the following:

Number of Sodas Marginal Utility (Utils) MU/\$2.00
0 0 0
1 4 2
2 2 1
3 1 0.5
4 -3 -1.50

Let’s say, after your second soda, you are debating whether to get a third soda or a bag of popcorn. This being your first bag of popcorn, you would see a high total utility of five. The bag of popcorn also costs two dollars, thereby making its marginal utility two and a half per dollar. In this case, you would want to go for the popcorn as you see a greater increase in satisfaction per dollar spent.

## Why Care About Marginal Utility?

Marginal utility can be very helpful, regardless if you are a business or a consumer. A business can use marginal utility to predict the behavior of consumers. This can help them make decisions pricing their goods and services, developing marketing strategies, and dealing with competitors.

Marginal utility empowers the business to convince consumers what they offer is important. Likewise, marginal utility empowers the consumer. It helps the consumer determine how they will spend their money.

As we saw in the soda example, a customer may be open to buying multiple goods or services. However, with each successive new unit, the consumer is less likely to allocate funds to the same good or service.

So, whether you want to be a smart shopper or an effective business analyst, your knowledge of marginal utility points you in the direction of efficiency and success.

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Author

Chris Kolmar

Chris Kolmar is a co-founder of Zippia and the editor-in-chief of the Zippia career advice blog. He has hired over 50 people in his career, been hired five times, and wants to help you land your next job. His research has been featured on the New York Times, Thrillist, VOX, The Atlantic, and a host of local news. More recently, he's been quoted on USA Today, BusinessInsider, and CNBC.

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