In economics, marginal utility (abbreviation "UM") is a way of measuring the value or satisfaction obtained by a customer consuming a product. As a general definition, UM is equal to change in total utility divided by the change in the quantity of goods consumed.
A common way to describe this concept is the utility a person derives from each additional unit of consumed good.
Steps
Part 1 of 3: Using the Marginal Utility Equation
Step 1. Learn about the economic concept of utility
The idea of "utility" is fundamental to understanding marginal utility. Roughly, utility is the "value" or "satisfaction" derived from a customer who consumes a certain number of goods. Of course it is difficult to assign a numerical value to this concept. A good way to do this is to think of utility as "the amount of money a customer could pay for the satisfaction received from an asset".
For example, let's say you are hungry and are buying fish to eat for dinner. Let's assume that a fish costs € 2. If you are so hungry that you are willing to pay € 8 for fish, fish is said to have 8 € of utility. In other words, you are willing to pay € 8 for the satisfaction obtained from the fish, regardless of its real cost.
Step 2. Find the total utility obtained from consuming a certain number of goods
"Total utility" is the concept of utility applied to more than one asset. If by consuming a good you get a certain amount of utility, consuming more than one will give a higher, lower or equal amount. This value is the total utility.
- Let's say, for example, that you intend to eat two fish. After eating the first one, however, you will not be as hungry as before. You would pay only 6 € for the extra satisfaction of the second fish. It won't have the same value when you are fuller. This means that the two fish have, together, a total utility of 14 €.
- Note that it doesn't matter whether you buy the second fish or not. The UM only considers how much you would pay for it. In real life, economists use complex mathematical models to predict how much a consumer would pay for a good.
Step 3. Find the total utility obtained from consuming a different number of goods
To find the MU, you will need two different total utility values. You will use the difference between the values to calculate the MU.
- Let's assume, in the previous example situation, you decide you are hungry enough to eat four fish. After the second fish you feel more full, so you would only pay 3 € for the next fish. After the third, you are almost completely full, so you would only pay 1 € for the last fish.
- The satisfaction you would get from fish is almost entirely obliterated by the feeling of being too full. We can say that the four fishes offer a total utility of 8 € + 6 € + 3 € + 1 € = 18 €.
Step 4. Divide the difference between the total utility by the difference between the units
The result is the marginal utility or utility generated by each additional unit consumed. In the above example, you would calculate the UM as follows:
- 18 € - 14 € = 4 €
- 4 - 2 = 2
- 4 €/2 = 2 €
- This means that, between the second and fourth fish, each extra fish is worth only € 2 of utility to you. This is an average value - the third fish is of course worth € 3 and the fourth € 1.
Part 2 of 3: Calculate the Marginal Unit for each Additional Unit
Step 1. Use the equation to find the MU of each additional unit
In the example above, we found the average MU of many consumed goods. This is one of the valid uses of UM. However, this value is often applied to the individual units consumed. This gives us the precise MU for each additional good (not an average value).
- Finding this value is easier than it looks. Use the normal equation to find the UM and use one as a change in the quantity of goods.
- In the example situation, you already know the UM value for each unit. When you hadn't eaten yet, the first fish's UM was 8 € (8 € of total utility - 0 € previous / variation of one unit), the MU of the second fish is 6 € (€ 14 total utility - the previous € 8 / one unit change) and so on.
Step 2. Use the equation to maximize utility
In economic theory, customers make decisions about how to spend money in an attempt to maximize their utility. In other words, customers want to get maximum satisfaction with their shopping. This means that customers will tend to buy products or goods as long as the marginal utility of buying one more product is less than the marginal cost (the price of one more unit).
Step 3. Determine the value of the lost utility
Let us take up the example situation again. At the beginning of the article, we established that each fish costs € 2. In the previous steps, we determined that the first fish has a MU of € 8, the second of € 6, the third of € 3 and the fourth of € 1.
With this information, you would not purchase the fourth fish. Its marginal utility ($ 1) is less than its marginal cost ($ 2). Essentially, you are running out of utility in the transaction, so it's not in your favor
Part 3 of 3: Using a Marginal Utility Table
| Tickets purchased | Total utility | Marginal Utility |
|---|---|---|
| 1 | 10 | 10 |
| 2 | 18 | 8 |
| 3 | 24 | 6 |
| 4 | 28 | 4 |
| 5 | 30 | 2 |
| 6 | 30 | 0 |
| 7 | 28 | -2 |
| 8 | 18 | -10 |
Step 1. Assign columns for quantity, total utility, and marginal utility
Almost all UM tables have at least these three columns. In some cases there are others, but these contain the most important information. Typically, they are arranged from left to right.
Note that column titles will not always be exactly these. For example, the "Quantity" column might be called "Purchased Items", "Purchased Units" or something similar. What matters is the information in the column
Step 2. Look for a trend towards diminishing returns
A classic UM table is often used to show that as a customer buys more units of an asset, the desire to buy "even more" drops. In other words, after a certain moment, the marginal utility of each additional good will begin to decrease. Eventually, the customer will begin to be less satisfied than before with each additional good.
In the example table above, this trend starts almost immediately. The first ticket of the festival offers a lot of marginal utility, but each ticket after the first gives less and less. After six tickets, each extra ticket has, in effect, a negative MU, which reduces total satisfaction. The explanation for this phenomenon is that, after six visits, the customer gets tired of seeing the same films over and over
Step 3. Maximize utility at the point where the marginal price exceeds the MU
The marginal utility table allows you to easily predict how many units a customer will purchase. As a reminder, customers have a tendency to buy as long as the marginal price (the cost of an additional unit) is greater than the MU. If you know the cost of the goods analyzed in the table, the utility maximum point is the last row where the MU is greater than the marginal cost.
- Let's assume that the tickets in the previous example cost more than € 3 each. In this case, the utility is maximized when the customer buys 4 tickets. The next ticket has a MU of € 2, which is less than the marginal cost of € 3.
- Note that the utility is not necessarily maximum when the MU starts to turn negative. It is possible that goods may benefit the customer, without being worth their cost. The fifth ticket in the table, for example, still has a positive MU of € 2. This is not a negative MU, but it still reduces the total utility, because it is not worth the cost.
Step 4. Use the table data to find additional information
When you have read the three main columns, it becomes easier to find more numerical data about the situation analyzed by the table. This is especially true if you are using a spreadsheet program that can do the math for you. Below you will find two types of data that you could enter in additional columns, to the right of the three mentioned above:
-
Average utility:
the total utility in each row divided by the quantity of goods purchased.
-
Consumer surplus:
the marginal utility of each row minus the marginal cost of the product. It represents the profit in terms of utility that the consumer obtains from the purchase of each product. Also called "economic surplus".
Advice
- It is important to understand that the situations in the previous examples are model situations. That is, they represent hypothetical (and not real) customers. In real life, customers are not entirely rational - they may, for example, not purchase the number of goods needed to maximize utility. Good business models are great tools for predicting customer behavior on a large scale, but they often don't exactly reproduce real life.
- If you add the customer surplus column to the table (as discussed above), the point where utility is maximized will be the last row before the customer surplus turns negative.
