# Utility Function Definition, Example, and Calculation

## What Is Utility Function?

In economics, utility represents the satisfaction or pleasure that consumers receive for consuming a good or service. Utility function measures consumers' preferences for a set of goods and services.

Utility is measured in units called utils—the Spanish word for useful— but calculating the benefit or satisfaction that consumers receive is abstract and difficult to pinpoint. As a result, economists measure utility in terms of revealed preferences by observing consumers' choices. From there, economists create an ordering of consumption baskets from least desired to the most preferred.

### Key Takeaways

• In economics, utility function is an important concept that measures preferences over a set of goods and services.
• Utility represents the satisfaction that consumers receive for choosing and consuming a product or service.
• Economists track consumer choices to ascertain one product's utility versus another and assign a numerical value to that utility.
• Company executives research consumers' utility to guide the company's sales and marketing plans, advertising, and new product offerings.
• Ordinal utility ranks choices by preference, whereas cardinal utility measures the utility received from a choice.

## Understanding Utility Function

In economics, the utility function measures the welfare or satisfaction of a consumer as a function of the consumption of real goods, such as food or clothing. Utility function is widely used in rational choice theory to analyze human behavior.

When economists measure or rank the preferences of consumers, it is referred to as ordinal utility. In other words, the order in which consumers choose one product over another can establish that consumers assign a higher value to the chosen product. Ordinal utility measures how consumers rank products, but it does not measure how much more one ranks above the other.

To better understand ordinal utility, consider the following example. Three contestants vie for first place in a dance competition. Contestant A is declared the winner. Contestant B is the runner-up, and contestant B ranked third. Ordinal utility reveals that the judges preferred contestant A over contestants B and C and contestant B over C. What ordinal function does not tell us is to what degree one was preferred over the other.

Mainly used in microeconomics, cardinal utility assigns a numeric value to the consumer's preference, indicating the degree to which one choice ranks above another. Cardinal utility will define how much more contestant A was preferred over contestants B and C, and so on.

When considering utility, it is important to understand the concepts of total utility and marginal utility. Marginal utility measures the satisfaction or benefits a person gets from consuming an additional unit of a product or service. Total utility measures the satisfaction or benefits a person gets from the total consumption—including marginal utility—of a product or service.

If consuming 10 units of a product yields 20 utils, and consuming one additional unit yields 1 util, the total utility is 21 utils. If consuming another unit yields .5 utils, the total utility would then become 21.5 utils.

Economists believe that the amount of satisfaction one receives from each additional unit of consumption diminishes with each unit consumed. This concept is called the law of diminishing marginal utility. Diminishing marginal utility doesn't state that consuming additional units will fail to satisfy the consumer; it states that the satisfaction from consuming more and more units is less than the first additional units consumed.

## How to Calculate a Utility Function

Utility functions are expressed as a function of the quantities of a bundle of goods or services. It is often denoted as U(X1, X2, X3, Xn).

A utility function that describes a preference for one bundle of goods (Xa) vs another bundle of goods (Xb) is expressed as U(Xa, Xb).

Where there are perfect complements, the utility function is written as U(Xa, Xb) = MIN[Xa, Xb], where the smaller of the two is assigned the function's value.

In certain situations, the goods may be considered perfect substitutes for each other, and the appropriate utility function must reflect such preferences with a utility form of U(Xa, Xb) = Xa+ Xb.

## Example of Utility Function

Let's say a consumer is shopping for a new car and has narrowed the choice down to two cars. The cars are nearly identical, except the second car has enhanced safety features. As a result, the second car costs \$2,000 more than the first car.

The incremental or marginal utility or satisfaction derived from car two could be represented numerically as the \$2,000 price difference between the two cars. In other words, the consumer is receiving \$2,000 in incremental or marginal utility from car two.

Furthermore, let's say that 100,000 consumers throughout the economy preferred car two to car one. Economists might infer that consumers, overall, received \$200 million (100,000 x \$2,000) worth of incremental utility from the safety features of car two. Utility is derived from the consumer's belief that they are likely to have fewer accidents due to the added safety features of car two.

Economists can't assign a true numerical value to a consumer's level of satisfaction from a preference or choice. Also, pinpointing the reason for purchase can be difficult; there are usually many variables to consider.

In the previous example, the two cars were nearly identical. In reality, there might be several features or differences between the two cars. As a result, assigning a value to a consumer's preference can be challenging since one consumer might prefer the safety features while another might prefer something else.

Tracking and assigning values to utility can still be useful to economists. Over time, choices and preferences may indicate changes in spending patterns and in utility.

Understanding the logic behind consumer choices and their level of satisfaction is not only important to economists but to companies, as well. Company executives can use utility to track how consumers view their products.

### Important

Utility function is essentially a "model" used to represent consumer preferences, so companies often implement them to gain an edge on the competition. For example, studying consumers' utility can help guide management on anything from marketing and sales to product upgrades and new offerings.

## Utility Function FAQs

### What Is Utility Function?

Utility describes the benefits gained or satisfaction experienced with the consumption of goods or services. Utility function measures the preferences consumers apply to their consumption of goods and services. For instance, if a customer prefers apples to oranges no matter the amount consumed, the utility function could be expressed as U(apples) > U(oranges).

### What Is the Difference Between Utility Function and Marginal Utility?

Utility function ranks consumers' consumption of goods or services by preference. Marginal utility measures the change in utility when the rate of consumption changes (i.e., how much more satisfaction is gained by consuming another unit of a good or service).

### Why Is Utility Function Important?

Economists use utility function to better understand consumer behaviors, as well as determine how well goods and services provide satisfaction to consumers.

Utility function can also help analysts determine how to distribute goods and services to consumers in a way that total utility is realized.

Companies can use utility function to determine which product(s) within their product line (or that of a competitor) consumers prefer. Knowing these preferences can help management teams enhance product development to assume a competitive advantage.

## The Bottom Line

Utility describes the benefit or satisfaction received from consuming a good or service. The unit of measurement economists use to gauge satisfaction is called util. Utility function measures consumers' preferences for bundles of goods or services. Ordinal utility ranks a customer's choice by preference, and cardinal utility assigns a numeric value to each preference to determine how much more one good is preferred over another.

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1. Oregon State University. "Module 2 Utility and Utility Functions."