Utility Function

The utility function mathematically represents the usefulness or satisfaction derived by an individual by consuming a basket of goods. This function translates every product bundle into a unit and measures individuals’ preferences for a collection of goods and services. This concept is crucial to elucidate human behavior and quantify consumer satisfaction.

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Although economists measure utility in units or utils, computing the satisfaction or benefit received by consumers is abstract. Thus, pinpointing it can be a challenge. Hence, they measure it in respect of revealed preferences by considering consumers’ choices. From there, economists establish an order of consumption baskets from the least favored to the most desired.

Utility function meaning refers to a special type of function that maps or connects the overall amount of utility consumers gained from bundles of goods or preferences to a set of numbers or a ranking mechanism. Generally, economists represent utility with ‘u’ and denote the utility derived by a consumer from preference ‘x’ using u(x). The use of this concept is common in rational choice theory; it helps in analyzing human behavior.

When economists rank or gauge consumers’ preferences, it is ordinal utility. Put simply, the sequence in which individuals choose one good over another can demonstrate that individuals place a higher value on the product they select. Ordinal utility gauges how individuals rank products. However, one must remember that it does not evaluate how the consumers rank them.

Let us look at an example to understand ordinal utility better. Suppose Harry, Ronald, and Jim competed in a singing competition. Judges declared that Harry was the winner and ranked Jim and Ronald second and third, respectively.

The ordinal utility concept shows that the judges chose Harry over Jim and Ronald and Jim over Ronald. That said, the ordinal function does not reveal to what degree the judges preferred each contestant to another. To know this, economists use cardinal utility. It involves quantifying consumers’ preferences. Thus, it can reveal to what degree the judges preferred Harry over the other two contestants.

Once individuals understand ordinal and cardinal utility, it is clear that the utility function gives a cardinal rating.

Gaining a comprehensive understanding of the logic behind the choices of consumers and their satisfaction level is not only crucial for economists. Companies can also utilize the concept to monitor how individuals view their goods. Moreover, organizations often use the utility function to gain an advantage over competitors.

Economists express utility function as a function of the size of a selection of products. They often represent it as u(x1,x2,xn).

When this function outlines a preference for a selection of products (xa) against another selection of products (xb), economists denote it as u(xa,xb).

If perfect complements exist, the utility function formula is u(xa,xb) = MIN(xa,xb).

In this case, the smaller one gets allotted the function’s value.

There are some situations where products are considered perfect substitutes for each another. In such cases, one must write the utility function as u(xa,xb) = (xa+xb)  to indicate the preferences.

Let us look at a few utility function examples to understand the topic better.

Suppose a consumer, David, is shopping for a refrigerator. After narrowing down his choice, he is confused between two products. They are almost identical, except the first refrigerator has two additional features. Hence, it costs more than the second one.

The marginal or incremental utility received from the first refrigerator could be quantified as the $100 price difference between them. In other words, David gets $100 in marginal utility from the first refrigerator.

Moreover, suppose 50,000 consumers in the country preferred the first refrigerator to the second one. Then, economists can determine that the consumers derived marginal utility worth $5 million from the first refrigerator’s additional features. The utility is received from the belief that they would probably have a better experience owing to the additional features of the first refrigerator.  

Suppose there are two baskets of goods. In one basket, there are five apples and two bananas. Whereas in the other basket, there are five bananas and two apples. When Jack was asked to assign a satisfaction value to each basket, he valued the overall utility of the first and second baskets as 10 utils and 5 utils, respectively. However, his satisfaction with apples is higher than that with bananas. Therefore, He prefers the first basket as it has more apples.

The following graph helps us get a clear idea of the utility function in economics.

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The horizontal or x-axis denotes the income, ‘M,’ available to a consumer. On the other hand, the vertical or y-axis represents the amount of utility an individual derives from consuming goods. The more one consumes a product, the higher the utility received from it. That said, owing to the law of diminishing returns, the shape of a utility function is quasi-concave. It denotes that marginal utility falls as the quantity of goods consumed by an individual concerning the income spent rises.

The following are the critical differences between the utility function and indifference curve:

A Cobb-Douglas utility function is a sub-category of utility functions. It is very flexible, allowing one to make adjustments to it. Economists use this concept to elucidate the marginal rate of substitution or MRS between two products.

One can draw an indifference curve using this function by following these steps:1. Spot the function — u(x1,x2).2. Set the level of utility to a constant level — u(x1,x2) = k.3. Solve for x2 to get a generic indifference curve.4. Assign an arbitrary value to k. Then, draw the indifference curve.

Yes, this function can be negative. After all, it is simply a way of denoting a preference relationship. Also, one must note that this function can represent only rational preference relations.  

It is a function of the prices of products and the budget or income of consumers. This function reflects the market conditions and consumers’ preferences.

This has been a guide to what is Utility Function. Here we explain its formula, examples, and graph and compare it with an indifference curve. You can learn more about it from the following articles –