Utility Function (Graph, Formula & Example)
By Steve Bain
The Utility Function in Economics adds a degree of measurable, or comparable, analysis for the indifference curves that we use in modeling consumer behavior. The numbers ascribed to these functions are meaningless in themselves, but they can be used for comparison purposes.
For economists the word utility means a great deal, and much of microeconomics is built on the notion of marginal utility, i.e., the value of one more good, or one more input unit in the production process. Total utility pales in significance when compared to marginal utility when considering, for example, the market price of goods. The whole Diamond Water Paradox is explained via the way in which consumers value the marginal unit rather than good itself.
With a utility function, we can add an extra degree or two of usefulness to our overall model of consumer behavior. When a consumer purchases a good, the price paid is always worth less to the consumer than the expected utility that will be gained from that good, otherwise no purchase would be made.
Marginal Utility & 'Utils'
If the utility function graph below looks familiar, that's because it is simply the indifference map that featured on my page about indifference curves. The only difference is that this time each curve has been given an arbitrary numerical value.
The numerical value relates to what economists call utils i.e., how much utility pertains to each indifference curve. If you have forgotten what these curves represent and need a refresher, have a look at my main article about:
'Utils' cannot be bought or sold, they can't be traded, and they can't be transferred. That's because they don't exist in the real world, they are just an arbitrary concept that serve a single purpose, and that is to compare/rank different levels of utility gained from baskets of goods and services. Keep in mind that the term 'utility' in economics is used exclusively for this purpose - to assign a numerical value to one basket of goods & services compared to another.
A Utility Function Example
Sticking with the same two-good model that I have used on related pages, let's consider the utility gained from a basket of biscuits and cheese. By observing how consumers spend their money on these items at various prices it is possible to deduce their preference - it's a process called revealed preference.
From this we can construct typical utility functions to estimate the utility gained from different combinations of biscuits and cheese. Let's keep this example really simple:
Utility Function Formula
U(B,C) = B + 10C
In words this means that the utility from biscuits and cheese equals one multiplied by the servings of biscuits plus ten multiplied by the servings of cheese. So, if we have two baskets of these goods with different quantities of each good, we can compare the overall utility of each basket:
- Basket A has 5 servings of biscuits and 2 servings of cheese, yielding 25 utils.
- Basket B has 10 servings of biscuits and 1 serving of cheese, yielding 20 utils.
Two things should be noted here:
- Basket A is preferred to Basket B because it gives more utility.
- This is the important bit - whilst A is preferred, we cannot determine by how much!
Take good note of point 2 here, because the numbers assigned here are not comparable in a mathematical sense. In other words, we cannot say that 4 baskets of A would give 100 utils and that 5 baskets of B would also give 100 utils. Utils are not additive in this manner, they can only be used to rank one basket as preferred to another, they cannot be used to measure by how much one is preferred to another.