# Utility and Utility Function

Utility, in Economics, is the capacity of a commodity to satisfy the wants of an economic agent. It may depend on the quantity or quality of a commodity, that is, an increase or decrease in quantity or improvement or deterioration in quality may increase or decrease utility derived from a commodity. We commonly assume that utility increased with an increase in the quantity consumed of a commodity.

The mathematical representation of utility is an utilily function as given below.

$U = f\left( {{x_1},{x_2},…,{x_n}} \right)$

where $$U$$ is the total utility, $$f$$ is a symbol to represent function and $${{x_1},{x_2},…,{x_n}}$$ are quantities of $$n$$ commodities. The above equation says that total utility is the function of quantities of $$n$$ number of commodities. $$U$$ is also commonly used as a symbol for function. In this case, utility function is written as follows:

$Utility = U\left( {{x_1},{x_2},…,{x_n}} \right)$

We will use the former symbol throughout the notes.

In the two goods case, the utility function is written as follow:

$U = f\left( {x,y} \right)$

where, $$x$$ and $$y$$ are quantities of two commodities, say, Good X and Good Y. The above equation says that total utility is the function of quantities of Good X and Y.

Utility is too subjective to give a universal definition. The explanation above is also not universally accepted explanation. So, we, in Economics, study some approaches of utility propounded by some great Economists.

There are mainly two approaches of utility – Cardinal and Ordinal. We will analyse both approaches in detail in separate articles.