Graphs easily describe the economic relationship between two variables; for example, a supply curve describes the relationship between price and quantity supplied. Economic relationships are also expressed as mathematical functions.

A function describes the relationship that exists between two or more variables. For example,

is a general statement that indicates the variable *q* is a function of the variable *p*. A specific functional form describes the exact relationship that exists between those variables; the function

indicates that for every one unit increase in *p*,* q*’s value increases by 5 units, or that *q *is five times greater than* p*. By identifying the exact relationship between variables, you’ve turned a general equation into a specific function.

Two variable functions are easily expressed with either an equation or a graph. However, for functional relationships involving three or more variables, you’ll find that equations are not only simpler than graphs, but also often a necessity. A functional relationship among three variables is

This equation indicates that *U* is a function “g” of the variables *x* and *y*. In such functions, *U *is called the dependent variable because its value depends upon the values of *x* and *y*. The variables *x* and *y *are called independent variables because their values are given and determine *U*’s value.

Business decision-making requires knowing the specific relationship among variables. The equation

indicates that a one-unit increase in the variable *x* causes a two-unit (2x) increase in *U*, while a one-unit increase in variable *y* causes a three-unit (3y) increase in *U*.