# How is Calculus Used in Economics?

by Shane HallAlthough introductory economics courses, such as those most college students must complete in the course of their studies, involve little math, an in-depth study of economics requires a rigorous understanding of mathematics, including calculus. Calculus provides the language of economics and the means by which economists solve problems. Calculus is especially significant in illustrating what a leading economist calls a key principle of economics.

## Identification

As an advanced branch of mathematics, calculus focuses heavily on functions and derivatives. Functions examine the relationship between two or more variables, or entities that take on different values. Mathematicians and economists often use letters, such as X and Y, to symbolize particular variables. If the value of Y changes as the value of X changes, then the two variables have a functional relationship. Derivatives, meanwhile, consider the rate of change in one variable relative to the change in another. Functions and derivatives relate to relevant concepts in economics.

## Function

Economic research often uses calculus to examine functional relationships. An example includes the relationship between the dependent variable income and various predictors, or independent variables, such as education and experience. If average income rises as years of education and work experience increase, then a positive relationship exists between the variables, namely that income is a function of education and experience. Differential calculus, the process of obtaining derivatives, enables economists to measure the average change in income relative to a single year's increase in education and/or experience.

## Effects

Derivatives in calculus, or the change in one variable relative to the change in another, are identical to the economic concepts of marginalism, which examines the change in an outcome that results from a single-unit increase in another variable. Marginal changes relate to an important principle in economics: the notion that people tend to think at the margin, according to Harvard economist Greg Mankiw, author of "Principles of Economics," a popular textbook in college economics courses. Mankiw writes that economists use the term "marginal changes" to describe small, incremental changes, such as incremental changes in work hours or factory output.

## Benefits

Calculus, by determining marginal revenues and costs, can help business managers maximize their profits and measure the rate of increase in profit that results from each increase in production. As long as marginal revenue exceeds marginal cost, the firm increases its profits.

## Significance

The amount of interest to be paid on a loan, whether for a home, motor vehicle or capital equipment for a business, is an important consideration for households and firms. Calculus provides a means for determining the amount of interest paid over the life of a loan.

#### References

- Humboldt College: Making Calculus Sensible With Economics
- "Principles of Economics (3rd ed.)"; N. Gregory Mankiw; 2004

#### Photo Credits

- calculatrice image by Danielle Bonardelle from Fotolia.com