An understanding of algebra is fundamental to understanding the complex mathematical and statistical methods taught in upper-level undergraduate and graduate-level economics courses. Algebra, for example, is necessary for understanding input-output analysis. This economic analysis technique illustrates the links among parts of an economic system, showing how changes in one part of the system affect other parts. The San Jose State University economics department, for example, uses the coal and steel industries to demonstrate the linkages in the economy. Coal provides necessary energy to produce steel, while steel is used to make tools that produce coal. Basic algebra in input-output analysis helps gauge the input requirements needed for specific levels of output.
Differential calculus examines the functional relationships between two or more variables, gauging the rate of change in a dependent variable relative to the change in the value of one or more independent variables. Economic research involves the use of calculus to examine functional relationships, such as the relationship between education and income. If income rises as years of education increase, then the two variables have a positive relationship. Calculus is especially significant in the economic analysis of margins, or the change in an outcome that results from a single-unit increase of input. For example, an economist may examine the change in business profit that results from an increase in production. If the increase in revenue exceeds the additional cost, then the company raises its profits.
This branch of algebra relates to the addition, subtraction, multiplication and division of matrices, or arrays of data displayed in rows and columns. The Dictionary of Statistics and Methodology states that regression analysis, a widely used form of statistical analysis in economics and other social sciences, uses matrix algebra techniques to simplify calculations involving two or more independent variables, which is often the case in many regression models. Linear programming, another technique used in economic and business analysis, relies on matrix algebra to help businesses and societies achieve their highest level of satisfaction relative to existing constraints, such as limited resources.
Economists rely on statistical methods, from correlation to regression techniques, to analyze economic data. These statistical methods require a rigorous understanding of mathematics, including algebra and calculus. Regression analysis, a technique used by many economic analysts, strives to predict the value of an outcome, or dependent variable, based on the values of known predictors, or independent variables, according to the Dictionary of Statistics and Methodology. For example, a regression equation may examine average wages in the manufacturing industry, asking what average wages can be expected based on known variables such as workers' education, work experience and other likely predictors.