by Tables are the simplest and most direct form for presenting economic data. When these data are displayed electronically in the format of an accounting income statement or balance sheet, the tables are referred to as spreadsheets. When the underlying relation between economic data is simple, tables and spreadsheets may be sufficient for analytical purposes. In such instances, a simple graph or visual representation of the data can provide valuable insight.
Complex economic relations require more sophisticated methods of expression. An equation is an expression of the functional relationship or connection among economic variables. When the underlying relation among economic variables is uncomplicated, equations offer a compact means for data description; when underlying relations are complex, equations are helpful because they permit the powerful tools of mathematical and statistical analysis to be used.
Functional Relations: Equations
The easiest way to examine basic economic concepts is to consider the functional relations incorporated in the basic valuation model. Consider the relation between output, Q, and total revenue, TR. Using functional notation, total revenue is
TR = f(Q)
Equation is read, “Total revenue is a function of output.” The value of the dependent variable (total revenue) is determined by the independent variable (output). The variable to the left of the equal sign is called the dependent variable. Its value depends on the size of the variable or variables to the right of the equal sign. Variables on the right-hand side of the equal sign are called independent variables. Their values are determined independently of the functional relation expressed by the equation.
Equation does not indicate the specific relation between output and total revenue; it merely states that some relation exists. Equation provides a more precise expression of this functional relation:
TR = P×Q
where P represents the price at which each unit of Q is sold. Total revenue is equal to price times the quantity sold. If price is constant at $1.50 regardless of the quantity sold, the relation between quantity sold and total revenue is
TR = f(Q)
Data in Table are specified by Equation and graphically illustrated in Figure.
Total, Average, and Marginal Relations
Total, average, and marginal relations are very useful in optimization analysis. Whereas the definitions of totals and averages are well known, the meaning of marginals needs further explanation. A marginal relation is the change in the dependent variable caused by a one-unit change in an independent variable. For example, marginal revenue is the change in total revenue associated with a one-unit change in output; marginal cost is the change in total cost following a one-unit change in output; and marginal profit is the change in total profit due to a one-unit change in output.
Relation Between Total Revenue and Output; Total Revenue = $1.50
