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

(2.2) TR = f(Q)

Equation 2.2 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 2.2 does not indicate the specific relation between output and total revenue; it merely states that some relation exists. Equation 2.3 provides a more precise expression of this functional relation:

(2.3) 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

(2.4) TR = $1.50  Q

Data in Table 2.1 are specified by Equation 2.4

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