Basic Assumptions and Examples of Cost Functions

Learning Objective 1 Describe linear cost functions and three common ways in which they behave

• graph of cost function is a straight line 
• variable, fixed, and mixed

Managers understand cost behavior through cost functions, which are the basic building blocks for estimating costs. A cost function is a mathematical description of how a cost changes with changes in the level of an activity relating to that cost. Cost functions can be plotted on a graph by measuring the level of an activity, such as number of batches produced or number of machine-hours used, on the horizontal axis (called the x-axis). The amount of total costs corresponding to—or dependent on—the levels of that activity are measured on the vertical axis (called the y-axis).

Basic Assumptions

Managers often estimate cost functions based on two assumptions:

1. Variations in the level of a single activity (the cost driver) explain variations in the related total costs.
2. Cost behavior is approximated by a linear cost function within the relevant range. Recall from Chapter 2 that a relevant range is the range of the activity in which there is a relationship between total cost and the level of activity. For a total Linear cost function, total cost versus the level of a single activity related to that cost is a straight line within the relevant range.

We use these assumptions throughout most, but not all, of this chapter. Not all cost functions are linear and can be explained by a single activity. Later sections will discuss cost functions that do not rely on these assumptions.