Before we discuss the issues related to estimating cost functions, we briefly review the three criteria laid out in Chapter 2 for classifying a cost into its variable and fixed components.
A particular cost item could be variable for one cost object and fixed for another cost object. Consider Super Shuttle, an airport transportation company. If the fleet of vans it owns is the cost object, then the annual van registration and license costs would be variable costs for the number of vans owned. But if a particular van is the cost object, then the registration and license costs for that van are fixed costs for the miles driven during a year.
Whether a cost is variable or fixed for a particular activity depends on the time horizon managers are considering when making decisions. The longer the time horizon, all other things being equal, the more likely the cost will be variable. For example, inspection costs at Boeing Company are typically fixed in the short run because inspectors earn a fixed salary in a given year regardless of the number of inspection-hours of work done. But, in the long run, Boeing’s total inspection costs will vary with the inspection-hours required. More inspectors will be hired if more inspection-hours are needed, and some inspectors will be reassigned to other tasks or laid off if fewer inspection-hours are needed.
Variable and fixed cost-behavior patterns are valid for linear cost functions only within a given relevant range. Outside the relevant range, variable and fixed cost-behavior patterns change, causing costs to become nonlinear (nonlinear means the plot of the relationship on a graph is not a straight line). For example, Exhibit 10-2 plots the relationship (over several years) between total direct manufacturing labor costs and the number of snowboards produced each year by Winter Sports Authority at its Vermont plant. In this case, the nonlinearities outside the relevant range occur because of labor and other inefficiencies (first because workers are learning to produce snowboards and later because capacity limits are being stretched). Knowing the relevant range is essential to properly classify costs.

Y-axis shows the total direct manufacturing labor costs in thousands from 0 to 350 dollars in increments of 50, and X-axis shows the number of snowboards produced from 0 to 8,000 in increments of 2,000. All values are approximate here. Details of the graph are as follows:
The relevant range is marked in the region from 2,000 snowboards produced to 6,800.
The number of snowboards produced is 2,000 when the total direct manufacturing labor cost is $100, and the number of snowboards produced is about 6,800 when the labor cost is $240.
The line is extended in both directions outside the relevant range with one of the end meeting the origin and the other going steadily upwards.