What are linear variable costs?

Variable costs are costs that change in proportion to changes in activity levels.

The equation for such cost is typically:

$VC_p^d = Q_p^d \times V_c^d$

Where $$VC_p^d$$ it the total variable cost of the period resulting from the volume of the cost driver $$d$$, $$Q_p^d$$, and $$V_c^d$$ the unit variable cost associated with this cost driver.

A cost is variable relative to a specific cost driver. For instance, in a context where processed batches vary greatly in size (i.e. a batch can be one from a dozen of units to several thousands), machine set-up costs (e.g. the cost of calibrating a batch) will be proportional to the number of batches, but not proportional to the number of units produced or sold. Therefore, if a cost does not seem to be proportional to a specific measure of activity, it may mean that its cost driver is another measure of activity. This is why, as we will see later, cost estimation goes through a phase in which we compare the appropriateness of different measures of activity as potential cost drivers.

A few characteristics of a linear variable cost are visible in the graph above. First, when the volume is 0, there is no cost. This indicates that costs here are purely variable (there is no fixed component). Second, the slope (increase in cost for a unit increase in cost driver) is constant, as indicated by the straight line.

A cost is linear variable when the cost per unit of cost driver is constant.

There are different kinds of variable costs; the key characteristic of linear variable costs is that the cost per unit does not change. If you divide total variable cost by the number of units, you shoud always find the same number.

Typical examples of variable costs include the consumption of raw materials or sales commissions which are typically proportionnal to respectively the number of units produced and the number units sold.