What are curvilinear variable costs?


Many costs which are considered variable are actually curvilinear. More specifically, you can distinguish between concave variable costs and convex variable costs.



Concave variable costs

Concave variable costs are costs that change in proportion to changes in activity levels and are characterized by a diminishing cost per unit of cost driver.

Variable costs are often concave because the more units you produce, the greater the efficiency in producing each unit (economies of scale, learning curve). Moreover, since you buy in greater quantities, you can often benefit from greater discounts. All this contributes to a progressive decrease in unit variable cost, \(V_c^d\).

As the previous graph illustrates, concave variable costs increase with the volume of activity but with a diminishing slope (next graph) resulting in a concavity.



Convex variable costs

Convex variable costs are costs that change in proportion to changes in activity levels and are characterized by an increasing cost per unit of cost driver.

Variable costs can also be convex because when you start exceeding practical capacity you incur congestion costs. Indeed, equipment need greater maintenance and may break more often, people have to be paid extra hours, and coordination is more complicated. All this contributes to a progressive increase in unit variable cost, \(V_c^d\).

As the previous graph illustrates, convex variable costs increase with the volume of activity but with an increasing slope (next graph) resulting in a convexity.

As we will see later, limiting analysis to a relevant range allows us to ignore these cost behaviors without much loss in accuracy.


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