Variable costs are such costs that change with the change in business activity level. For example if production level changes then some costs of production will change as well. This change can either be in the same direction (direct relationship) i.e. if activity increases then cost increases as well OR it can be in the opposite direction (inverse relationship) i.e. if activity increases then cost decreases. Here activity level is an independent variable whereas, cost is a dependent variable.
When the two variables are drawn on the piece of graph and the resultant is a straight line then it means that there is a linear relationship between the variables. This relationship occurs when the rate of change in a dependent variable is constant for a unit change in independent variable and this is only possible when the two variables are drawn in a straight line as the slope of straight line remains the same at different points on the straight line.
Figure 1 can be a graph of total variable cost against activity level that is increasing with the increase in activity level
Figure 2 can be a graph of total fixed cost against activity level
Figure 3 can be a graph of per unit fixed cost against activity level when activity level is increasing
However, if the two variables drawn on the graph results in a “curve” formation rather than a straight line then two variables are said to have curvilinear or non-linear relationship. This happens when the rate of change in dependent variable is not constant for a unit change in independent variable. This can happen due to number of factors. For example business activity of any kind is not undertaken in a closed system or simply in isolation therefore, variables like prices, government regulations, holidays etc affect the relationship between production and cost of production and thus it will not be in a straight line form or linear form.
Figure 4 can be a graph of telephone charges when every additional minute consumed is charged at lesser tariff
Figure 5 can be a graph of total wages where piecemeal system is in place and labour is compensated at higher rate for each extra unit produced.
Figure 6 can be a graph in a situation where labour cost first increases as a result of less experience and then decreased because of learning effect and then increased again as labour hours get scarce.
Majority of costs in real life are of curvilinear nature i.e. they depict non-linear relationship because of environmental factors (for example inflation) and also when observed over a longer range of time. We use linear relations to understand the cost behaviour as it is much easier to describe and to understand. And that is why we convert non-linear variable costs into linear variable cost using linear approximation method.