where, ‘Q’ is the total output.
As output rises, average variable cost falls initially due to the occurrence of increasing returns (when total variable cost rises less than proportionately to output). It is minimum at the optimum capacity of output. At this level of output, all the factors used by the firm are being employed as efficiently as possible.
Beyond the optimum capacity, the average variable cost will rise steeply because of the operation of diminishing returns (when total variable cost rises more than proportionately to output). This is illustrated in Fig. 9.4. Graphically, the average variable cost curve is U- shaped due to the operation of the law of returns.
This curve is drawn by considering the average variable cost (AVC) at each level of output derived from the slope of a ray drawn from the origin to the point on the total variable cost (TVC) corresponding to the particular level of output. The slope of the ray through the origin declines continuously until the ray becomes tangent to the total variable cost. To the right of this point, the slopes of rays through origin start increasing.
Thus, the AVC falls initially as the productivity of the variable factor (s) increases; reaches a minimum, when the plant is operated (with the optimal combination of fixed and variable factors), and rises beyond that point.
If the total variable cost curve is a linear curve, the average variable cost will be constant and is equal to marginal cost (derivative of total cost with respect to output or change in total cost divided by change in output). Suppose,
TVC = bQ
AVC = b = MC