However, the cost y concept is more frequently used both by businessmen and economists in the form of cost per unit, or average costs rather than as total costs. We, therefore, pass on to the study of short-run average cost curves.
Average Fixed Cost (AFC):
Average fixed cost is the total fixed cost divided by the number of units of output produced. Therefore,
AFC = TFC/Q
Where Q represents the number of units of output produced.
Thus average fixed cost is the fixed cost per unit of output. Suppose for a firm the total fixed cost is Rs. 2,000 when output is 100 units, average fixed cost (AFC) will be Rs. 2,000/100 = Rs. 20 and when output is expanded to 200 units, average fixed cost will be Rs. 2,000/200 = Rs. 10. Since total fixed cost is a constant quantity, average fixed cost will steadily fall as output increases.
Table 19.2. Average Fixed Cost, Average Variable Cost and Average Total Cost:
Therefore, average fixed cost curve slopes downward throughout its length. As output increases, the total fixed cost spreads over more and more units and therefore average fixed cost becomes less and less. When output becomes very large, average fixed cost approaches zero.
Consider Table 19.2 where total cost is Rs. 50 when one .unit of output is produced, the average fixed cost is obviously Rs. 50(50/1=50). On raising output to 2 units, average fixed cost will be Rs. 25. (i.e. 50/2 = 25). Further, if output is increased to 8 units, average fixed cost falls to Rs. 6.25 (i.e. 50/8 = 6.25). Average fixed cost curve (AFC) is shown in Fig. 19.2.
It will be seen that average fixed cost curve continuously falls throughout. Mathematically speaking, average fixed cost curve approaches both axes asymptotically. In other words, AFC curve gets very nearer to but never touches either axis.
The average fixed cost curve, AFC, possesses another important property. If we pick up any point on the average fixed cost curve and multiply the average fixed cost at that point with the corresponding quantity of output produced, then the product is always the same. This is because the product of the average fixed cost and the corresponding quantity of output will yield total fixed cost which remains constant throughout. A curve with such a property is called rectangular hyperbola.
Average Variable Cost (AVC):
Average variable cost is the total variable cost divided by the number of units of output produced. Therefore,
AVC = TVC
Where Q represents the total output produced.
Thus average variable cost is variable cost per unit of output. The average variable cost will generally fall as output increases from zero to the normal capacity output due to the occurrence of increasing returns. But beyond the normal capacity output average variable cost will rise steeply because of the operation of diminishing returns.
Thus, in Table 19.2 average variable cost can be obtained from dividing total variable cost (TVC) by output. It will be seen from Table 19.2 that when two units of output are being produced, average variable cost can be found by dividing Rs. 35 by 2 which is equal to Rs. 17.50.
Likewise, when five units of output are being produced, average variable cost becomes Rs. 79. The average variable cost curve is shown in Fig. 19.2 by the curve AVC which first falls, reaches a minimum and then rises.
Average total cost (ATC) is the sum of the average variable cost and average fixed cost. Therefore, as output increases and average fixed cost becomes smaller and smaller, the vertical distance between the average total cost curve (ATC) and average variable cost curve (AVC) goes on declining. When average fixed cost curve (AFC) approaches the X-axis, the average variable cost curve approaches the average total cost curve (ATC).
Relationship between AVC and Average Product:
Average variable cost bears an important relationship with the average product per unit of the variable factor. Let Q stand for quantity of total product produced; L for the amount of the variable factor, say labour, used and w for the price per unit of the variable factor and AP for the average product of the variable factor. We assume that the price of the variable factor remains unaltered as more or fewer units of the variable factor are employed.
Total product (or output Q) = AP x L
Where AP stands for average product of labour, the variable factor and L for the amount of labour used.
Average variable cost (AVC) = TVC/Q
Since the total variable cost (TVC) is equal to the amount of the variable factor (L) employed multiplied by the price per unit (w) of the variable factor, (TVC = L.w.). Therefore
AVC = L.w/Q
Since Q = AP x L
A VC = L.w/AP x L = w/AP = w (1/AP)
Thus, given the price of the variable factor w, the average variable cost is equal to the reciprocal of the average product (1/AP is the reciprocal of AP) multiplied by a constant w. It follows that average variable cost and average product of the variable factor vary inversely with each other.
Therefore, when average product of the variable factor rises in the beginning as more units of the variable factor are employed, the average variable cost must be falling. And when the average product of the variable factor falls, the average variable cost must be rising.
At the level of output at which the average product of the variable factor is maximum the average variable cost is minimum. Thus the average variable cost (AVC) curve looks like the average product (AP) curve turned upside down with minimum point of the AVC curve corresponding to the maximum point of the AP curve.
Average Total Cost (ATC):
The average total cost or what is simply called average cost is the total cost divided by the number of units of output produced.
Average total cost = Total Cost/Output
or ATC = TC/Q
Since the total cost is the sum of total variable cost and the total fixed cost, the average total cost is also the sum of average variable cost and average fixed cost.
This can be proved as follows:
ATC = TC/Q
Since TC = TVC + TFC
Therefore, ATC = TVC + TFC/Q
= TVC/Q + TFC/Q
= AVC + AFC
Average total cost is also known as unit cost, since it is cost per unit of output produced. As the average total cost is the sum of average variable cost and average fixed cost, in Table 19.2 it can be obtained by summing up the figures of columns 5 and 6 corresponding to different levels of output.
Thus, for example, with two units of output, average total cost is Rs. 25 + Rs. 17.50 = Rs. 42.50 and with three units of output it is equal to Rs. 16.67 + Rs. 20 = Rs. 36.67 and so on for other levels of output.
Alternatively, the average total cost can be obtained directly from dividing the total cost by the number of units of output produced. Thus average total cost of 2 units of output is equal to Rs. 85/2 or Rs. 42.50. Likewise, when output is raised to 6 units, total cost rises to 240 and average total cost works out to be Rs. 240/6 = Rs. 40.
It follows from above that the behaviour of the average total cost curve will depend upon the behaviour of the average variable cost curve and average fixed cost curve. In the beginning, both AVC and AFC curves fall, the ATC curve therefore falls sharply in the beginning.
When AVC curve begins rising, but AFC curve is falling steeply, the ATC curve continues to fall. This is because during this stage the fall in AFC curve weighs more than the rise in the AVC curve. But as output increases further, there is a sharp rise in AVC which more than offsets the fall in AFC.
Therefore the A TC curve rises after a point. Thus, the average total cost curve (ATC) like the A VC curve first falls, reaches its minimum value and then rises. The average total cost curve (ATC) is therefore almost of a ‘U’ shape.