Average and Marginal Costs
For an analysis of price and output policy of a firm, average cost curves, that is, per unit cost curves, are more extensively used than total cost curves because they are more usable. Per unit cost curves are (a) the average total cost curve, (b) the average fixed cost curve, (c) the average variable cost curve and (d) the marginal cost curve.
Average total cost (ATC) or simply average cost (AC) is obtained by dividing the total cost (TC) by output (O). Thus
AC = TC/O
Average fixed cost (AFC) is obtained when the total fixed cost is divided by output. Thus
AFC = TFC/O
When the total variable cost is divided by output, we get average variable cost (AVC). Thus
AVC = TVC/O
The marginal cost (MC) is the change in total cost resulting from a one-unit change in output. Thus, for example, the marginal cost of the fifteenth unit is the change in total cost when the production is increased from fourteen units to fifteen units per period.
The mechanical formal properties of the family of cost curves can be put thus:
“The curve MC necessarily intersects AVC and ATC at their respective minima; the minimum of ATC lies at a larger output than the minimum of AVC; the curve AFC is in every case of a given fixed shape—a so-called rectangular hyperbola.”
The study of these cost curves are of importance to the firm. The firm, considering the cost variations in conjunction with the price variations, shown by its demand curve, should be able to select the price or output which will maximize its profit.
This analysis of average and marginal costs in the short-term is based on the assumption that the prices of inputs which the firm employs are given and do not change by reason of variations in the firm’s output. So cost variation reflects only varying efficiency due to varying proportions of fixed to variable factors and not due to any variations in wage rates or other factor prices. If variations in factor prices on account of variations in the firm’s output are taken into account, the analysis becomes quite complicated.
Shape of Average Variable Cost Curve
We noted that the AVC curve in the short-run is U-shaped or dish-shaped. But this is not the exact description in every respect of the short-run variation experienced by all firms and industries. It is so because there are very significant differences in (i) the proportion of variable to fixed costs and (ii) the shape of the variation in average variable costs from firm to firm and industry to industry. These differences are reflected in a rather flat or shallow U-shape in the average variable cost curve. In figures, three types of shape of the AVC have been presented.
In fig, a clear U-shaped average variable cost curve is shown. Here, average variable costs rise rather steeply as output moves in either direction from the minimum. So there is only a small range of plant utilization giving reasonable efficiency. Plants which have certain technical peculiarities might show such cost behaviour.
But it is possible to come across cost behaviour between wide extremes. One such extreme case is presented in fig, where the average variable cost curve is a very wide and flat-bottomed U showing no cost variation over a considerable range of output. Here the rate of utilization of the plant “could be varied from possibly 20 per cent to 90 per cent of maximum capacity without influencing variable cost very much.”
Another extreme case of average variable cost curve is presented in fig. Here it is practically V-shaped. “This would indicate that only at one critical rate of utilization was any reasonable approach made to the attainable efficiency of the plant.”
For more than half a century ago, economists began to measure the cost curves of manufacturing firms. Such studies have shown that in most manufacturing industries, and in some others, the average variable cost curve is shaped with a long, flat portion in the middle and sharply rising sections at each end, that is, a saucer-shaped curve as shown in fig.
For such a curve, there is a large range of output over which average variable cost is constant. The cause of this type of curve is that “firms design plants to have this property so that they can accommodate the inevitable seasonal and cyclical swings in demand for their products. In such cases, the fixed factor is divisible. Because of divisibility some of the fixed factor can be left unemployed.
So there is no need to depart from the most efficient ratio of labour used to capital used as production is decreased. “The divisibility of the fixed factor means that diminishing returns does not apply, because variations in output below full capacity are accomplished by reducing the input of both labour and capital. Thus, average variable costs can be constant over a large range, up to the point at which all of the fixed factor is used.”A When a firm has many plants, a similar situation will occur.
When the fixed factor is indivisible, the usual U-shaped average variable cost will occur. These are thoroughly discussed under modern theory of costs.
Long-run Cost Curve: The Envelope Curve
In the long-run, all factors are variable. This means that the firms in the long-run have to choose the nature and amount of plant and equipment, as well as the size of their labour force. While making the choice, the firm tries to avoid being technically inefficient, that is, not to use more of all inputs than are necessary. Besides being technically efficient, it also wishes to be economically efficient. It means that from among the many technically efficient options, it chooses the one that produces a given level of output at the lowest possible cost.
The long-run cost curve is a planning curve which guides the entrepreneur in his decision to plan the future expansion of his output. In the long-run the firm can build any desired scale of plant as all resources are variable. It can change the quantities of all inputs and thus change the scale of production. There is no average fixed cost curve in the long-run. Our concern is with long-run average cost curve, long-run total cost curve and the long-run marginal cost curve only.
The long-run average cost curve (LAC) is derived from short-run cost curves. Each point on LAC corresponds to a point on a SAC. At that point SAC is tangent to LAC.
Let us start, as a first approximation, with the possibility that the firm. with the available technology, can build only three alternative scales of plant-a small plant, a medium plant and a large plant-are represented by SAC1, SAC2 and SAC3 respectively. Which plant the firm chooses will depend upon the quantity of output that it plans to produce in the long-run.
Each SAC is the short-run average cost curve for a given scale of plant. In fig, the three plants have been presented.
The firm will always wish to produce the output at an average cost as low as possible. Suppose the firm wants to produce OQ output. For this the suitable plant is SAC1 because this quantity can be produced at an average cost of QA which is lower than the average cost of any other plant.
If OQ is produced by the medium plant SAC2, the average cost of producing this output will be QA’ which is higher than QA. For OQ1 output, the firm will be indifferent between SAC1 and SAC2 plants because in both plants its average cost is the same, that is, Q1B. If the output is to be raised to the level of OQ2, the medium-sized plant SAC2 will be preferred.
It is because for producing OQ2, the average cost of plant SAC, is Q2C’ which higher than Q2C, the average cost of plant SAC2. Similarly, for output OQ3, the firm will construct and use large-size plant SAC3 since it will produce at a lower average cost of Q3D, whereas in the case of plant SAC2, the average cost at Q3D’ is higher.
Now it is possible to define the long-run average cost curve. “It shows the least possible cost per unit of producing various outputs when the firm has time to build any desired scale of plant.” In terms of fig, the solid portions of SAC curves form the long-run average cost curve. “The broken line portions of the SAC curves are irrelevant. The firm would never operate on the broken line portions in the long-run since it could reduce costs by changing scale of plant instead.”
Let the assumption of the existence of only three plants be dropped and suppose that the available technology includes unlimited plant sizes as shown in fig. Each plant is suitable for a certain level of output. In the figure SAC1, SAC2, SAC3, SAC4, SAC5,…. are a series of SAC curves such as those of fig.
The outer portions of the SAC curves form the long-run average cost curve, LAC. “Each point of this curve shows the minimum (optimal) cost for producing the corresponding level of output. The LAC curve is the locus of points denoting the least cost of producing the corresponding output. It is a planning curve because on the basis of this curve the firm decides what plant to set up in order to produce optimally (at minimum cost) the expected level of output.”
In the traditional theory of the firm the long-run average cost curve, LAC, is U-shaped and it is often called the “envelope curve” because it ‘envelopes’ the SAC curves. The U-shape of the LAC in the traditional theory is based on the laws of returns to the scale of plant. Because of the economies of scale made possible by the large size of the plant, the unit cost of production, that is, the average cost, decreases.
In the traditional theory, the economies of scale exist only to a certain size of the plant–the optimum plant size. This size fully exploits the economies of scale. Increase in the plant beyond the optimum size leads to diseconomies of scale, arising from managerial inefficiencies. “It is argued that management becomes highly complex, managers are overworked and the decision making process becomes less efficient. The turning-up of the LAC curve is due to managerial diseconomies of scale, since the technical diseconomies can be avoided by duplicating the optimum technical plant size.”
The traditional U-shaped LAC is based on the following assumptions:
- Each plant is designed to produce optimally a single level of output;
- Plant is totally inflexible;
- There is no reserve capacity, not even to meet seasonal variation in demand;
- State of technology is given; and
- Factor prices are given.
The Optimum Scale of Plant
The optimum scale of plant is a term which is applied to the most efficient of all scales of plant that the firm can build. This scale of plant is the one whose SAC curve forms the minimum point of LAC curve. It is SAC7 in fig, SAC7 curve is tangent to the LAC curve at the minimum point of both. It is necessary that the firm will always construct optimum scales of plant and operate them at optimum rates of output. They will do so under conditions of pure competition in the long-run. Under conditions of pure monopoly, oligopoly and monopolistic competition, however, they are not likely to do so.
Long-run Marginal Cost
The long-run marginal cost curve shows the change in the long-run total cost when one more unit is produced. Here the firm has enough time to make change in output by varying all inputs used. In fig, long-run marginal cost curve (LMC) has been graphed. It can be seen in the figure that LMC is less than LAC where long-run average is decreasing. It happens so from zero output to Q. This relationship is true in the case of short-run average and marginal cost curves too.
When in order to produce a given output-OQ2 in fig, the firm constructs the appropriate scale of plant, the short-run marginal cost equals short-run average cost. At this output, that is, OQ2, the firm’s proper plant SAC2 is tangent to the LAC curve.
The long-run marginal cost is derived from SMC curves, but it does not envelope them. LMC curve is formed from points of intersection of SMC curves with vertical lines to the X-axis drawn from the point of tangency of the corresponding SAC curves and LAC curve. LMC is equal to the SMC for the output, such as OQ2, OQ3, OQ in fig, at which the corresponding SAC is tangent to the LAC.
For level of output to the left of tangency, the SAC > LAC. At the point of tangency SAC = LAC. At the minimum point A on LAC, the LMC curve intersects the LAC curve. To the left of A, the LMC curve lies below LAC curve, whereas to the right of A, the LMC curve lies above LAC curve. At point A,
SAC4 = SMC4 = LAC = LMC
(2) Modern Theory of Costs
(i) Short-run Cost Curve
The U-shaped cost curve of the traditional theory has been questioned on (a) theoretical ground as well as (b) on the basis of empirical studies. In 1939 George Stigler suggested a flat-bottomed short-run average variable cost curve. Greater attention has been paid to analysing the long-run average cost curve which, it has been shown, takes the L-shape rather than U-shape. Let us examine these in some details.
The modern theory, like the traditional theory, makes a distinction between short-run and long-run.
Average Fixed Cost
There is a more detailed analysis of fixed cost. It is the cost of the physical and personnel organisation of the firm. Components of the fixed cost are almost the same as in the traditional theory. The firm chooses the plant size with some reserve capacity to meet seasonal and cyclical fluctuations in demand.
This capacity gives the firm greater flexibility for repairs of broken-down machinery with no disturbance to the smooth flow of the production process. Technology also makes it necessary to build into the plant some reserve capacity.
In the case of land and buildings too reserve capacity is built so that future expansion is not dependent on the acquisition of new land or new buildings. Some reserve capacity is built at the organisational and administrative level so that the firm can increase output to some extent without increase in administrative staff. Under the influence of all these factors the average fixed cost curve of the firm has the shape as in the traditional theory with some variation as shown in fig.
There is an absolute limit on the short-run expansion of the firm set by the largest capacity units of machinery, boundary B in the figure. Smaller capacity of the firm is given by the boundary A. But it is not an absolute boundary. There is the possibility of increasing output in the short-run up to boundary B by
(i) paying overtime to labour for working longer hours; or
(ii) by buying some additional small-unit machinery.
In the former case the AFC curve is shown by the dotted line, while the latter case it shifts upward but starts falling again. QAQB is the reserve capacity built in the plant.
Average Variable Cost
Components of the average variable cost of the modern theory are almost the same as in the traditional theory. Buy the AVC curve in the modern theory has a saucer-type shape as given in fig. The reasons were also given while discussing the various shapes of the AVC in terms of figs. The saucer-type shape is broadly U-shaped but has a flat stretch over a range output corresponding to the reserve capacity of the plant.
Average Total Cost
The average total cost is the sum of the average fixed cost and average variable cost. It has been presented in fig. The ATC curve falls continuously up to the level of output OQ at which the reserve capacity is exhausted. Beyond this output it starts rising.
(ii) Long-run L-shaped Scale Curve
Empirical evidence collected by economists does not show any U-shape in the long-run. It seems likely that almost all long-run average cost curves are L-shaped as shown in fig.
It can be seen in the diagram that there is a rather rapid downward slope in the early part of the curve. It is so because at very low levels of output the spreading of fixed costs over more and more units as output rises means that the average costs fall quite sharply when production increases.
“One reason why empirical studies do not bear out the U-shaped curves of economic theory may be that the theory assumes that there is no technological progress, while in practice there is. The existence of technological progress might explain why one would find L-shaped long-run average cost curves in empirical studies, even in a world where long-run average cost curves would be U-shaped if there were no technical progress.”
Another cause of the L-shaped long-run average cost is “learning”. “There is a good deal of evidence to show that the cost of a product depends not only the aggregate amount of product produced since the firm first began to make it.”
It is for the reason that as more units of a product are produced, the firm learns to produce it more efficiently. “Even with a given technology, a firm can ‘learn’ to produce at a lower unit cost the longer the period of time that has elapsed since a previous observation and the greater the aggregate amount of that product that has consequently been made.