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In this article we will discuss about the short run and long run cost curves with the help of graphs.
Short Run Cost Curves:
We initiate our discussion on the short run cost curves in this article. We start with the marginal cost.
(i) Marginal Cost:
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Marginal cost (MC) is the extra cost of producing one more unit of output. To make our observations clear, Let us assume that fixed costs are of the value of $40. This amount will remain constant throughout the act of production. Let the variable cost be $ 10 per unit. Moreover, as the variable units go on increasing this cost will continuously increase as a multiple of 10.
Column I depicts the Units of Production in the hypothetical example (Table 4.2). In column II exhibits the $ 40 as Fixed Cost. This remains constant throughout the act of production. Column III explains Variable Cost of production at the rate of $ 10 per unit of variable inputs. Column IV portrays Marginal Output that changes. In column V we have the Total Cost which is the sum of fixed and variable costs. Column VI includes the Marginal Cost per unit of output produced. This is a ratio of marginal or additional variable cost (which is 10) divided by marginal units of output produced. Accordingly marginal cost is 10, 4 = 2.5, 10, 7 = 1.42…..etc.
We can observe that, the marginal cost behavior exhibits three phases of change. To begin with from 2 units of production to 3 units of production the marginal cost decreases from 2.5 to 1.42. Then between 3 to 4 units of production it remains constant. Finally, from unit 4 onwards marginal cost continuously increases from 1.42 to 10. The three phases marked as Diminishing Marginal Cost, Constant Marginal Cost and Increasing Marginal Cost exactly correspond with Increasing Marginal Returns, Constant Marginal Returns and Diminishing Marginal Returns on the output or returns side, where returns diminish, costs increase and both are constant for the same units of output.
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(ii) Average Costs:
Average cost is expressed as a ratio of Total Cost to Total Output units produced. Since total cost has fixed and variable costs as two components, we would have three types of average costs. These are average fixed cost, average variable cost and average total cost.
Table 4.3
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We need to look carefully that in the table 4.3, production units are shown in Column l, 7 units are produces. Total Output is shown in column II. Column lll exhibits Average fixed cost which is a ratio of Total Fixed Cost to Total Output. Column IV includes the Average Variable Cost. It is a ratio of Total Variable Cost to Total Output. Finally, column V has Average Total Cost for different units. It is a ratio of Total Cost to Total Output. It must be observed that ATC is exactly equal to AFC+AVC.
The behavior of the three average cost varieties is an interesting and significant part of Cost Analysis. We are mainly interested in the behavior of Average Total Cost (column V) which is composed of two components, Average fixed cost and Average Variable Cost. The behavior of Average Total Cost (ATC) is jointly determined by AFC and AVC. AFC continuously falls.
Therefore AFC tends to pull ATC in its own direction and causes its fall. AFC falls sharply in the initial stage from 10 to 3.63 but it slows down in its rate of fall towards the end such as from 1.60 to 1.54. The effect of the fall in AFC is the progressive reduction in the value of ATC. AVC initially decreases from 2.5 to 1.82 to 1.7 but it subsequently rises from 1.67 to 1.73 to 2 to 2.30. The effect of AVC on ATC is initially reductive but when it starts rising, it attempts to pull ATC in its own direction.
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(iv) Total Cost Curves:
Now, we need to have an understanding of the total cost curves. We begin our observation the help of the figure 4.1. The figure 4.1 depicts Total Cost (TC), Total Fixed Cost (TFC) and Total Variable Cost Curves (TVC). Total Fixed Cost remains constant at $40. Total Variable Cost increases proportionately as 10, 20, 30, 40, 50 and 60. The Total Cost as a sum of the two (Total Fixed and Total Variable Costs) increases as 50, 60, 70, 80, 90 and 100. In the figure 4.1 three cost curves have been drawn portrayed.
(v) Short Marginal and Average Cost Curves:
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The figure 4.2 exhibits varying output units on the horizontal X- axis and different cost amounts on the vertical Y- axis. All the four cost curves have been drawn on the basis of respective tabulated values in the tables above. Marginal Cost varies as 2.5, 1.42, 1.42, 2.0, 5.0 and 10.0. Accordingly the Marginal Cost Curve has been drawn. It shows an initial downward trend but a subsequent sharp rise. Average Fixed Cost is based on the values 10, 3.63, 2.22, 1.73, 1.60, and 1.54 therefore AFC falls continuously. However, initially it falls sharply and then with a slower pace.
AFC first falls sharply and then its curve becomes flatter. AVC is based on the cost values 2.5, 1.82, 1.67, 1.73, 2.0 and 2.33. Therefore Average Variable Cost initially falls moderately and then it rises continuously but moderately. Since Average Total Cost is combination of both Average Fixed Cost and Average Variable Cost, it has a mixed behavior. It is based on the values 12.5, 5.45, 3.89, 3.46, 3.60 and 3.80. The behavior of ATC is to be explained in terms of the joint behavior of AFC and ATC. It is necessary to examine ATC more with awareness.
Behavior of ATC:
It is interesting to note the behaviour of the Average Total Cost curve. ATC shows three distinct phases. Initially it slopes downward. It reaches a minimum point and then starts constantly rising upwards. It is also called Short Run (SAC) ‘U’ Shaped Cost Curve. Average Total Cost curve passes through three stages. Initially it falls, then it reaches a minimum and is nearly constant; finally it starts increasing. The justification of such behavior of the ATC is as in the case of the laws of variable returns.
In the short run, internal economies such as better and efficient performance of machine and manager, better supervision and avoidance of waste, etc. are examples of internal economies. The shape of ATC also depends on the diverse nature of the fixed and variable inputs. So long as fixed and indivisible factors are not used to their highest capability, the ATC keeps on falling downwards. Once the fixed capacity is folly utilized the ATC reaches a minimum point. This is the point of optimum utilization of fixed factors. If the output continues to increase beyond this point the fixed factors get over utilized and therefore the ATC rises upwards.
The Relation between the Average and Marginal Cost Curves:
It would be interesting to understand the relation between the average cost and marginal cost curves. Basically there is a relationship between the average and marginal quantities. The average cost and marginal cost curves reflect the same relationship as shown in figure 4.2 a.
When the marginal cost curve is less than average cost, the AC curve falls and when marginal cost is greater than average cost, the AC curve rises.
Since, cricket is a very popular sport, let us take the instance from the cricket to illustrate the relation between the average and marginal quantities. Let us assume that there is a cricketer whose batting average in ODIs is 55 runs. If in his next innings he scores less than 55, say 50 runs, then his average score will fell because his additional score is less than his average score. On the other hand, if he scores more than 55, say 75 runs in his next innings, then his average score will increase as because the marginal score is greater than his previous average score. In another situation, if he scores 55 runs in his next innings then his average score will remain the same.
Long Run Cost Curves:
In the long run the division between fixed and variable factors becomes futile. Long run of a firm is a period sufficiently long during which at least one (or more) of the fixed factors become variable and can be replaced.
Long run is an analytical concept. As far as time is concerned there is no specified limit on the number of years to distinguish between short run and long run period. The life span of the fixed factors affect the determination of long run period of the factor. Depending upon length of the long period, the long run cost curve will behave in one way or the other. If all the factors are perfectly variable and there are no fixed factors at all then the Long Run Average Cost Curve will be a horizontal line parallel to X axis.
If some of the fixed factors have an unlimited capacity to produce then the long run Average Cost Curve will continuously fall downward. If some of the factors are variable while a few other factors continue to be fixed even in the long run then LAC will be ‘U’ shaped but flatter than SAC. The diagram 4.3 shows the LAC.
Besides internal economies that a firm enjoys in the short run, it has the benefit of the scale economies in the long run. Every fixed factor with its given life span constitutes a scale of production which in the short run cannot be altered. In the long run each of these factors can be altered and replaced. This allows change in the scale of production. An old machine can be changed by a new one which has better capacity, a manager can be replaced at the end of the contract period with another more qualified and experienced person.
Such changes make productive activities more efficient and therefore are called economies (advantages) of the scale. Since the long run goes on combining such individual advantages it is also called a chain of the short runs. The LAC is U-shaped. The reason behind the U-shape of LAC is the law of returns to scale. The ‘U’ shape exhibits the falling downwards, reaching the minimum and the rising phases of the Long run Average Curve. It is less distinct or flatter than SACs. The reason is that as more factors become divisible and variable in the long run.
Some of the factors may still continue to be fixed even in the long run to make it fall and rise. The variations in the scale economies marks the three phases of the Long-run average Cost. Initially the cost decreases and the returns increase. This is the phase of Economies or increasing returns. Then at output level Q2 LAC is almost constant. This is the Stage of Optimum Utilization of Scale Advantages. Beyond this point LAC rising upwards. In this phase cost increases and returns decreases. This is the phase of diseconomies of the scale. Under these long run conditions no further output can be advantageously produced beyond Q2.
LAC curve is also termed as ‘envelope curve’ because no part of the SAC curve can ever be below the LAC curve. From figure 4.3 it can be observed and it becomes evident that the Long ran Average cost Curve (LAC) is made up by a chain of three short run cost curves SAC 1, SAC2 and SACs. In between them there may be many more SACs. We have also drawn LMC which is the Long run Marginal cost Curve. It intersects LAC at the minimum point of LAC which is N2 at output level Q2.
Relationship of the Short-Run Average Cost Curves and the Long-Run Average Cost Curve LAC:
In the short run, some inputs are fixed and others are varied to increase the level of output. The long run is a period of time which the firm can vary all its inputs. In long run none of the factors is fixed and all can be varied to expand output. The long run production function has thus no fixed factors and the firms has no fixed costs in the long run. It is conventional to regard the size or scale of plant as a typical fixed input. The term ‘plant’ consists of capital equipment, machinery, land etc. In the short run, the size of the plant is fixed and cannot be increased or decreased. This implies that there can be no change in the amount of capital equipment in the short run, in order to increase or decrease the level of output.
On the other hand, in the long run there can be changes in the plant implies that there can be changes in capital equipment, machinery, land etc. We can therefore understand that in the short run, a business firm is attached with a given plant. Whereas, in the long run, a business firm moves from one plant to another. In the long run, a business firm can select a larger plant if it has to increase its output or can select and move to a smaller plant if it has to reduce its output. We can therefore say that the long run cost of production is the least possible cost of producing a given quantity of output when all the inputs are variable.
Long run average cost is long-run total cost divided by the level of output. Long run average cost curve depicts the least cost possible average cost for producing various levels of output. As shown in the figure 4.3a the short run average cost curves which are also known as plant curves. They are so called because each short run average cost curve corresponds to a particular plant. It is assumed that the three possible sizes of plant as portrayed by the short- run average cost curves SACa, SACb and SACc.
In the short run, the firm can operate on any short -run average cost curve, given the size of the plant. As far as the long run is concerned the firm can take the liberty of determining which size of plant or on which short-run average curve should the firm operate in order to produce a given level of output at the minimum possible cost.
It can be observed from the figure 4.3a that the firm will operate on the short-run average cost curve SACa up to OR amount of output. Though the firm can produce with short-run average cost curve SACb, it will prefer SACa because up to OR amount of output, production on SACa curve involves lower cost than on SACb. For example let us consider the level of output OQ which is produced with SACa. It will cost QA per unit and if it is produced with SACb, it will cost QB per unit.
We can easily observe that QA is smaller than QB. The short run curve SACa can be used for producing economically all the output levels up to OR instead of SACb. Therefore, even in long run the firm will produce any output up to OR on SACa. Now, if the firm plans to produce an output larger than OR but less than OT it will not be economical for the firm to produce on SACa. We can observe from the figure 4.3a that the outputs which are larger than OR and less the OT, can be produced at a lower cost per unit on SACb rather than on SACa. We can further see that the output OS if produced on SACb costs SD per unit which is lower than SE which is the cost incurred when OS is produced on SACa. Now again if the firm has to produce an output which is more than OT, the firm will employ plant corresponding to the short run average cost curve SACc.
As depicted in the figure 4.3a, there are three sizes of plants. The long run average cost curves depicts the least possible average cost of producing various levels of output when all factors including the size of the plant have been adjusted. The long run average cost curve has curls in it. Let us now suppose that the size of the plant can be varied by infinitely small gradations so that there are infinite number of plants corresponding to which there will be a smooth and continuous line.
In other words, every point on the long run average cost curve is tangent with short-run average curve. Thus, if a firm desires to produce a quantity of output, the firm will decide a particular point on the long-run average cost curve corresponding to that output and operate on the corresponding short-run average cost curve.
In the figure 4.3b It is very interesting to note that for producing OQ level of output the corresponding point on the long-run average cost curve LAC is A at which the short-run average cost curve SACb is tangent to the long-run average cost curve LAC. The firm further decides to produce output OR which corresponds to a point B on the long-run average cost curve LAC for which there is a corresponding short-run average cost curve SACc.
The long-run average cost curve LAC is also called an envelope curve because the long- run average cost curve envelops an array of short-run average cost curve from below. A very important and interesting characteristics to note is that the long-run average cost curve LAC is not tangent to the minimum points of the short-run average cost curves. When long-run average cost curve is declining as shown in figure 4.3b till the output level OS, the long- run average cost curve LAC is tangent to the falling portions of the short-run average cost curves.
In contrast, when the long-run average cost curve is rising, it will be tangent to the rising portions of the short-run average cost curves. The long-run average cost curve is also termed as ‘Planning curve’ because a business firm can plan to produce an output in the long run by choosing a plant on the long-run average cost curve.
Modern Approach of Cost Curves:
The economists associated with the modern approach of cost curve include Sargent, Andrews, Stigler, Florence and Friedman etc. In the traditional theory of costs, cost curves are ‘U’ shaped. Whereas, in modern theory cost curves are of ‘L’ shaped. Modern theory is also based on two time periods i.e. (i) Short Run and (ii) Long Run.
(i) Average Variable Cost:
According to the modern theory, the short run average variable costs curve is saucer – shaped. It has a flat stretch over a range of output. Flat stretch represents the built in reserve capacity of the plant.
There are different reasons for a firm to have reserve capacity:
(1) To meet seasonal and cyclical fluctuations in demand,
(2) It provides freedom to an entrepreneur to increase output up to desire level,
(3) Due to change in technology etc.
Fig 4.3b, Derivation of long-run average cost curve
Figure 4.4 shows that the falling portion (PM) of SAVC shows reduction in cost whereas the rising portion (NS) of the SAVC shows the increase in cost. The MN portion shows that SAVC is equal to the marginal cost.
(ii) Short Run Average Cost Curve:
According to modern theory AC curve is continuously falling up to a given level of output as shown in figure 4.5. Thereafter AC Curve is rising upward. It means AC will rise if output is increased beyond reserved capacity.
(iii) Short Run Marginal Cost Curve:
In the beginning, MC is below to AVC. From point P to J marginal cost is horizontal which mean AVC=MC. After point J, MC rises above to AVC, as shown in figure 4.6.
(iv) Long Run Cost Curves:
In the modern theory long run average cost curve and long run marginal cost curve are ‘L’ shaped.
(a) Long Run Average Cost Curve:
There are two main causes of L – shape of LAC – (a) Technological Progress and (b) Learning by doing, (figure 4.7).
(b) Long Run Marginal Cost Curve:
The shape of MC is depends upon the relation between LAC and LMC Curve is shown in figure 4.8 and figure 4.9 respectively.
Figure 4.9 shows that when LAC Curve is of inverted J-shaped then LMC is below than LAC Curve. When LAC is constant, LMC also become constant.
A note on the Modern Theory:
In the era of modern theory, the U -shape of the cost curves has been challenged by a class of economists. The U-shape of both short-run average cost curve and long-run average cost curve has been challenged.
The findings of the recent empirical studies refute the U-shape of short-run average cost curve. They opine that short-run average cost curve has a saucer type shape. The saucer shape of the average variable cost curve means that there is a flat stretch over a certain range of output in it. This flat stretch in the sort-run average cost curve is owing to the reserve capacity which is deliberately built in the plant size while designing it. This reserve capacity adds flexibility in the production.
Another significant development is that the long-run average cost curve LAC has been described to be L-shaped instead of U-shaped. There are arguments to explain the L-shape of the long-run average cost curve. The first argument is that a firm continues to enjoy technical or production economies even after minimum optimum scale is arrived. Another argument is that the managerial science develops such an optimum managerial arrangement which doesn’t allow the long-run average cost to turn up.
The learning curve is an important modern concept which reflects that the cumulative experience in the production of a product over time enhances the efficiency in the use of inputs and thereby lowers cost per unit of output.
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