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The study of cost-output relationship has two aspects: 1. Cost-output relationship in the short run, and 2. Cost-output relationship in the long run.
The short run is a period which does not permit alterations in the fixed equipment (machinery, buildings, etc.) and in the size of the organization. As such, if any increase in output is desired, it is possible within the range permitted by the existing fixed factors of production.
The long run is a period in which there is sufficient time to alter the equipment (machinery, buildings, land, etc.) and the size of organization. As such, in the long run, output can be increased without any limits being placed by the fixed factors of production as they themselves are capable of being changed.
Aspect # 1. Cost-Output Relationship in the Short Run:
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i. Average Fixed Cost Output:
The greater the output, the lesser the fixed cost per unit, i.e., the average fixed cost. The reason is that total fixed costs remain the same and do not change with a change in output.
The relationship between output and fixed cost is a universal one for all types of business.
Thus, average fixed cost falls continuously as output rises. The reason why total fixed costs remain the same and the average fixed cost falls is that certain factors are indivisible. Indivisibility means that if a smaller output is to be produced, the factor cannot be used in a smaller quantity. It is to be used as a whole.
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ii. Average Variable Cost and Output:
The average variable costs will first fall and then rise as more and more units are produced in a given plant. This is so because as we add more units of variable factors in a fixed plant, the efficiency of the inputs first increases and then decreases. In fact, the variable factors tend to produce somewhat more efficiently near a firm’s optimum output than at very low levels of output.
But once the optimum capacity is reached, any further increase in output will undoubtedly increase average variable cost quite sharply. Greater output can be obtained but at much greater average variable cost. For example, if more and more workers are appointed. It may ultimately lead to overcrowding and bad organization. Moreover, workers may have to be paid higher wages for overtime work.
iii. Average Total Cost and Output:
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Average total costs, more commonly known as average costs, will decline first and then rise upward. The significant point to note here is that the turning point in the case of average cost comes a little later in the case of average variable cost.
Average cost consists of average fixed cost plus average variable cost. As we have seen, average fixed cost continues to fall with an increase in output while average variable cost first declines and then rises. So long as average variable cost declines the average total cost will also decline. But after a point, the average variable cost will rise. Here, if the rise in variable cost is less than the drop in fixed cost, the average total cost will still continue to decline.
It is only when the rise in average variable cost is more than the drop in average fixed cost that the average total cost will show a rise. Thus, there will be a stage where the average variable cost may have started rising yet the average total cost is still declining because the rise in average variable cost is less than the drop in average fixed cost. The net effect being a decline in average cost.
The least cost-output level is the level where the average total cost is the minimum and not the average variable cost. In fact, at the least cost-output level, the average variable cost will be more than its minimum (average variable cost). The least cost- output level is also the optimum output level. It may not be the maximum output level. A firm may decide to produce more than the least cost-output level.
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iv. Short-Run Output Cost Curves:
The cost-output relationships can also be shown through the use of graphs. It will be seen that the average fixed cost curve (AFC curve) falls as output rises from lower levels to higher levels. The shape of the average fixed cost curve, therefore, is a rectangular hyperbola.
However, the average variable cost curve (AVC curve) starts rising earlier than the ATC curve. Further, the least cost level of output corresponds to the point LT on the ATC curve and not to the point LV which lies on the AVC curve.
Another important point to be noted is that in Fig. 3.2 the marginal cost curve (MC curve) intersects both the AVC curve and ATC curve at their minimum points. This is very simple to explain. If marginal cost (MC) is less than the average cost (AC), it will pull AC down. If the MC is greater than AC, it will pull AC up. If the MC is equal to AC, it will neither pull AC up nor down. Hence, MC curve tends to intersect the AC curve at its lowest point.
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Similar is the position about the average variable cost curve. It will not make any difference whether MC is going up or down. LT is the lowest point of total cost and LV is the lowest point of variable cost.
The inter-relationships among AVC, ATC, and AFC can be summed up as follows:
1. If both AFC and AVC fall, ATC will also fall.
2. If AFC falls but AVC rises:
(a) ATC will fall where the drop in AFC is more than the rise in AVC.
(b) ATC will not fall where the drop in AFC is equal to the rise in AVC.
(c) ATC will rise where the drop in AFC is less than the rise in AVC.
Aspect # 2. Cost-Output Relationship in the Long Run:
Long-Run Costs:
To study the cost-output relationship in the long run, it would be necessary to explain the concept of long-run costs.
The long run is a period long enough to make all costs variable including such costs as are fixed in the short run. In the short run, variations in output are possible only within the range permitted by the existing fixed plant and equipment. But in the long run, the entrepreneur has before him a number of alternatives which includes the construction of various kinds and sizes of plants.
Thus, there are no fixed costs since the firm has sufficient time to fully adapt its plant. And all costs become variable. In view of this, the long-run costs will refer to the costs of producing different levels of output by changes in the size of plant or scale of production. The long-run cost-output relationship is shown graphically by the long- run cost curve—a curve showing how costs will change when the scale of production is changed.
The concept of long-run costs can be further explained with the help of an illustration. Suppose that at a particular time, a firm operates under average total cost curve U2 and produces OM. Now it is desired to produce ON. If the firm continues under the old scale, its average cost curve will be NT. If the scale of firm is altered, the new cost curve will be U3. The average cost of producing ON will then be NA.
NA is less than NT. So the new scale is preferable to the old one and should be adopted. In the long run, the average cost of producing ON output is NA. This may be called as the long-run cost of producing ON output. It may be noted here that we shall call NA as the long-run cost only so long as the U3 scale is in the planning stage and has not actually been adopted. The moment the scale is installed, the NA cost will be the short-run cost of producing ON output.
To draw a long-run cost curve, we have to start with a number of short-run average cost curves (SAC curves), each such curve representing a particular scale or size of the plant, including the optimum scale. One can now draw the long-run cost curve which tangential to the entire family of SAC curves, that is, it touches each SAC curve at one point.
In this connection the following points are to be noted:
1. The LAC curve is tangential to the various SAC curves. It is said to envelop them and is often called as the “envelope curve” since no point on an SAC curve can ever be below the LAC curve.
2. The LAC curve is U-shaped or like a “dish.” The U-shape of the LAC curve implies lower and lower average cost in the beginning until the optimum scale of the enterprise is reached. And successively higher average costs thereafter, i.e., with plants larger than that of the optimum scale.
The tendency for the long-run average costs to fall as the firm expands its scale of operations is a reflection of cost economies available with the increase in size, while the ultimate rise in the long-run cost curve is largely due to the eventual setting in of diseconomies of scale.
The SAC curve also has a U-shape but the difference is that LAC curve is flatter, that is, U-shape of the LAC curve will be less pronounced. Such economies are possible in the long run. Likewise, some of the diseconomies, which are faced in the short run may not be faced in the long run.
3. The long-run average cost curve can never cut a short-run average cost curve (though they are tangential to each other). This implies that for any given output, average cost cannot be higher in the long run than in the short run. This is because any adjustment which will reduce costs is possible to make in the short run as well as in the long run. On the other hand, it is not always possible in the short run to produce a given output in the cheapest possible way.
4. LAC curve will touch the “optimum scale” curve at the latter’s least cost point, i.e. N1.
5. LAC curve will touch SAC curves lying to the left of the optimum scale curve at the left of their least-cost points.
6. LAC curve will touch SAC curves lying to the right of the optimum scale curve at the right of their least-cost points.
Thus it will be seen that LAC curve is tangential to the minimum cost point in the case of the optimum scale SAC and not in the case of other SAC curves.
A firm is not interested in achieving the minimum cost output for a given plant. On the other hand, it is interested in producing a given output at the minimum cost. The LAC curve helps a firm to decide the size of the plant to be adopted for predicting the given output. For outputs less than the low-cost combination at the optimum scale, that is, when the firm is operating subject to increasing returns to scale, it is more economical to underuse a slightly larger plant operating a less than its minimum cost output level than to overuse a smaller plant.
Conversely, at outputs beyond the optimum level, that is, when the firm experiences decreasing returns to scale, it is more economical to overuse a slightly smaller plant than to underuse a slightly larger one.
An example will make it easier to understand why a firm may choose to operate plants at other than their minimum cost-output (optimum capacity) levels. Suppose a firm has a choice to use any of the four plants, A, B, C, and D arranged in order of increasing size. The average cost curves for the plants are AA1, BB1, CC1, and DD1, respectively. The firm’s long-run average cost curve will be the scalloped curve ARSTD1. This curve consists of the lowest segments of all the short-run average cost curves.
As it is clear from Fig. 3.5, output OP can be obtained from an output less than the minimum unit cost-output OP, a firm can have either plant A or plant B, but it will find it cheaper to have plant B and underuse it rather than have plant A. If the firm desires an output OP2, i.e., an output more than the minimum unit cost output OP, it can have either plant C or plant D, but it will find it more economical to have plant C and overuse it rather than have plant D.
Thus, in managerial decision-making, the usefulness of the long-run cost curve lies in its ability to assist the management in the determination of the vest size of the plant to construct when a new one is being built or an old one is being expanded. As the long-run cost curve can help the entrepreneur in planning the best scale of plant, or the vest size of the firm for his purposes, it is also known as the planning curve. At the planning stage, management is faced with the problem of selecting one of the several possible sizes of plant.
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