In the short run, there is only one short run average cost (SAC) curve corresponding to one (fixed) plant. However, in the long run, a firm has a number of alternatives with regard to the scale of production.
For each scale of production, the firm has an appropriate short run average cost curve. The long run average cost (LAC) curve can be derived from a number of short run average cost curves, corresponding to different plant sizes.
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In the words of GL. Thirkettle,
“Long run average cost (LAC) is the average cost per unit of output when the entrepreneur has time to vary all the factors of production so that he has the most profitable size of the plant and the best proportion of fixed and variable factors for any given output”.
In order to derive the LAC curve, consider three methods of production, each with different plant size—a small plant, a medium plant and a large plant; at a given state of technology at a particular point of time. The three plants operate with short run average costs denoted by SAC1, SAC2 and SAC-, respectively (Fig. 11.11).
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Each plant is suitable for a particular range of output. Within this range, output can be varied by varying the quantity of variable inputs. The choice of plant depends on planned or expected output firm chooses the short run plant capable of producing planned output at the lowest average cost in the long-run.
If the firm starts production with small plant (represented by SAC1), it can operate this plant with the least possible cost for various levels of output up to OQ1. For producing an output level beyond OQ, (possible on account of rise in demand), average cost in small plant is higher (DF>GF in Fig. 11.11).
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Thus, in the long run, the firm sets up a medium plant (bigger sized plant) represented by SAC2, if it expects more demand in future. The average cost for this plant is lower than small plant. However, this plant was not suitable for output lower than OQ1, since average cost with this plant is at higher level of HI than average cost with small plant, i.e., JI.
However, if the firm anticipates a rise in demand beyond OQ2, it will install a large plant (still bigger sized plant) to reduce the cost per unit. For output level beyond OQ2, the medium plant entails higher average cost than the large plant, while large plant is too large for output level below OQ2.
In the long run, the firm may prefer to operate on a falling (rising) portion of a short run average cost than at a minimum point of some other short run average cost curve (for a particular level of output), as the latter may involve relatively higher average cost in the long run.
In Fig. 11.11, ‘K’ is the minimum point of SAC3. But, the firm would rather operate on the falling portion of SACV corresponding to OQ3 level of output. Similarly, the firm may operate on the rising portion of some SAC in preference of the minimum point of some other SAC.
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The reason is that it is not the efficiency for a given plant that matters, but efficiency overall. Such change reduces the costs. Thus, in the long run, the firm may use various plants below its full capacity or beyond the optimum capacity.
In the short run, the firm will choose that plant, which will help it to minimise the cost of product. In the long run, however, the firm can build a plant, the size of which leads to lowest average cost for any given level of output.
The long run average cost curve is shown by dark line in Fig. 11.11. It consists of some (lower) segments of all the short run average cost curves. It is wavery. Long-run average cost curve can never cut any short-run average cost curve.
Till now we have taken the three plant case. It can be extended to a multiple plant case, each plant being used to produce only that output, which can be produced most efficiently. Suppose, if the size of the plant is varied by infinitely small amount, such that there are infinite number of plants.
Corresponding to these plants, there will be numerous short run average cost curves resulting in smooth continuous curve without any scallop. Fig. 11.12 illustrates such a smooth long run average cost (LAC) curve. Each point on this curve shows the minimum cost of producing the corresponding level of output.
No portion of it ever lies above any portion of the SAC curves. The LAC curve shows the locus of points representing the least unit cost of producing different outputs with optimum plant size. It shows lower frontier of all short-run cost curves.
Any point above LAC curve is inefficient as it shows higher per unit cost of producing that level of output. Further, any point below the LAC curve is desirable, but not attainable. If the firm plans to produce a particular level of output in the long run, it will choose a point on the LAC curve corresponding to that level of output and will then plan to build a relevant plant and operate on the corresponding short run average cost curve.
LAC curve is sometimes called the planning curve of a firm as it helps the firm to decide what plant to set up in order to produce any level of output at the minimum cost in the long run. It is a guide to the entrepreneur in his decision to plan the future expansion of output. At any time, the firm operating with certain plant must base its current price and output decisions upon the cost schedule with the existing plant.
Since LAC envelopes (or supports) the SAC curves, it is also known as envelope curve. It is clear from the Fig. 11.12 that LAC curve is tangent to the whole set of SAC curves relevant for different plant sizes. However, LAC curve is not tangent to the minimum points of all the short run average cost curves.
The point of tangency occurs to the falling portion of the SAC curves for points lying to the left of the minimum point ‘M’ of the LAC. The point of tangency for outputs larger than OQ occurs to the rising part of the SAC curves.
Thus, at the falling part of the LAC, the plants are not worked to full capacity and to the rising part of the LAC, the plants are overworked. Only at the minimum point ‘M’, the plant is optimally used. In case of constant return to scale, however, the LAC curve touches the minimum point of all SAC curves.
In which case the LAC curve will be a horizontal straight line parallel to X-axis. Under constant returns, every plant is equally efficient, since the lowest point of the average cost curve is the same for all these plants. According to Robinson, Stigler, Kaldor and others, this happens only, when all the factors of production are perfectly divisible.
Thus, a horizontal LAC curve is only theoretically possible, when the factors are so adjusted that the long run proportions between them are the same at all levels of output. Even according to George Stigler “constant returns is not a necessary characteristic of the production function”.