LONG RUN COST FUNCTION

-KISHORE RAVEENDRAN

LONG RUN COST FUNCTION• In the long-run a firm can amend its size and

organization to violate demand conditions. In other words, in the long-run the firm can adjust its scale of operations or size of plant to produce any required output in the most efficient way. Thus, in the long run fixed factors can be altered. Management can be restructured to run a firm of a different size. Capital can also be used differently. In short, all factors are variable in the long run and therefore the scale of operations can be altered.

• Thus, in the long-run all costs are variable (i.e. the firm faces no fixed costs). The length of time of the long-run depends on the industry. In some service industries, such as dry-cleaning, the period of the long-run may be only a few months or weeks. For capital intensive industries, such as electricity-generating plant, the construction of a new plant may take many years and hence long-run may be many years. The length of time of the long-run depends upon the time required for the firm to be able to vary all inputs

• In the long run, a firm can have a large number of alternative plant sizes. For a certain level of output, a plant of a particular size will be most suited.

The above figure is drawn on the assumption that there are three plants and they are depicted by the short run average cost curves SAC1, SAC2, SAC3. A given plant is best suited for a particular level of output.

OL can be produced at a lower cost with the plant SAC1 than with the plant SAC2.

The cost of producing OL output on plant SAC1, is AL and it is less than the cost of producing the same output with plant SAC2.

The difference in cost is equal to AB. If the firm wants to produce ON output it can

produce it either by plant SAC1 or plant SAC2.But it would be advantageous for the firm to use

the plant SAC2 for ON level of output because the larger output OM can be obtained at the lowest average cost from this plant.

Thus, output larger than ON but less than OQ can be produced at a lower average cost with plant SAC2. For output larger than OQ, the firm will have to employ plant SAC3.

For instance, output OP can be produced at average cost of PE with plant SAC3.

It is clear from the above analysis that in the long run the firm has a choice regarding the employment of a plant and it will employ that plant which yields possible minimum average cost for producing a given output.

Long run Smooth Envelope Curve

• The LAC curve is not tangent to the minimum points of the short run average cost curves. This exception occurs at the optimum level of output.

The output OM at which the lowest point of SAC3 coincides with the minimum point on the LAC curve at point R.

The plant SAC3 which produces the optimum output OM at the minimum cost RM is the optimum plant.

For outputs less than OM the lowest long run costs occur on the falling portions of SAC curves.

LAC curve is tangent to falling portions of SAC1 and SAC2 at points S and T respectively, but points of S and T are not the minimum points of SAC1 and SAC2.

• On the other hand, for outputs greater than OM, the lowest long run average costs occur on the rising portions of short run average cost curves.

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