In the long run, firms can adjust their size and operations to meet demand efficiently, as all factors of production become variable. The duration of the long-run varies by industry, allowing firms flexibility in choosing the most cost-effective plant size for production. The document outlines the relationship between short-run average cost curves and the long-run average cost curve, indicating that firms will select the plant that minimizes average costs for their desired output levels.

1. LONG RUN COST
FUNCTION
-KISHORE RAVEENDRAN

2. 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.

3. • 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 electricitygenerating 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.

4.  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.

5.  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.

6.  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.

7. 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.

8. 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.