Long run average cost

Long run average cost (LAC) curve.


Long run is a period of time in which all factors can be varied. So, there is no existence of any fixed cost as there is no fixed factor. So while deriving LAC we are needed to consider the short run average cost (SAC) curves only.

It is to be noted that in the short run the firm is tied with a given plant. But in the long run the firm moves from one plant to another.

The long run cost of production is the least possible cost of producing any given level of output when all inputs are variable including of curves the sizes of the plant.

LAC is the long run total cost divided by the level of output. LAC curve depicts the least possible average cost for producing all possible levels of output.
In order to understand the matter, consider the three short run average cost curves as shown in the following figure.


We know that in the long run the firm may run in various plants. In the above figure, there are three technically possible sizes of plant, and that no other size of plant can be built.

Now if the firm wants to produce OA amount of output it will incur lower cost on SAC1 them on SAC2. Because, cost on SAC1, AL<> amount of output varies. 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 numerous short run average cost curves. In that case, the long run average cost curve will be a smooth and continuous line without any scallops as shown in the following figure.

This long run average cost curve is so drawn as to be tangent to each of the short run average cost curves. The LAC is nothing else but the locus of all the tangency points since every point on the LAC represents a tangency point with some SAC curves.

If a firm desires to produce particular output in the long run, it will pick a point on the LAC curve corresponding to that output and it will then build a relevant plant and operate on the corresponding SAC curve.

In the figure above, for producing output OM the corresponding point on the LAC is G at which SAC1 is tangent to LAC. Thus, if a firm desires to produce at OM the firm will construct a plant corresponding to SAC1 and operate at the point G on LAC. Similar would be the case for all other outputs in the long run. But it is to be noted that all tangency points may not be the lowest point on the corresponding SAC. As we can see in the SAC1 in out figure, G is the tangency point and F is the lowest/ minimum point of SAC1. Similarly for SAC7, T is the tangency point but J is the minimum point of SAC7. But in SAC4 both the tangency point and the minimum point is the same, P. So the LAC is tangent to the falling portions of SAC1, SAC2 and SAC3 since LAC is falling too. LAC is falling until outputs are less on OQ. For outputs equal to more than OQ. LAC is rising so it will be tangent to the rising portions of SAC5, SAC6 and SAC7. This is caused because of the relevant plant’s optimal capacity.

In this way we can derive a LAC curve which first falls and then rises. So LAC is also a ‘U-shaped’ curve.