Long-Run Cost Curve

 

In the long run, all the factors of production are variable. There are no fixed factors and no fixed costs in the long run.

Types of Long Run Cost Curve:

a.      Long Run Total Cost (LTC)

It is the cost incurred by all the factors of production in the long run.

b.     Long Run Average Cost (LAC)

It is obtained by dividing LTC by the level of output. It shows the functional relationship between the total output and the total cost of production. Mathematically;

LAC=LTC/Q

c.      Long Run Marginal Cost Curve (LMC)

It is defined as the addition in the long run total cost as the result of the increase in the output by one unit.

Mathematically;

LMC=dLTC/dQ

 

Each point of the LAC curve is a point of tangency with the corresponding SAC curve. The point of tangency occurs to the falling part of the SAC curves for points lying to the left of M. since the slope of the LAC is negative up to M, the slope of the SAC cures must also be negative, because at the point of tangency the two curves have the same slope. By the same logic, the point of tangency for outputs larger than Q occurs to the rising part of the SAC curves. Only at the minimum point M of the LAC is the corresponding SAC also at a minimum. At

the falling part of the Lac curve the plants are not worked to full capacity. To the rising part of the LAC curve the plants are overworked. Only at the minimum point M is the plant optimally employed.

The LMC is derived from the SMC curves but does not envelop them. The LMC is formed from points of intersections of the SMC curves with vertical lines drawn from the points of tangency of the corresponding SAC and the LAC curve. So they are equal at a. this implies LMC >SMC1 to the left of a. At a, LMC=SMC1 (the same additional costs accrue to both the short-run and the long-run costs so that SAC1=LAC). To the right of a, LMC<SMC1 (more incremental cost is added to the short-run cost than to the long-run cost). At the minimum point of the LAC, the LMC intersects the LAC. At this point, SAC=SMC=LAC=LMC.