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Marginal costs in the long run

15 February, 2016 - 09:58

Just as there is a relationship between the marginal and average cost curves in the short run, there is a complementary relationship between the two in the long run also. In the long run all costs are variable. Hence, the long run marginal cost (LMC) is defined as the increment in cost associated with producing one more unit of output when all inputs are adjusted in a cost minimizing manner.
LMC =\frac{\Delta LTC}{\Delta Q}

\mid Long run marginal cost is the increment in cost associated with producing one more unit of output when all inputs are adjusted in a cost minimizing manner.

Figure 8.6 illustrates a LMC curve where there are initially declining marginal costs, then constant marginal costs and finally increasing marginal costs. The associated data are presented in Table 8.3. This example has been constructed with three linear segments to the LMC curve in order to show the relationship between returns to scale and long run marginal costs: the LATC still has a smooth U shape, and intersects the LMC at the minimum of the LATC. The logic for this occurrence is precisely as in the short run case: whenever the marginal cost is less than the average cost the latter must fall, and conversely when the marginal cost is greater than the average cost.

Figure 8.6 LMC and LAC with returns to scale
The LMC cuts the LAC at the minimum of the LAC.
 
Table 8.3 Long run costs and returns to scale
Output LMC LAC Scale
0 80 80.00 Increasing returns to scale
100 72 76.00
200 64 72.00
300 56 68.00
400 48 64.00
500 40 60.00
600 40 56.67
700 40 54.29
800 40 52.50
900 40 51.11
1000 40 50.00
1100 44 49.27
1200 48 49.00
1300 52 49.08 Decreasing returns to scale
1400 56 49.43
1500 60 50.00
1600 64 50.75
1700 68 51.65
1800 72 52.67
1900 76 53.79
2000 80 55.00