The derivation LAC is shown in fig 2.6.
It will be seen from fig. 2.6 that, up to OB amount of output, the form will operate on the SAC1, though it could also produce with SAC1; because up to OB output, production on SAC, caused lower cost than on SAC1.
For instance if the level of output OA is produced with SAC1 it will cost AL per unit and if it is produced with SAC2 it will cost AH per unit. Here (AH > AL). If a firm wants to produce OC output it will cost low if operate on SAC2 and not in SAC, up to OD output a firm will produce on SAC If he wants to produce more than OD, it is wiser to shift to SAC3.
Therefore, a firm always tries to remain at the minimum points of SAC in long-run. So long- run average cost is nothing but the locus of minimum points of SACs as shown in fig. 2.7.
The LAC is ‘U’ shaped but flatter than SAC curves. Since LAC envelops a number of SACs, it is referred as the envelope curve or a planning curve. Similarly, LMC is also derived from the SMCs. The relationship between LMC and LAC is same as that of short-run.
The shape of LMC that is ‘U’ shaped is due to operation of law of increasing returns and diminishing returns in the production. The explanation is same as explained in case of U-shape of SAC.