# Average and Marginal Cost Curves of a Firm in the Long-Run

Updated on June 1, 2014 Introduction

Long-run is defined as that period in which both fixed and variable factors are variable and both the factors can be adjusted. Over a long period, the firm can expand its output by enlarging the size of the existing plant or by building a new plant of a greater productive capacity.

Long-run is a period long enough to enable all costs to vary. The firm can expand its plant to meet the long-term increase in demand or reduce its plant capacity to adjust itself to a drop in demand. Likewise, there is sufficient time for installing new plants. Unwanted building can be sold and administrative and marketing staff can be altered. Therefore, the dichotomy between fixed and variable costs disappears in the long-run. In the short-run the firm must be content with the best utilization of the given plant, but in the long-run, it can choose any plant size from among the many feasible plant sizes.

The long-run average cost curve (LAC) is the envelopes of the various short-run average cost curves. When all factors of production can be used in varying proportions the scale of operations can be altered. Each time the scale of operation changes, a new average cost curve will have to be drawn for the firm. Look at the figure given below.

Let there be three plants represented by their average cost curves SAC1, SAC2 and SAC3. Each curve represents the scale of the firm. Originally, the firm has a plant size relating to SAC1. Now the firm produces OM4 output with M4E1 as the average cost.

Suppose the demand for the product increases, so that the firm wants to expand its output from OM4 to OM1. OM1 output can be produced by using the same plant. The average cost will rise from M4E1 to M1E2 in the long-run. However, OM1 output can be produced by installing a new plant shown by SAC2 with a higher capacity. If the firm operates on a plant relating to SAC2, the average cost of OM1 output will be M1R. SAC3 relates to the plant of a much higher capacity. The above analysis is a simple model based on three possible plant sizes. In reality, a firm can make a choice from a variety of plants. This is shown in the following figure 2.

Planning Curve

The LAC curve shows the lowest AC of producing each output when all inputs can be varied freely. A ration entrepreneur would select the optimum scale of the plant. The optimum scale of plant is that plant size at which SAC is tangent to the LAC, such that both the curves have the minimum point of tangency.

In figure 3 at OM1 level of output, SAC is tangent to LAC at both the minimum points. Thus, OM1 is the optimum scale of output, as it has the minimum per unit cost. Since the LAC curve envelopes all SAC curves, it is called as the envelope curve. LAC is also known as the planning curve, since it guides the entrepreneur in his decision to plan for the future expansion of his output.

The LAC will be a horizontal line if the factors are perfectly divisible and the prices of inputs remain constant. The reason for horizontal line is due to neither economies nor diseconomies in production. Such an LAC curve is shown in figure 3, where it is tangent to the curves SAC1, SAC2 and SAC3 at their minimum points. The implication of a horizontal LAC is that all plants can be operated at their minimum cost. However, for different levels of output, separate plants will be used. For instance, plants relating to SAC1, SAC2, and SAC3 will be used for OM1, OM2 and OM3 levels of output respectively. Since the minimum costs of all the plants are identical, the optimum scale of the plant will be indeterminate as every level of output is an optimum one.

Why LAC Curve First Falls and Then Rises

The LAC curve first falls due to the operation of the various economies of scale, as discussed earlier. The LAC curve rises after a point because of the emergence of diseconomies of scale.

L-Shaped Lon-run Average Cost Curve

Various questionnaires and engineering studies suggest the possibility of an L-shaped long-run average cost curve. Long-run costs may be divided into production costs and managerial costs. Production costs fall continuously with increases in output. However, the managerial costs may rise at a higher level of output. Since the fall in production cost is more powerful than the rise in managerial costs, the LAC falls with an increase in the scale of production. Technical progress is the most important contributory factor for the ‘L’ shaped curve.

Long-run Marginal Cost Curve

The long-run average cost curve has also its counterpart marginal cost curve known as long-run marginal cost curve. The LMC can be easily derived from LAC and it bears a similar relation between SAC and SMC.

The following relationships may be observed between LMC and SMC.

(1) At output OM1, SMC1 = LMC. At SMC2, LMC = SAC2 = LAC.

(2) SAC1 = LAC(at tangency) and SMC1 = LMC (an intersection). Similarly, for output levels OM and OM2, the relationship can be traced.