Long run average cost curve (LAC curve)

Long run is a period of time during which the firm can vary all its inputs. Thus, all the factors in the long run are variable, unlike the short run, where one variable factor is fixed and others are variable. For instance, in the short run, the firm’s location is fixed, but in the long run, the firm can move from one place to another. A long run cost curve represents the functional relationship between output and the long run cost of production. A long run average cost curve is made up of many short run average cost curves as a business in long run will be able to change all its inputs. Let us understand this with the help of a diagram. To understand how long run average cost curve is derived we consider three short run average cost curves. Short run cost curves are also called as plant curves. In the short run the firm can be operating on any short run average cost curves given the size of the plant. Given the size of the plant, the firm will be increasing or decreasing its output by changing the amount of the variable inputs. But in the long run, the firm chooses with which size of plants or on which short average cost curve it should operate to produce a given level of output so that total cost is minimum. This may be depicted in the form of a diagram. As shown in the diagram, to produce up to OB amount of output, the firm will operate on the SAC1 though it can operate on SAC2 selecting SAC1 would results in lower cost than SAC2. For example, if the level of output OA is produced with SAC1, it will cost AL per unit and same quantity is produced on SAC2 it will cost AH which is more than AL. Similarly, if the firm plans to produce OC quantity, it will select SAC2 plant, instead of SAC1, where cost is CK which is lesser than CJ. Hence in the long run the firm has a choice in the employment of plant and it will employ that plant which yields minimum possible unit cost for producing a given output.

Since in the long run the size of the plant can be varied by infinitely small gradations, there will be numerous average cost curves. By combing all these short run average cost curves, Long run average cost curve may be obtained, which would be a smooth curve enveloping all these short run average cost curves. Hence it is known as Envelop Curve or Planning Curve. Every point on the long run average cost curve will be a tangency point with some short run AC curve. If a firm desires to produce any particular output, it then builds a corresponding plant and operates on the corresponding short run average cost curve. This could be shown in the form of a graph. For producing OM level of output, the corresponding point on the LAC curve is G and short run average cost curve is SAC2, is tangent to the long run AC at this point. If larger output OV has to be produced, then it uses SAC3. It should be noted that LAC is not a tangent to the minimum points of the SAC curves. When the LAC curve is declining it is tangent to the falling portions of the short run cost curves and when the LAC curve is rising it is tangent to the rising portions of the short run cost curves. LAC curve would be always U shape because of operation of returns to scale.

When the LAC curve is declining, it is tangential to the falling portions of the short run cost curves and when the LAC curve is rising, it is tangential to the rising portions of the short run cost curves. Thus, for producing output less than OT at the lowest possible unit cost, the firm will construct the relevant plant and operate it at less than its full capacity, i.e., at less than it’s minimum average cost of production. On the other hand, for producing output larger than OT, the firm will construct a plant and operate it beyond its optimum capacity. OT is the optimum output. This is because, OT is being produced at the minimum point of LAC and the corresponding SAC i.e. SAC4. Other plants are either used at less than their full capacity or more than their full capacity. Only SAC4 is being operated at the minimum point.

Problem on cost:
1. Calculate TFC, TVC, AVC, AFC, AC and MC from the following information
 Units Total cost (TC) 0 50 1 130 2 180 3 190 4 220 5 270

Solution:

 Units TC TFC TVC AFC AVC AC MC 0 50 50 0 0 0 0 0 1 130 50 80 50 80 130 80 2 180 50 50 25 25 90 50 3 190 50 10 16.67 3.3 63.33 10 4 220 50 30 12.5 7.5 55 30 5 270 50 50 10 10 54 50  