Importance of Long Run Average Total Cost Curve in a Firm

The Long Run Average Cost (LRAC) curve shows average cost at each possible level of output, when all the inputs are variable and any desired capacity of plant can be built whereas the SRAC curves represent cost of producing an output level when at least one factor of production is constant. Let us try to explain this statement.

We are aware that ATC is dependent on quantity of output. Suppose, in the short-run, there are four different plants of different capacities, viz. plant 1, plant 2, plant 3 and plant 4, where plant 1 is smaller in size than plant 2 and plant 2 is smaller than plant 3 which is smaller than plant 4. The ATCs of these four plants are represented by ATC₁, ATC₂, ATC₃ and ATC₄ respectively.

These cost curves are short run cost curves since these firms cannot change their production capacities and if a firm wants to change output, it will have to do so within its own production capacity. In other words, a firm will move, in terms of cost, along the ATC if it changes output, but the ATC which represents plant capacity cannot be changed.

For instance, ATC of the smallest plant is ATC,, which shows average total cost corresponding to different levels of output where the total production capacity of the plant is constant. It is true not only for plant 1, but also for other plant sizes, viz. plant 2, plant 3 or plant 4.

But in the long run, the firm can choose the most cost efficient plant size among these four plant capacities.

In figure 9.7 we observe that, so long as the firm produces any quantity less than 15 units, it will select the smallest capacity because, this scale of production minimizes cost of production up to 15 units. To establish this point, let us consider that the firm produces any quantity less than 15 units, say 11 units of output.

Now, in the long run, to produce 11 units it will use the smallest capacity (equal to the capacity of plant 1) because if it does so, production cost per unit of output becomes ‘ns’, whereas, if the firm produces the same quantity with enhanced capacity (say, equal to plant 2), production cost will increase to ‘ms’ (ms > ns).

Figure 9.7 also reveals that when production exceeds 15 units but remains less than or equal to 21 units, increase in plant size will help the firm of ensure the lowest cost of production.

For, throughout this range of output, smaller or larger size of plant than plant 2 raises average cost since ATCs of both smaller (represented by ATC,) or larger (represented by ATC₃) plant sizes lie above ATC₂. Similarly, when the range of output lies between 22 to 29 units, plant capacity equal to plant 3 will minimize cost of production.

In the long run, when the firm has the option to vary capacity of plant, unlike the case of short run, it will choose different plant capacities for different levels of output in order to minimize cost of production. So, the long run cost curve of this firm will be ‘abcde’.

At this stage, we can relax the assumption that there are only four scales of operation. Actually, there may be more scales of a plant. As the number of scale increase kinks at the points of intersection of two successive short-run average cost curves would be less pronounced. Thus, more the number of scales, smoother is the LRAC curve.