Returns to Outlay and Shape of the Cost Function

In this article we will discuss about the returns to outlay and shape of the cost function.

In the long run, if the quantities of all the inputs to be used by the firm, can be increased in the same proportion, then only we would obtain the returns to scale. Therefore, in the discussion of returns to scale, we always assume that the firm uses the inputs in a constant (or fixed) proportion.

But, in the real world, it is often found that although in the long run, the quantities of all the inputs to be used by the firm can be changed, they cannot be changed, however, all in the same proportion.

That is, along with the change in the quantities used of the inputs, the ratio in which they are used also changes. Since the input ratio does not remain constant we cannot obtain, as per definition, any estimate of the returns to scale in this case.

Under the circumstances, we may use the total outlay of the firm as an index of changes in the quantities used of the inputs and, thereby, obtain the returns to outlay in place of returns to scale.

In the long run, if the firm increases its output by increasing (in the same proportion or in different proportions) the quantities of the inputs to be used by it, then also we obtain certain laws of increase in output along with changes in its total outlay. These laws are called the laws of returns to outlay.

Just like the returns to scale, in the initial stages of production increase in the long run, we obtain that output would be increasing more than in proportion to increase in the firm’s outlay, because of the economies of scale, and as a result, the firm’s long-run average cost (LAC) would be decreasing. This process of decreasing LAC with increases in output, may be called the increasing returns to outlay.

Again at a certain point of increasing outlay and increasing output, the firm’s LAC becomes minimum. If the firm’s outlay increases beyond this point, then owing to diseconomies of scale output would be increasing less than in proportion to increase in outlay, and as a result, LAC would be increasing. This process of increasing output and increasing LAC may be called the decreasing returns to outlay.

Lastly, there may be a stage between the process of increasing and decreasing returns to outlay where the firm’s output may be increasing just in proportion to increase in outlay, and as a result, LAC here may remain constant at its minimum level. This process of increasing output, and LAC remaining constant at its minimum, may be called the constant returns to outlay.

In the long run, if it is not possible to increase the quantities of all the inputs to be used by the firm in the same proportion, i.e., if output in the long run is to be increased by increasing the input quantities in different proportions, then the concept of returns to outlay rather than that of returns to scale becomes more relevant.

It may be noted here that if, in the long run, it is possible to increase all the input quantities in the same proportion, then the input quantities and the firm’s outlay would all increase in the same proportion, the input prices remaining the same. In this case, the concept of returns to scale and that of returns to outlay would become identical.