What is Returns to Scale?

What is Increasing Returns to Scale | Decreasing Returns to Scale | Constant Returns to Scale?

Introduction

In previous sessions, we have discussed in detail about the relationship between a variable input and the output of a firm in context of Total Product of the variable input, Average Product of the Variable Input and the Marginal Product of the Variable Input.

For a firm as we know, there can be two segmentation based on timeline i.e., the Short Run and the Long Run. Short Run for a firm is a period of time in which at least one factor or input cannot be varied i.e., to say it will remain fixed or constant or unchanged. Fixed here in this context meaning the level of employment of that input cannot be increased or decreased. And Long Run for a firm is a time period in which all the factors or input are variable i.e., to say the level of employment of all the inputs can be increased or decreased in order to achieve the desired level of output.

All of the above products i.e., Total Product, Average Product and Marginal Product, of the variable input were discussed in context of short run as we had kept one of the input or factor constant and the other only variable. And in the context of short run only, we further discussed the concept of Law of Diminishing Marginal Product.

The Law of Diminishing Marginal Product is also known as Law of Diminishing Marginal Returns or Law of Variable Proportions.

But in this session, we are moving forward to discuss, what will happen when we change the context of time i.e., in the Long Run when all the inputs or factors of production are variable and its level of employment can be changed in order to achieve the desired level of output.

Returns to Scale

The Law of Diminishing Marginal Product stated that Marginal Product of a variable input initially increases as the level of employment of the variable input or factor is increased and keeps increasing till the factor proportions are in favor of the output. But after reaching a certain level of employment of the variable input, further increases in the amount of variable input leads to adverse factor proportions for the output which results into decrease in the Marginal Product of the variable input. Thus this phenomenon of gradual increase in Marginal Product of the variable input initially up to a certain point of employment of the variable input and subsequent fall in the same is what defines the Law of Diminishing Marginal Product or Law of Variable Proportions.

It is also known as Law of Variable Proportions because the factor proportion of employed resources or inputs changes which leads to the happening of the phenomenon of this law. Factor Proportions can be defined as the ratio of inputs which are combined in order to produce the output. As we have assumed in the previous discussion while understanding the same that we take only two factors or inputs employed by the firm which are Labor (L) and Capital (K). And in the discussion we kept the input labor as the variable input and capital as the fixed input as in the short run at least one input needs to be fixed or constant. Now as we keep on increasing the variable input, the factor proportion changes. Initially the change in factor proportions proves to be favorable to the production process hence resulting in increase in the Marginal Product of the variable input and hence even the output. But after a certain level of employment of that variable input, here labor, the factor proportions turn unfavorable to the production process and hence decreasing the Marginal Product of each additional unit of variable input.

But in the long run for a firm, all the factors of production or input becomes variable. In our discussion as we had kept the labor as variable and capital as fixed input in the short run, in the long run both of them becomes variable and the employment level of both of them can be changed. So what will happen to the output when both labor and capital can be changed or becomes variable?

The discussion surrounds that if in the long run both the factors can be changed or becomes variable, in what proportions are those inputs or factors are changed and what result we get in form of a change in production with the change in the proportion of both the inputs.

For simplicity, we will discuss what will be the change in production if both the inputs are changed or increased by the same proportions or are scaled up in the same proportion.

The above scenario can be divided into different cases as follows.

Case 1) Constant Returns to Scale

When both the inputs are increased or scaled up in the same proportion i.e., there is proportional increase in both inputs and if it results into increasing the output by same proportion, the production function is said to be giving Constant Returns to Scale.

Case 2) Increasing Returns to Scale

When both the inputs are increased or scaled up in the same proportion i.e., there is proportional increase in both inputs and if it results into increasing the output by larger proportion, the production function is said to be giving Increasing Returns to Scale.

Case 3) Decreasing Returns to Scale

When both the inputs are increased or scaled up in the same proportion i.e., there is proportional increase in both inputs and if it results into increasing the output by smaller proportion, the production function is said to be giving Decreasing Returns to Scale.

We will understand the above case with a simple illustration.

Let us consider a case where in a production process in the long run, all the inputs are doubled. Now after doubling the input if…

Case 1 – If the output gets doubled too - this is a case of Constant Returns to Scale

Case 2 – If the output is more than doubled – this is a case of Increasing Returns to Scale

Case 3 – If the output is less than doubled – this is a case of Decreasing Returns to Scale

Means what we are trying to study is, if we scale or increase all the inputs in equal proportion used by a firm in production in the long run, what change it will lead to the quantum of production. What returns or product in form of change in output we get on scaling all inputs in equal proportion is what we define as the Returns to Scale.

Conclusion

In this session, we discussed in detail about the Returns to Scale in the Long Run for a firm. And we also discussed each of the cases of Returns to Scale i.e., Constant Returns to Scale, Increasing Returns to Scale and Decreasing Returns to Scale.