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# Returns to Scale

We know now that the law of diminishing returns discusses the relationship between factors of production and production output. However, remember that it operates within the boundaries of the short run. What actually happens in the long run? Let us look at returns to scale and Cobb Douglas Production Function.

## Returns To Scale

It is important to realize that the study of production completely differs according to the time frame. Recollect that we take the help of the law of diminishing returns to study production in the short run, whereas in the long run, the returns to scale are at the helm.

Again, the long run is a long enough period in which we can alter both fixed and variable factors. Thus, in the long run, we aim to study the effect of the changes in all the inputs on the production output.

However, these changes are not random. All the factors are increased or decreased together. This is also known as changes in scale, hence the name return to scale.

Thus, in the long run, we proportionately vary the inputs and observe the relative change in production. Of course, the return to scale can be of three types- increasing, decreasing and constant.

### Constant Returns to Scale

For constant returns to scale to occur, the relative change in production should be equal to the proportionate change in the factors.

For example, if all the factors are proportionately doubled, then constant returns would imply that the production output would also double. Interestingly, the production function of an economy as a whole exhibits close characteristics of constant returns to scale.

Also, studies suggest that an individual firm passes through a long phase of constant return to scale in its lifetime. Lastly, it is also known as the linear homogeneous production function.

### Increasing Returns to Scale

Here, the proportionate increase in production is greater than the increase in inputs. Note that upon expansion, a firm experiences increasing returns to scale. The indivisibility of factors is another reason for this.

Some factors are available in large units, such that they are completely suitable for large-scale production. Evidently, if all the factors are perfectly divisible then there might be no increasing returns. Further, specialization of land and machinery can be another reason.

### Decreasing Returns to Scale

An incidence of decreasing returns to scale would mean that the increase in output is less than the proportionate increase in the input. Generally, this happens when a firm expands all its inputs, especially a large firm.

When the firm expands to a very large size, it becomes difficult to manage it with the same efficiency as before. Hence, the increasing complexity in management, coordination, and control eventually leads to decreasing returns.

## Cobb Douglas Production Function

The Cobb Douglas production function {Q(L, K)=A(L^b)K^a}exhibits the three types of returns:

• If a+b>1, there are increasing returns to scale.
• For a+b=1, we get constant returns to scale.
• If a+b<1, we get decreasing returns to scale.

## Solved Example Cobb Douglas Production Function

Q: If the production function of a firm is Q=A(L^0.1)K^0.9, what can you conclude about its production according to the Cobb-Douglas Production Function.

Ans: Here a=0.9 and b=0.1. Further a+b=1, which implies that the firm has experiences constant returns to scale.

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