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# Explanation of Law of Returns to Scale

In our earlier posts, we have explain about the production function and law of variable production. If you are yet to read, then you can find them here – meaning of production function and law of variable production. Now here in this post, we are going to explain about the law of returns to scale, which is a long-run theory of production in which all factors of production – specially capital & labor – are variable. We employ the modern form of production function with two variable factor inputs , i.e. Q = f(K,L), to analyze the whole story.

## What does the term ‘returns to scale’ refer to?

Before understanding this law, it is good to understand the meaning of the term ‘returns to scale’. The term, returns to scale, means what happens to returns when scale of production changes. Here, returns refers to output under production, and scale refers to the size of employment of factors – labor and capital for ease of exposition. That is, the term imply what happens to output when labor and capital are increased in the same proportion.

As oppose to the term diminishing returns, which explain short-run change in output due to change is variable factors of production given the fixed factor (law of variable proportion), returns to scale explain the long-run change in output due to proportionate change in factor inputs.

## What are the basic assumptions?

Mainly, this law rests on following two assumptions:

• All factors can be used proportionately in the production i.e. factors can be used in fixed proportion (say, ratio of capital to labor equals ratio of labor to land, because proportion is the equality of rations). This is the one important feature of the classical production function.
• Technique of production remains constant, if changed, causes output to change more than the scale or size effect.

## Statement of law

Employing factor inputs proportionately i.e. increasing the production scale, it is likely that output may increase more than proportionately as the inputs, increase at same proportion as the inputs or increase less than proportionately as the inputs (not assumed to decrease). This is what the law of returns to scale says about. This argument indicates that there are three possible cases of returns to scale: increasing returns to scale, constant returns to scale and decreasing returns to scale.

## Increasing returns to scale

Output increases more than proportionately as the inputs. In other terms, doubling or trebling the inputs more than doubles or trebles the output. For instance, output increases by 110 percent when inputs increase by 100 percent. The main factor behind the IRS is the emergence of economies of scale. More specifically, factors contributing IRS are indivisibility of factors that they are available in a lumpy style, specialization of labor and use of specialized machinery possible as the scale of production increases, and dimensional economies (e.g. doubling the sides of a cube more than doubles the volume).

## Constant returns to scale

Output increases at the same percentage as the inputs i.e. doubling or trebling the inputs doubles or trebles the output. For example, output increases by 100 percent when inputs increase by 100 percent. The main cause of the emergence of CRS is the balance between economies of scale and diseconomies of scale.

## Decreasing returns to scale

Output increases less than proportionately as the inputs. Put another way, doubling or trebling inputs less than doubles or trebles the output. For instance, say, output increases by 90 percent when inputs increase by 100 percent. The main cause of the DRS is the emergence of the diseconomies of scale as the scale of production remarkably increases. More specifically, the causes of the DRS are: entrepreneur is considered as the fixed factor of production and accordingly the operation of law of diminishing returns; dis-management regarding coordination, communication and control; and depletion or exhaustion of natural resources.

## Final note on law of returns to scale

In nutshell, there are both economics and diseconomies of scale that they simultaneously operate in the production activities no matter what the size of production is. When economies of scale out-weight diseconomies of scale, IRS emerges. On the contrary, when diseconomies of scale more than offset the economies of scale, DRS emerges. Off course, CRS appears when these opposite forces equal. Empirical studies regarding the law of returns to scale have found the operation of IRS at initial stage or small-scale of operation, CRS at medium scale of operation and DRS at large-scale of operation. Amongst them, CRS was found to exist for longer period of scale of operation than others.

Some economists argue that entrepreneur is the fixed factor and cannot be used in the fixed proportion with other factors. This view contends the law of returns to scale as a special case of law of variable proportion because entrepreneur is a fixed factor and rests of others are variable. This argument has certainly posed the challenge in the operation of law of returns to scale. But, if we take entrepreneur as the human effort rather than number, certainly this law seems to be logical and operational because entrepreneurial effort directly varies with the scale of operation irrespective of the number of entrepreneurs.

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