# Law of Returns

14/03/2020

The law of returns to scale describes the relationship between outputs and scale of inputs in the long-run when all the inputs are increased in the same proportion. In the words of Prof. Roger Miller, “Returns to scale refer to the relationship between changes in output and proportionate changes in all factors of production. To meet a long-run change in demand, the firm increases its scale of production by using more space, more machines and labourers in the factory’.

#### Assumptions

(i) All factors (inputs) are variable but enterprise is fixed.

(ii) A worker works with given tools and implements.

(iii) Technological changes are absent.

(iv) There is perfect competition.

(v) The product is measured in quantities.

Explanation

Given these assumptions, when all inputs are increased in unchanged proportions and the scale of production is expanded, the effect on output shows three stages: increasing returns to scale, constant returns to scale and diminishing returns to scale.

#### 1. Increasing Returns to Scale

Returns to scale increase because the increase in total output is more than proportional to the increase in all inputs.

The table reveals that in the beginning with the scale of production of (1 worker + 2 acres of land), total output is 8. To increase output when the scale of production is dou­bled (2 workers + 4 acres of land), total returns are more than doubled. They become 17. Now if the scale is trebled (3 workers + о acres of land), returns become more than three-fold, i.e., 27. It shows increasing returns to scale. In the figure RS is the returns to scale curve where R to С portion indicates increasing returns.

#### Causes of Increasing Returns to Scale

Returns to scale increase due to the following reasons:

(i) Indivisibility of Factors

Returns to scale increase because of the indivisibility of the factors of production. Indivisibility means that machines, management, labour, finance, etc. cannot be available in very small sizes. They are available only in certain minimum sizes. When a business unit expands, the returns to scale increase because the indivisible factors are employed to their maximum capacity.

(ii) Specialization and Division of Labour

Increasing returns to scale also result from specialization and division of labour. When the scale of the firm is expanded there is wide scope of speciali­zation and division of labour. Work can be divided into small tasks and workers can be concentrated to narrower range of processes. For this, specialised equipment can be installed. Thus with specialization, efficiency increases and increasing returns to scale follow.

(iii) Internal Economies

As the firm expands, it enjoys internal economies of production. It may be able to install better machines, sell its products more easily, borrow money cheaply, procure the services of more efficient manager and workers, etc. All these economies help in increasing the returns to scale more than proportionately.

(iv) External Economies

A firm also enjoys increasing returns to scale due to external econo­mies. When the industry itself expands to meet the increased long-run demand for its product, external economies appear which are shared by all the firms in the industry.

When a large number of firms are concentrated at one place, skilled labour, credit and transport facilities are easily available. Subsidiary industries crop up to help the main industry. Trade journals, research and training centres appear which help in increasing the productive efficiency of the firms. Thus these external economies are also the cause of increasing returns to scale.

### 2. Constant Returns to Scale

Returns to scale become constant as the increase in total output is in exact proportion to the increase in inputs. If the scale of production in increased further, total returns will increase in such a way that the marginal returns become constant. In the table, for the 4th and 5th units of the scale of production, marginal returns are 11, i.e., returns to scale are constant. In the figure, the portion from С to D of the RS curve is horizontal which depicts constant returns to scale. It means that increments of each input are constant at all levels of output.

### Causes of Constant Returns to Scale

Returns to scale are constant due to:

(i) Internal Economies and Diseconomies: But increasing returns to scale do not continue indefinitely. As the firm expands further, internal economies are counterbalanced by internal diseconomies. Returns increase in the same proportion so that there are constant returns to scale over a large range of output.

(ii) External Economies and Diseconomies: The returns to scale are constant when external diseconomies and economies are neutralised and output increases in the same proportion.

(iii) Divisible Factors: When factors of production are perfectly divisible, substitutable, and homogeneous with perfectly elastic supplies at given prices, returns to scale are constant.

### 3. Diminishing Returns to Scale

Returns to scale diminish because the increase in output is less than proportional to the increase in inputs. The table shows that when output is increased from the 6th, 7th and 8th units, the total returns increase at a lower rate than before so that the marginal returns start diminishing successively to 10, 9 and 8. In the figure, the portion from D to S of the RS curve shows diminishing returns.

Causes of Diminishing Returns to Scale

Constant returns to scale is only a passing phase, for ultimately returns to scale start diminishing. Indivisible factors may become inefficient and less productive. Business may become unwieldy and produce problems of supervision and coordination. Large management creates difficulties of control and rigidities. To these internal diseconomies are added external diseconomies of scale.

These arise from higher factor prices or from diminishing productivities of the factors. As the industry continues to expand, the demand for skilled labour, land, capital, etc. rises. There being perfect competition, inten­sive bidding raises wages, rent and interest. Prices of raw materials also go up. Transport and marketing difficulties emerge. All these factors tend to raise costs and the expansion of the firms leads to diminish­ing returns to scale so that doubling the scale would not lead to doubling the output.

For the management increasing, decreasing or constant returns to scale reflect changes in pro­duction efficiency that result from scaling up productive inputs. But returns to scale is strictly a production and cost concept. Management’s decision on what to produce and how much to produce must be based upon the demand for the product. Therefore, demand and other factors must also be considered in decision making.

### Laws of Constant Returns

The Law of Constant Returns is said to operate when the additional investment of labour and capital yields the same return as before.

It means the return from investment remains the same as the business is expanded or contracted.

In other-words, it can be said that “whatever the scale of production, the cost of the product per unit remains the same.”

According to Stigler – “When all the productive services are increased in a given proportion, the product is increased in the same proportion.”

Law of Constant Return remains active for some-time. From where the activeness of Law of Increasing Return ends, from there the Law of Constant Return starts and after the end of the activeness of this Law of Diminishing Return starts operation.

In other-words, it can be said that when the business moves towards the optimum, the returns increase and when it goes beyond the optimum the returns decrease. But if after having reached the optimum point, the industry is stabilized at the level of output, the returns continue to be the same; and they are said to be constant.

This law can be illustrated by the following example:

 Unit of Labour and Capital Total Production of Fan Marginal Production of Fan 1 2 3 4 5 30 60 90 120 150 30 = (30-0) 30 = (60-30) 30 = (90-60) 30 = (120-90) 30 = (150-120)

From this table it is clear that by increase in the unit of labour and capital, total production increases but the marginal production remains constant i.e., 30 is the constant figure; and this figure is Law of Constant Return.

Diagrammatic Representation:

This Law of Constant Returns can be represented in a diagram as follows:

On OX axis unit of labour and capital and on OY axis marginal production of fan has been shown. AB line is the Law of Constant Return because it shows that in-spite of increase in the unit of labour and capital marginal production of fan is the same. In other-words, here AB line is the Law of Constant Return.

Why Law of Constant Returns?

In every industry, we find the influence of man and nature. Nature controls the supply of raw-materials while man directs the manufacturing side. If there is an industry where the cost of raw-materials and the manufacturing costs are half and half, we can say that both man and nature influence equally. Such an industry would be subject to the Law of Constant Returns. For example – The woolen blanket weaving industry. Here the cost of wool is supposed to cost as much as the other manufacturing costs put in the manufacturing.

Further, if there is an integration of the extractive and manufacturing industries like sugar-making and cane-growing, steel making and iron-ore mining the Law of Constant Returns may operate. Here, the two aspects of the industry are combined, viz., the agricultural aspect which is subject to the law of diminishing returns and the manufacturing aspect which is subject to the Law of Increasing Returns.

It is possible for these two tendencies to counter­balance each other with the result that the Law of Constant Returns may operate. Thus, we find that in every industry there are two tendencies and constantly at work viz., one of diminishing returns and the other of increasing returns. Whenever this scale of production is increased the cost of raw materials and other factors may go up on account of increased demand.

This tends to raise the cost of production per unit or to bring about the operation of the Law of Diminishing Returns. But the larger the scale the greater the economies in the use of machinery, division of labour, buying and selling, research and publicity etc.

In actual life, however, either the tendency of diminishing returns is stronger or the increasing returns tendency is stronger. Thus, the operation of the Law of Constant Returns is rather rare and if at all it operates, it lasts only for a short period of time.

There are mainly two factors which give rise to the Law of Increasing Returns to scale:

1. Indivisibilities of the factors of production.
2. Specialisation of factors of production.