# MU OER PORTAL/Temp/Returns to scale.doc

• Definition

The law of returns to scale describes the relationship between outputs and the scale of inputs in the long-run when all the inputs are increased in the same proportion.

According to the Roger Miller, the law of returns to scale refers “to the relationship between the changes in output and proportionate change in all factors of production”. The firm increases its scale of production by using more space, more machines and labourers (as a input) in the factory, to meet a long-run change in demand.

• Law of returns to Scale:

The laws of returns to scale are often confused with ‘returns to scale’. By “returns to scale” is meant the behaviour of production or returns when all productive factors are increased or decreased simultaneously and in the same ratio.

When all inputs are changed in the same proportion, we call this as a change in scale of production. The way total output changes due to change in the scale of production is known as returns to scale.

Thus, whereas in the short-run change in output is associated with the change in factor proportions, and change in output in the long-run is associated with change in the scale of production. Thus returns to scale is the long-run concept.

A layman would perhaps expect that with doubling of all productive factors, the output will also double and with trebling of factors of production, production would also be trebled, and so on. But actually this is not so. In other words, when all inputs are increased in the same proportion, the total product may increase at an increasing rate, ar a constant rate or diminishing rate. Accordingly the returns to scale could be ‘increasing, ‘constant’, or ‘decreasing’.

• Assumptions:
1. All factors (inputs) are variable but enterprise is fixed.
2. A worker works with given tools and implements.
3. Technological changes are absent.
4. There is perfect competition.
5. The product is measured in quantities.
• So now let us examine three different cases;
1. Increasing returns to scale
1. Constant returns to scale and
1. Decreasing returns to scale.
1. Increasing returns to Scale:

This situation occurs if a percentage increases in all inputs results in a greater percentage change in output. For e.g. a 10 % increase in all inputs causes a 20% increase in output.

By increasing its scale, the firm may be able to use new production methods that were infeasible at the smaller scale. For instance, the firm may utilize sophisticated, highly efficient, large-scale factories. It also may find it advantageous to exploit specialization of labour at the large scale. This is shown in the following example.

 Inputs (Units) Output (Units) 2 capital + 2 Labour 200 4 Capital + 4 Labour 500

The table shows that the input is increasing by 100%, on the other hamd the output is increased by 150%. This shows the increasing returns to scale. As changes in the output is more than the change in input.

• Causes of Increasing Returns to scale
1. Indivisibilities: According to economist like Kaldor, learner, knight and Joan Robinson, an important cause of indivisibility. Indivisibility means that certain factors are available only in some minimum sizes. Certain inputs particularly machinery, management etc. are available in large and lumpy units. Such inputs cannot be divided into small sizes to suit the small scale of production. For e.g. there cannot be half a machine, half a computer or half a manager. Such inputs have to be employed even if the scale of production is small. Therefore, as the scale of production increases, these indivisible factors are utilized better and more efficiently. This leads to increasing returns to scale.
1. Greater Specialization: As the scale of production increases, the efficiency of labour increases due to division of labour and specialization of labour. Similarly, when the scale of production increases, it becomes possible to use specilaised machines and the services of specialized and expert management.

This results in productivity of inputs leading to increasing returns to scale. According to Prof. Chamberlin returns to scale in the initial stages increases due to the fact that the firm can introduce the specialization of labour and machinery.

1. Constant returns to Scale

Constant returns to Scale: It occurs if a given percentage change in all inputs results in an equal percentage in output. For instance, if all inputs are doubled, output also doubles; a 10% increase in inputs would imply a 10% increase in output; and so on. Under constant returns, the firm’s input are equally productive whether or smaller or larger levels of output are produced.

A common example of constant returns to scale occurs when a firm can easily replicate its production process.

For, instance a manufacturer of electrical company finds that it can double its output by replicating its current plant and labour force, that is, by building an identical palnt beside the old one.

Similarly, chain of dry cleaners can increase its volume of service by increasing its number of outlets (with designated number of workers per outlets). So long as all necessary inputs are readily available the firm can increase in proper proportion to inputs via replication, and constant returns to scale will hold. This can be explained in the following example.

 Inputs (Units) Output (Units) 2 capital + 2 Labour 200 4 Capital + 4 Labour 400

The above example shows that as the inputs (i.e. labour and capital) increased to 100%, output also increased to 100%.

• Causes of constant Returns to scale
1. Limits of Economies of scale: Increasing returns to Scale cannot go on indefinitely. There is a limit to these economies of scale When the economies of scale are exhausted and diseconomies are yet to start, there may be a briefs phase of constant returns to scale.
1. Economies of Scale: It refers to the situation which increases in the scale of production give rise to certain benefits to the producers.
1. Divisibility of Inputs: Constant returns to scale may occur in certain productive activities where the factors of production are perfectly divisible. For example, we may double the output by setting up two plants (factories) which use the same quantity and the same type of workers, machinary, raw materials and other inputs.
1. Decreasing Returns to scale:

It occurs if a given percentage increase in all inputs results in a smaller percentage increase in output. The most common explanation for decreasing Returns involves organization factors in very large firms. As the scale of firms increases, the difficulties in Coordinating and monitoring the many management functions. Coordinating production and distribution of 12 products manufactured in four separate plants typically means incurring additional costs tor management and information systems that would be unnecessary in a firm one-quarter size. As a result, proportional increases in output require more than proportional increases in inputs. The following example will explain decreasing returns to scale.

 Inputs (Units) Output (Units) 2 capital + 2 Labour 200 4 capital + 4 Labour 300

The above shows, that inputs ate increases to 100% but the increase output is 50%, which shows that there is decreasing returns to scale.

• Causes of Decreasing Returns to scale.
1. Complexity of management: Increase in the scale of production on beyond a point may create the problem of proper management, leading to a decrease in managerial efficiency. Large scale of production creates the problem of lack of proper, larger bureaucracy, red tapism, lengthy Chain of Communication and command between the top management and men on the production line. As a consequence of all these, the overall efficiency of management decreases.
1. Entrepreneur is a fixed factor: According to some economist decreasing returns to scale arise because entrepreneur is a fixed and indivisible factor. An increase in scale may come to a point where the abilities and Skills of the entrepreneur may be fully utilised. An increase in the scale beyond this point may decrease the efficiency of the entrepreneur. This gives rise to diseconomies of scale.
1. Exhaustibility of Natural Resources: Another factor responsible for the diminishing returns in some activities is the limitation of natural sources. For example, if we double the fishing fleet, the number of fish Catch will not double because the availability of fish may decrease when fishing is carried out on an increasing scale.