Law of Returns to a Scale (Long Run Production Analysis) through the use of ISO QUANTS

The laws of returns to scale can also be explained in terms of the isoquant approach. The laws of returns to scale refer to the effects of a change in the scale of factors (inputs) upon output in the long-run when the combinations of factors are changed in some proportion.

If by increasing two factors, say labour and capital, in the same proportion, output increases in exactly the same proportion, there are constant returns to scale.

If in order to secure equal increases in output, both factors are increased in larger proportionate units, there are decreasing returns to scale. If in order to get equal increases in output, both factors are increased in smaller proportionate units, there are increasing returns to scale.

The returns to scale can be shown diagrammatically on an expansion path “by the distance between successive ‘multiple-level-of-output’ isoquants, that is, isoquants that show levels of output which are multiples of some base level of output, e.g., 100, 200, 300, etc.”

1. Increasing Returns to Scale

Figure shows the case of increasing returns to scale where to get equal increases in output, lesser proportionate increases in both factors, labour and capital, are required. It follows that in the figure

The increasing returns to scale are attributed to the following factors:

1. There may be indivisibilities in machines, management, labour, finance, etc. Some items of equipment or some activities have a minimum size and cannot be divided into smaller units. When a business unit expands, the returns to scale increase because the indivisible factors are employed to their full capacity.
2. Increasing returns to scale also result from specialisation and division of labour. When the scale of the firm expands, there is wide scope for specialisation and division of labour. Work can be divided into small tasks and workers can be concentrated to narrower range of processes. For this, specialized equipment can be installed. Thus with specialization, efficiency increases and increasing returns to scale follow.
3. 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.
4. 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.

100 units of output require 3C + 3L

200 units of output require 5C + 5L

300 units of output require 6C + 6L

so that along the expansion path OR, OA > AB > BC. In this case, the production function is homogeneous of degree greater than one.

2. Decreasing Returns to Scale

Figure shows the case of decreasing returns where to get equal increases in output, larger proportionate increases in both labour and capital are required. It follows that

100 units of output require 2C + 2L

200 units of output require 5C + 5L 300 units of output require 9C + 9L so that along the expansion path OR, OG < GH < HK.

In this case, the production function is homogeneous of degree less than one.

Returns to scale may start diminishing due to the following factors:         

1. Indivisible factors may become inefficient and less productive.
2. The firm experiences internal diseconomies. Business may become unwieldy and produce problems of supervision and coordination. Large management creates difficulties of control and rigidities.
3. 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.

3. Constant Returns to Scale

Figure shows the case of constant returns to scale. Where the distance between the isoquants 100, 200 and 300 along the expansion path OR is the same, i.e., OD = DE = EE It means that if units of both factors, labour and capital, are doubled, the output is doubled. To treble output, units of both factors are trebled. It follows that

100 units of output require 1 (2C + 2L) = 2C + 2L

200 units of output require 2(2C + 2L) = 4C + 4L

300 units of output require 3(2C + 2L) = 6C + 6L

Returns to scale are constant due to the following factors:

1. The returns to scale are constant when internal economies enjoyed by a firm are neutralized by internal diseconomies so that output increases in the same proportion.
2. Another reason is the balancing of external economies and external diseconomies.
3. Constant returns to scale also result when factors of production are perfectly divisible, substitutable, and homogeneous and their supplies are perfectly elastic at given prices.

That is why, in the case of constant returns to scale, the production function is homogeneous of degree one.