Returns to Scale

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Returns to Scale

If all inputs are changed simultaneously (possible only in the long run), and say increased proportionately, then the concept of returns to scale has to be used to understand the behaviour of output. The behaviour of output is studied when all factors of production are changed in the same direction and proportion.
In the long run, output can be increased by increasing the ‘scale of operations’. When we speak of increasing the ‘scale of operations’ we mean increasing all the factors at the same time and by the same proportion. For example, in a factory, in the long run, the scale of operations may be increased by doubling the inputs of labour and capital. The laws that govern the scale of operation are called the laws of returns of scale.
The laws of returns to scale always refer to the long run because only in the long run are all the factors of production variable. In other words, only in the long run is it possible to change all the factors of production. Thus the laws of returns to scale refer to that time in the future when changes in output are brought about by increasing all inputs at the same time and in same proportion.
Returns to scale are classified as follows:
Increasing Returns to Scale (IRS): If output increase more than proportionate to the increase in all inputs.
Constant Returns to Scale (CRS): If all inputs are increased by some proportion, output will also increase by the same proportion.
Decreasing Returns to Scale (DRS): If increase in output is less than proportionate to the increase in all inputs.
For example, if all factors of production are doubled and output increases by more than two times, then the situation is of increasing returns to scale. On the other hand, if output does not double even after a cent per cent increase in input factors, we have a diminishing returns to scale.
The general production function is:
Q = f (L, K)
If land, K, and labour, L, is multiplied by h and Q increases by  , we get,
Q = f(hL, hK)
We have constant, increasing or decreasing returns to scale, respectively depending upon, whether  = h,  > h or  < h.
For example, if all inputs are doubled, we have constant, increasing or decreasing returns to scale, respectively, if output doubles, more than doubles or less than doubles (Figure 6.8).
The firm increases its inputs from 3 to 6 units (K, L) producing either double (point B), more than double (point C) or less than double (point D) output (Q).
Increasing returns to scale arise because as the scale of operation increases, a greater division of labour and specialisation can take place and more specialised and productive machinery can be used. Decreasing returns to scale, arise primarily because as the scale of operation increases, it becomes more difficult to manage the firm. In the real world, the forces for increasing or decreasing returns to scale often operate side by side, with the former usually overwhelming the latter at small levels of output and the reverse occurring at very large levels of output.
If all the factors of production are increased in a particular proportion and the output increases in exactly that proportion then the production function is said to exhibit CRS. Thus if labour and capital are increased by 10% and the output also increases by 10% then the production function is CRS.
If you look at Figure 6.9, to produce X units of output, L units of labour and K units of capital are needed (point a). If labour and capital are now doubled (as is possible in the long run), so that there are 2L units of labour and 2K units of capital, the output is exactly doubled i.e., equals 2X (point b). Similarly, trebling input achieves treble the output and so on.
If all the factors of production are increased in a particular proportion and the output increases by more than that proportion then the production function is said to exhibits IRS. For example, in many industrial processes if all inputs are doubled, factories can be run in more efficient and effective ways, there by actually more than doubling output. If the factors of production are increased in a particular proportion and the output increases by less than that proportion than the production function is said to exhibit DRS. For example, if capital and labour are increased by 10% and output rises by less than 10% the production function is said to exhibits decreasing returns to scale.
If you look at Figure 6.11, to produce X units of output L units of labour and K units of capital are required. By doubling the input, the output increases by less than twice its original level. For example, if inputs are 2L and 2K, output level a is reached, which lies below the one showing 2X.
Causes of Increasing Returns to Scale: Increasing returns to scale are due to technical and/or managerial indivisibilities. One of the basic characteristics of advanced industrial technology is the existence of mass production methods. Mass production methods (like the assembly line car industry) are processes available only when the level of output is large. They are more efficient than the best available processes for producing small levels of output. For example, increasing returns of scale may occur because each worker has specialised in performing a simple repetitive task rather than many different tasks. As a result labour productivity increases. In addition, a larger scale of operation may permit the use of more productive specialised machinery, which was not feasible on a lower scale of operation.
Cause of Decreasing Returns to Scale: The most common causes are “diminishing returns to management”. The management is responsible for the coordination of the activities of the various sections of the firm. Even when authority is delegated to individual managers (production manager, sales manager, etc.) the final decisions have to be taken by the board of directors. As the output grows, top management becomes eventually overburdened and hence less efficient in its role as coordinator and ultimate decision-maker. Although advances in management science have developed numerous management techniques, it is still a commonly observed fact that as firms grow beyond the appropriate optimal, management diseconomies creep in. These may result because as the scale of operations increases, communication difficulties make it more and more difficult to run the business effectively.
Another cause for decreasing returns may be found in the exhaustible natural resources: doubling the fishing fleet may not lead to a doubling of the catch of fish; or doubling the plant in mining or an oil extraction field may not lead to a doubling of output.