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In a two factor framework, a simultaneous and proportionate change in both inputs brings out a change in output through a change in the scale of production. It is explained in terms of returns to scale or Laws of returns to scale.
They can be expressed when we move from one point to another on an expansion path. In simple words, returns to scale are associated with the rate at which output increases when inputs are increased proportionately or they are associated with the change in scale of operation. However, increase in output is not always in proportion to the change in inputs; it may be more than proportionate, proportionate or, less than proportionate.
To be specific, when quantum of both the inputs is doubled in the production process, output may become more than double or double or less than double. Accordingly, we can explain three laws of returns to scale – increasing, constant and decreasing. To illustrate them, we will use the following Table-8.2.
Table-8.2 presents the case of a firm which follows a technology that requires 10 units of labour and 20 units of capital to produce 40 units of output. To increase output, the firm successively increases both inputs in multiple of 10 units of labour and 20 units of capital. As a result, output increases but not in equal proportion, as can be seen from the table.
Based on increase in output, following observations can be made:
i. Initially every proportionate increase in inputs, up to 40 units of labour and 80 units of capital, results into a more than proportionate increase in output. This situation can be termed as increasing returns to scale.
ii. Subsequent proportionate increase in inputs, up to 60 units of labour and 120 units of capital, results into a proportionate increase in output or a constant returns to scale.
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iii. Finally, further proportionate increase in inputs, up to 80 units of labour and 160 units of capital, results into a less than proportionate increase in output leading to decreasing returns to scale.
Increasing Returns to Scale:
Increasing returns to scale occur when output increases more than proportionately than that of inputs i.e., if both inputs are doubled the output will become more than double. They are also indicative of decreasing costs. Graphically, they can be exhibited on an expansion path or a scale line, as in Figure 8.12.
The figure shows that when all the inputs are doubled (1L + 1K to 2L + 2K) the output became three times (Q to 3Q). Such a change is depicted by the distance along the scale line between successive multiple isoquants (i.e., 100,200,300 and so on) which goes on decreasing (OP > PR > RS) thereby implying that a lesser and lesser increase in inputs will bring a proportionate increase in output.
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Such an increase in output may arise due to many factors which includes:
i. Increase in scale of operation,
ii. A greater division of labour,
iii. Higher degree of specialization, and
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iv. Use of more specialized and productive equipments.
A root cause of increasing returns to scale is the scale economies, which may be internal or external in nature.
Constant Returns to Scale:
Constant returns to scale occur when output increases in the same proportion as the increase in inputs. It means that if all the inputs are doubled, output will also double. It is synonymous with linear homogenous production function or homogenous production function of degree one. Figure-8.13 exhibits constant returns to scale on an isoquant map and scale line.
The figure shows that the successive isoquants are at equi-distant from each other along the scale line i.e., OP = PR = RS, depicting doubling of output as a result of doubling of inputs and so on.
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Such a situation is observed when a firm transits from a state of increasing returns of scale to decreasing returns of scale and, hence, theoretically should prevail for a very short time. However, several empirical studies, especially those related to linear homogenous production function, have shown that most industries operate for long under the conditions of constant returns to scale only.
Decreasing Returns to Scale:
Decreasing returns to scale occur when output increases in a lesser proportion as compared to increase in inputs. It is, thus, synonymous with increasing cost. On a scale line, it is exhibited by a progressively larger distance between successive multiple isoquants, i.e., OP < PR < RS, as shown in Figure-8.14.
It means more and more inputs are required to obtain an equal increment in output.
Decreasing returns to scale arise primarily because of the following:
i. As the scale of operation increases, it becomes more and more difficult to manage the firm. The management becomes over-burdened and hence less efficient in its role as a coordinator and decision maker.
ii. Another cause of decreasing returns to scale can be found in the exhaustible nature of resources, e.g., doubling the inputs in a mining plant may not result in doubling of the output.
Various kinds of diseconomies of scale, also result in such decreasing returns of scale.
Three Kinds of Returns to Scale Simultaneously:
It should be clarified that the above mentioned three different kinds of returns to scale do not apply to three different production functions. They are rather parts of a single production function but observed at three different phases of production.
The three phases can be elaborated as follows:
i. To begin with, when scale of production is increased, the firm extracts benefits from various kinds of economies of scale. This facilitates increasing returns to scale or decreasing cost condition.
ii. After a point, there is a phase of constant returns to scale where output increases in the same proportion as inputs.
iii. If the firm continues to expand beyond this stage, a point will reach where it will suffer from scale diseconomies and will witness decreasing returns to scale or increasing cost conditions.
These three phases are shown graphically in Figure-8.15 in which an expansion path (OA) starting from the point of origin has been depicted. It represents all the three phases.
Following discussion may be carried out on the basis of Figure-8.15:
i. Up to point S on the ray OA, the distance between the successive isoquants showing equal increments in output goes on decreasing. This implies that up to this point, equal increments in output are obtained from the successively smaller increases in inputs (RS < PR < OP). It means that a situation of increasing returns to scale has prevailed.
ii. Between point S and U, equal proportionate increments in output are obtained from successive equal increase in inputs (ST = TU). As such, constant returns to scale are in force.
iii. Beyond point U, the distance between the successive isoquants representing equal increments in output along the ray OA increases. It implies that increasingly more quantities of both inputs are required to obtain an equal amount of output increase successively (UV > VW). It means that diminishing returns to scale are in operation.
It shows that the three phases of increasing, constant and diminishing returns to scale operate on a single production function.
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