Returns to Scale

Returns to Scale

Meaning

In the run all factors are variable; hence the expansion of output may be achieved by varying all factor-inputs. When we change all factor-inputs in the same proportion, the scale of production is also changed. The study of the effect of change in the scale of production on the amount of output comes under the head of returns to scale.

Thus, the term returns to scale refers to the changes in output as all factor-inputs change by the same proportion in the long run.

Or, in other words, the law expressing the relations between varying scales of production and quantities of output is called returns to scale. In short, returns to scale refer to the effects of scale relationship.

Three Types

Now the question is at what rate the output will increase when all factor- inputs are varied in the same proportion. There can be three possibilities in this regard. The increase in output may be more than, equal to, or less than proportional to the increase in factor-inputs. Accordingly, returns to scale are also of three types-increasing returns to scale, constant returns to scale and diminishing returns to scale.

1.      Increasing Return to Scale 

Increasing Returns to scale refers to a situation where the total output increases in a greater proportion than the increase in units of factor inputs.

   When the increase in output is more than proportionate to the given increase in the quantities of all factor-inputs, it is termed as increasing returns to scale.

   For instance, if the increase in factor-inputs is 100 percent and the resultant increase in output is 150 percent, it is increasing returns to scale. We give an Illustration of increasing returns of increasing return to scale by a diagram. Form O three lines OS, OQ and OR are drawn cutting is the product curve 2, curve 3 at various points. Increasing returns to scale is shown as:

OR  > RP > PG

Or    OR₁  > R₁P₁>  P₁G₁

Or    OR₂ > R₂P₂ > P₂G₂

            It means in this case, a doubling of inputs results in more than doubling of output. It is explained in the following example–

Scale of Production          Total Output      (Machine + Labor)                 (Units)

1Machine + 2 Labor                     100 2Machine + 4 Labor                     250

Causes for the operation of increasing returns to scale

Why does increasing returns to scale operate? The reasons for the operation of increasing returns to scale are found in the form of economics of large-scale production. They are:

(i)      Labor Economies. They are also known as the economies the economies of specialization and division of labor. Division of labour and specialization are possible more in large-scale operation. Different types of works can specialize and do the job for which they are more suited. A worker acquires greater skill by devoting his attention to a particular job. Quality and speed of work both improve. This results in a sharp increase in output per man. Thus in short, with growing scale come, increasing specialization and increasing returns to scale.

(ii)     Technical economies. The main technical economies result from the indivisibilities that are characteristic of the modern industrial techniques of production. Several capital goods, because of the strength and weight required, will work only if they are of a certain minimum size. It may be technically possible to build smaller models of them; but it will not always be possible to use such models. Besides this, there is a general principle that as the size of a capital good is increased, its total output capacity increases far more rapidly than the cost of making it. To double the size and output capacity of a blast furnace for instance, we do not have to double the materials required. This is known as the principle of indivisibility 

(iii)    Marketing Economies. Advertising space (in newspapers and magazines) and time (on television radio) and the number of salesmen do not have to rise proportionately with the sales. Thus the selling cost per unit of output falls with scale. 

(iv)    Managerial Economies. Managerial economies arise from specialization of management and mechanization of managerial function. Large firms make possible the division of managerial tasks. This division of decision-making in large firms has been found very effective in the increase of the efficiency of management. Besides, large firms apply techniques of management involving a high degree of mechanization, such as telephones, telex machines, television screens and computers. These techniques save time and speed up the processing of information's.

     As the business firms continues to expand it gradually exhausts the economies, which cause the operation of, increasing returns to scale. Beyond this point, further increases in the scale of operation are accompanied by constant returns to scale.

(v)      Economies Related to Transport and Storage Costs. Because a large firm uses it’s own transport means and larger vehicles, per units transport costs would fall. Similarly, storage cost will also fall with the size.

As a result of all these economies firm's long run average and marginal cost decline with the increase in output and scale of production.

2-Constant returns to Scale

Thus the constant returns to scale means that if all factor-inputs are varied at a certain percentage rate, output will change by the same rate. 

Or, when the increase in output is proportional to the increase in the quantities of all factor-input; it is termed as constant returns to scale.

The constant returns to scale sometimes referred to by economists in managerial language, a production curve showing constant returns to scale is often called" Linear and homogeneous". The Cobb-Douglas production function evolved by American economists Paul Douglas and C. W. Cobb is a linear and homogeneous function. Following Figure illustrates content returns to scale.

OR = RP = PG

   Or        OR₁ = R₁P₁ = P₁G₁

                       OR₂ = R₂P₂ = P₂G₂

Scale of Production       Total Output      (Machine + Labor)                (Units)

1Machine + 2 Labor                     100 2Machine + 4 Labor                     200

3 Diminishing Returns to Scale

When the increase in output is less than proportionate to the given increase in the quantities of all factor-inputs, it is termed diminishing returns to scale. For instance, if the increase in factor-inputs is 20 percent and the resultant increase in output is less than 20 percent (say 15 percent) or a doubling of inputs causes a less than a doubling of output, it is diminishing returns to scale. This is explained in the following example-  

Scale of Production          Total Output      (Machine + Labor)                 (Units)

1Machine + 2 Labor                    100 2Machine + 4 Labor                    150

The result is diminishing return to scale. Diminishing returns to scale implies that for a given increase in output factor is required. In other words, proportionate increase in input factors will be more than proportionate increase in output. This Fig illustrates the application of diminishing returns to scale. 

Here: -

OR < RP < PG

   Or        OR₁ < R₁P₁ < P₁G₁

                       OR₂ < R₂P₂< P₂G₂