Long -Run Production Function [With All Inputs Variable] /Returns to Scale
Long-Run Production Function[With All Inputs Variable] /Returns to Scale
Returns to Scale measures the increase in output when all
the inputs are increased in the same proportions.
The concept of returns to scale is a long-run phenomenon. It
explains the behavior of output in response to a proportional and simultaneous
change in inputs.
When a firm expands its scale by increasing all the inputs
proportionately, then, there are three technical possibilities, and,
accordingly, there are three kinds of returns to scale:
1. The total output may increase more than proportionately, i.e, increasing returns to scale.
2. The total output may increase proportionately, i.e, constant returns to scale.
3. The total output may increase less than proportionately, i.e, diminishing returns to scale.
Increasing returns to scale: It is said to operate when the firm increases the quantity of all the factors proportionately. It leads to a more than proportionate increase in output. Suppose if all the inputs are increased to double and output increases more than double, then it is said to be increasing returns to scale.
Returns to scale can be explained more clearly with the help of isoquant curves.
In the figure, the scale line[Expansion Path] OP represents different quantities of inputs while the proportion between both factors remain constant. 100 units of output can be produced with the help of the input combination shown by point A. As the output is increased to 200 units, the input combination changes to point B. The distance AB is less than OA in the expansion path. It means that a 100 unit increase in output now requires a relatively lesser increase in inputs than the previous. Further the output increases by 300,400,500, and 600 units, the factor input combination points shift to C, D, E, F representing the lesser quantity of inputs. The distance between the factor combination points goes on gradually decreasing.[OA>AB>BC>CD>DE>EF] It shows that the additional inputs required to produce a proportionate increase in output, decline.
It can also be shown through input-output relation through the total product curve.
There are many reasons for increasing returns to scale which are as follows:
1- As the scale of production increases, it gives the possibilities for the proper utilization of equipment, machinery, and techniques to increase output and reduce cost.
2- As the scale of operation increases, the labor can be trained and assigned to the specialized task for which he best suited and able to acquire additional expertise by repetitive experiences.
3- Specialized machines are generally more productive than less specialized machines. The capacity of these machines is very large and can be used only for large output. When the scale increases, it becomes feasible to utilize its capacity properly and maximize the output at a minimum cost.
4- The concept of indivisibility has a close bearing on the law of increasing returns. When the scale of production is expanded by increasing all inputs, the productivity of indivisible factors increases exponentially and it results in increasing returns.
5- As output increases, it becomes possible to enjoy internal and external economies of scale-like financial, marketing, and risk-bearing economies, etc. It reduces the cost of production and results in increasing returns.
Constant returns to scale: When the change in output is proportional to the change in inputs, it exhibits constant returns to scale. Suppose if all the inputs are increased to double and output also increases exactly double, then it is said to be constant returns to scale. It is also said the linear homogeneous production function. It shows that with constant returns to scale, there will be one input proportion that remains constant.
Constant returns to scale will operate when internal and external economies reach their limits and diseconomies are yet to begin. It also takes place where factors of production are perfectly divisible and the capital-labor ratio is fixed.
From this diagram, it is clear that as the output is increased to 200 units, the input combination changes to point B. The distance AB is equal to OA in the expansion path. The distance between the factor combination points are equal [OA=AB=BC=CD=DE=EF] It shows that a proportionate increase in inputs yields a proportionate increase in output.
In this diagram, TP curve is a straight line that shows that the same quantity of inputs is required to get the same level of output.
Diminishing returns to scale: When a certain proportionate change in inputs leads to a less than proportionate change in output, it results in diminishing returns to scale. Suppose if all the inputs are increased to double and output increases less than double, then it is said to be diminishing returns to scale.
It shows that a proportionate increase in output requires a more than proportionate increase in inputs.
From this diagram, TP curve is bending towards the X-axis that shows that a more quantity of inputs is required to get the same level of production.
Causes for diminishing returns to scale:
1. The Law of Diminishing Returns operates because of the wrong combinations of the factors. When the fixed factor reaches its maximum capacity and there is no further possibility of the specialization of the variable factor, it results in diminishing returns.
2. It operates because of inefficient and mismanagement due to overgrowth and expansion of the firm.
3. As a firm increases its scale of operations, it becomes difficult to co-ordinate, control, and manage the firm properly.
4. It operates due to the scarcity of the factors of production.
5. It also arises because the factors of production are imperfect substitutes for one another. In other words, the elasticity of substitution between factors is not infinite.
When the firm increases the scale by increasing all the factors of production in the same proportion, the marginal product increases at first, then constant, and ultimately start decreasing for the further increases in the scale of production.
Thus, there are three stages in the behavior of the marginal product.
It will be clear more with the numerical example given below:
The above diagram depicts the marginal product curve which goes upwards from A to B, showing increasing returns to scale. From B to C, it is horizontal, showing constant returns to scale, and from C to D, downwards going slope, showing the diminishing returns to scale.
The concept of returns to scale helps the producer to select the most favorable combination of inputs so that he can able to maximize the output with a minimum cost of production.
TP curve is bending towards the y-axis which shows that less quantity of inputs is required to get the same level of production.
1- As the scale of production increases, it gives the possibilities for the proper utilization of equipment, machinery, and techniques to increase output and reduce cost.
2- As the scale of operation increases, the labor can be trained and assigned to the specialized task for which he best suited and able to acquire additional expertise by repetitive experiences.
3- Specialized machines are generally more productive than less specialized machines. The capacity of these machines is very large and can be used only for large output. When the scale increases, it becomes feasible to utilize its capacity properly and maximize the output at a minimum cost.
4- The concept of indivisibility has a close bearing on the law of increasing returns. When the scale of production is expanded by increasing all inputs, the productivity of indivisible factors increases exponentially and it results in increasing returns.
5- As output increases, it becomes possible to enjoy internal and external economies of scale-like financial, marketing, and risk-bearing economies, etc. It reduces the cost of production and results in increasing returns.
Constant returns to scale: When the change in output is proportional to the change in inputs, it exhibits constant returns to scale. Suppose if all the inputs are increased to double and output also increases exactly double, then it is said to be constant returns to scale. It is also said the linear homogeneous production function. It shows that with constant returns to scale, there will be one input proportion that remains constant.
Constant returns to scale will operate when internal and external economies reach their limits and diseconomies are yet to begin. It also takes place where factors of production are perfectly divisible and the capital-labor ratio is fixed.
From this diagram, it is clear that as the output is increased to 200 units, the input combination changes to point B. The distance AB is equal to OA in the expansion path. The distance between the factor combination points are equal [OA=AB=BC=CD=DE=EF] It shows that a proportionate increase in inputs yields a proportionate increase in output.
Diminishing returns to scale: When a certain proportionate change in inputs leads to a less than proportionate change in output, it results in diminishing returns to scale. Suppose if all the inputs are increased to double and output increases less than double, then it is said to be diminishing returns to scale.
From the above diagram, it is clear that as the output is increased to 200 units, the input combination changes to point B. The distance AB is more than OA in the expansion path. The distance between the factor combination points goes on increasing [OA<AB<BC<CD<DE<EF]
It shows that a proportionate increase in output requires a more than proportionate increase in inputs.
From this diagram, TP curve is bending towards the X-axis that shows that a more quantity of inputs is required to get the same level of production.
Causes for diminishing returns to scale:
1. The Law of Diminishing Returns operates because of the wrong combinations of the factors. When the fixed factor reaches its maximum capacity and there is no further possibility of the specialization of the variable factor, it results in diminishing returns.
2. It operates because of inefficient and mismanagement due to overgrowth and expansion of the firm.
3. As a firm increases its scale of operations, it becomes difficult to co-ordinate, control, and manage the firm properly.
4. It operates due to the scarcity of the factors of production.
5. It also arises because the factors of production are imperfect substitutes for one another. In other words, the elasticity of substitution between factors is not infinite.
When the firm increases the scale by increasing all the factors of production in the same proportion, the marginal product increases at first, then constant, and ultimately start decreasing for the further increases in the scale of production.
Thus, there are three stages in the behavior of the marginal product.
It will be clear more with the numerical example given below:
|
Laws of Returns to Scale |
||||
|
Serial No. |
Scale |
Total Product in Units |
Marginal Product in Units |
3 Stages |
|
1 |
I Capital + 3
Worker |
6 |
6 |
Stage-1: Increasing Returns |
|
2 |
2 Capital + 6
Worker |
15 |
9 |
|
|
3 |
3 Capital + 9
Worker |
25 |
10 |
|
|
4 |
4 Capital + 12
Worker |
36 |
11 |
|
|
5 |
5 Capital + 15
Worker |
47 |
11 |
Stage-2: Constant Returns |
|
6 |
6 Capital + 18
Worker |
58 |
11 |
|
|
7 |
7 Capital + 21
Worker |
65 |
7 |
Stage-3: Decreasing Returns |
|
8 |
8 Capital + 24
Worker |
70 |
5 |
|
The above diagram depicts the marginal product curve which goes upwards from A to B, showing increasing returns to scale. From B to C, it is horizontal, showing constant returns to scale, and from C to D, downwards going slope, showing the diminishing returns to scale.
The concept of returns to scale helps the producer to select the most favorable combination of inputs so that he can able to maximize the output with a minimum cost of production.
Dr. Swati Gupta
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