Law of Returns to Scale : Variation of Output in the Long Run

    Law of Returns to Scale  

     In the long run all factors of production are variable as the firm has sufficient time to make adjustment in all the factors of production. However, in the long – run, output can be increased by changing all the factors of production in the same proportion or in different proportions.

       When all inputs are changed in the same proportion, we call this as change in the scale of production. The way total output changes due to change in the scale of production is known as the “law of returns to scale”.

   Definition:

      ” The term returns to scale refers to the change in output as all factors change by the same proportion”. …..Koutsoyiannis

    “Returns to scale relates to the behaviour of total output as all inputs are varied and is a long run concept”….. Leibhafsky

    

   Assumption :

     This law is based on the following assumptions :

   1. All the factors of production (such as land, labour, and capital) but organisation are variable.

  2. The law assumes a constant  technological state. It means that there is no change in technology during the time considered.

  3.  The market is perfectly competitive. 

  4. Outputs or returns are measured in physical terms.

     Three Phases of Returns to Scale:

              According to the law of Returns to scale, when all the factor inputs are varied in the same proportion, then the scale of production may take three forms:

    1. Increasing Returns to Scale

   2. Constant Returns to Scale

   3. Diminishing Returns to Scale 

   1. Increasing Returns to Scale  :

     In the first stage of Returns to Scale, the proportionate increase in the output is more than the proportionate increase in inputs.

      For example, if all inputs are increased by 100 percent and the output increases by more than 100 Percent (say 150 %) the increasing returns to scale will operate.

   Example :

SN	Inputs (Units)	Output (Units)
1.	1 Capital + 1 Labour	100
2.	2 Capital +  2 Labour	250

 

       The main reason behind increasing Returns to Scale is Economies of Large Scale. 

 Economies mean the benefits because of the large scale of production. Economies of scale are of two types – 

  Internal Economies and External Economies.

     Internal Economies:

       Internal economies means the benefits of large scale production available to an organisation with in its own operation, eg. Managerial economies are achieved by dividing labour and specialisation.

    External Economies :

      External economies means the benefits of large scale production shared by all the firms of an industry when the industry as a whole expands, eg. Better infrastructural facilities, better transportation etc.

  

  2. Constant Returns to Scale:

   In the second stage of Returns to Scale, the proportionate increase in the total output is equal to the proportionate increase in inputs.

    Thus, if all inputs are increased by 100 percent and as a consequence output also increases by 100 percent, returns to scale are constant.

   Example:

SN	Inputs (Units)	Output (Units)
1.	1 Capital +  1 Labour	100
2.	2 Capital + 2 Labour	200

 

        Once the firm has achieved the point of optimum capacity, it operates on constant Returns to Scale. After the point of optimum capacity, the economies of production are counterbalanced by the diseconomies of production.

    3. Diminishing Returns to Scale:

      In the third stage of Returns to Scale, the proportionate increase in the total output is less than the proportionate increase in inputs.

     Thus, if all the inputs increases by 100 percent, then the increase in output will be less than 100 percent (say by 50%), decreasing returns to scale will operate.

   Example:

SN	Inputs (Units)	Output (Units)
1.	1 Capital +  1 Labour	100
2.	2 Capital + 2 Labour	150

 

      The main reason behind diminishing returns to scale is Diseconomies of Large Scale. Diseconomies of scale means that it has become difficult to manage its operations.  Diseconomies of Scale are of two types like – 

   Internal Diseconomies and External Diseconomies.

     Internal Diseconomies:

     Internal diseconomies means the disadvantage of large scale production that a firm has to suffer because of its own operations. For example: technological diseconomies because of the heavy cost of wear and tear.

     External Diseconomies:

    External diseconomies means the disadvantage of large scale production that all the firms of the industry have to suffer when the industry as a whole expands. For example, stiff competition etc.

  

   Question : Give a comparison between the Law of Variable Proportions and Returns to Scale.

 Answer:  

    Comparison between Law of Variable Proportion and Returns to Scale : 

    1. The ‘Law of Variable Proportions’  relates to  “Returns  to a Factor” where as the ‘Returns to Scale’ relate to  the“Scale of Production”.

   Returns to a factor means the change in output when the quantity of one factor is changed, remaining other factors constant.

   Returns to Scale, means change in the physical output when the quantity of all the factors is increased simultaneously and in the same proportions.

  2. The ‘Law of Variable Proportions’ studies the effect of change in one input on the output, whereas ‘Returns to Scale’ studies the effect of change in all inputs on the output.

  3. The ‘Law of Variable Proportions’ is a short – run phenomenon, whereas the ‘Returns to Scale’ is a long – run phenomenon.

   

   4. The ‘Law of Variable Proportions’ takes account of the “change in factor proportions”. Whereas ‘Returns to Scale’ takes “factor proportions to be unchanged”. 

 

Distinction between Returns to a Factor and Returns to Scale:   

SN	Returns to a Factor	Returns to Scale
1.	Quantity of only one factor is changed i.e. only one factor is variable	Quantity of all the factor inputs is changed i.e. all the factors are variable.
2.	Operates in the short – run. It is associated with the notion of short -run production function.	Operates in the long -run. It is associated with the long – run production function.
3.	Factor proportion changes.	Factor proportion remains the same.
4.	No change in the scale of production.	Change in the scale of production.