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Distinguish between Returns To Scale & Returns To Variable Factor. 

Posted- 2301 days ago
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The difference between returns to a variable factor and returns to scale flow from the Law of Diminishing Returns and must be understood in the parameters of the concepts of short-run and long-run.

Short run is a period when production can be increased only with increase in variable factors because fixed factors are constant; the firms cannot change their sizes and scales in the short run. When output  is increased by more quantities of variable factors with the fixed factor held constant, the the proportion between the fixed and variable factos changes and the change in output  follows the Law of Variable Proportions  in terms of which initially the total rises at a higher rate, then  it become constant because marginal product reaches zero and eventually it falls.  This locus of the marginal product (MP) i.e. incremental output is called the Law of Variable Proportions.

Long run is defined as a period which allows the firm  to change their sizes and scales to increase output  i.e. in the long run all factors are variable but even in this case initially there are increasing returns to scale i.e. the total output rises with fast speed, then it becomes constant and eventually the total output falls because marginal product  (MP) becomes negative.  This situation is subservient to the Law of Diminishing Returns to Scale.

The above material explains the effierence between the returns to a factor (which is in the shot run) and returns to scale (which refers to the long run).  This is very importaant and a fvourtine question of the examiners. 

law of return to variable  law of return to scale
it is in shortperiod it is in long period
only one factor varied  all factors varied
the factor ratio remains unchanged  the factor ratio changes

all the 3 stages doesn't appear.diminishing return will appear

all the 3 stages will appear
returns to factor returns to scale
this law is applicable in the short period this law is applicable in the long period
at least some factors of production are fixed  and only  other factors are varying all the factors of production are varying
the factor inputs are not changed in the same propotion the factor inputs are changed in the same propotion

there are three stages:

increasing returns to factor

diminishing returns to factor

negative returns to factor

there are three stages:

increasing returns to scale

decreasing returns to scale

constant returns to scale

production is of variable propotion type production is of constant propotion type
scale of producion is changed scale of production is not changed