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Distinguish between Returns To Scale & Returns To Variable Factor.
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 shortrun and longrun.
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.


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 