Can You Explain The Law Of Return To Scale?

As we know that law of variable of proportion such law is concerned with short run
Q = f (L) while capital is kept constant this law is based upon three laws of production, increasing returns, constant returns, and decreasing returns. But we have long run situation also where both labor and capital are variable, Q= f (L, K) in this situation when firms changes both labor and capital the effects of production will be analyzed with the name of returns to scale. There will be the operation of the increasing return to scale, constant return to scale and decreasing return to scale. Before analyze them we present the concept of homogeneous production function.

This is production function where each factor input is multiplied by a constant (K) then the constant is completely factored out. We take the long run P.F.
Q= f (L, K).
Multiplying it by K and giving it the name of Qn.
Qn= f (kL, kK).
Qn= kf (L, K).
The last expression show that new level of output Qn= to the multiple of original level of output (f (L, K)) and a constant k.
Thus the function where k can be completed be factored out is known as homogeneous factor production function. While the production functions where K cannot be factored out is known as homogeneous production function.

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