# Can You Explain The Law Of Return To Scale?

Returns to scale
In production, returns to scale refers to changes in output subsequent to a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRTS). If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportion, there are increasing returns to scale (IRS)

Short example: Where all inputs increase by a factor of 2, new values for output should be:

Twice the previous output given = a constant return to scale (CRTS)

Less than twice the previous output given = a decreased return to scale (DRS)

More than twice the previous output given = an increased return to scale (IRS)

Assuming that the factor costs are constant, a firm experiencing CRTS will have constant average costs, a firm experiencing DRS will have increasing average costs and a firm experiencing IRS will have decreasing average costs.
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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.
thanked the writer.