For $Y=F(K,L)= 2L$

If I multiply them by an constant $z$:

$Y= F(zK,zL0)$, i'll get $2(zL) = z(2L)$. Inputs increase proportionally therefore constant returns to scale.

This doesnt seem right because the outputs are determined by one variable.

  • $\begingroup$ So? As long as the definition is satisfied it is satisfied. $\endgroup$
    – Giskard
    Feb 18 '18 at 15:37

Returns to scale is a concept that we use to think about how output changes as we continually add more inputs. It does not matter if your production function takes one input or $N$ inputs. All that matters is how inputs behave within the function itself. Another way to think about this is to consider that a production function with a single input can exhibit decreasing, constant, or increasing returns to scale.

For example:

  1. $f(L) = L^2$ exhibits increasing returns to scale.
  2. $f(L) = L$ exhibits constant returns to scale
  3. $f(L)= L^{\frac{1}{2}}$ exhibits decreasing returns to scale

Your production function is linear in its one input [case number 2 above] and so it exhibits constant returns to scale. That is, the answer to your question is yes.


Return to scale is a long run concept and as underlying production function is dependent upon a single variable i.e. labour so there must be discussion upon whether it is a increasing returns to a factor or constant return to a factor. Because it is only short run in which we have one input and other inputs are fixed.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.