<p>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. </p>

<p>For example: </p>

<ol>
<li>$f(L) = L^2$ exhibits increasing returns to scale. </li>
<li>$f(L) = L$ exhibits constant returns to scale</li>
<li>$f(L)= L^{\frac{1}{2}}$ exhibits decreasing returns to scale</li>
</ol>

<p>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. </p>

CC BY-SA 3.0
2018-02-18T16:13:27.230Z
2018-02-18T16:13:27.230Z
123
<p>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.</p>

CC BY-SA 3.0
2018-02-18T20:18:22.200Z
2018-02-18T20:18:22.200Z
akshit arora
<p>For $Y=F(K,L)= 2L$</p>

<p>If I multiply them by an constant $z$:</p>

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

<p>This doesnt seem right because the outputs are determined by one variable.</p>

CC BY-SA 3.0
2018-02-18T15:37:45.080Z
So? As long as the definition is satisfied it is satisfied.
Giskard
<production-function>
Is it constant returns to scale if the output of a production function is purely a function of one variable?
Azman
# Is it constant returns to scale if the output of a production function is purely a function of one variable?

(Asked by: username_0 on 2018-02-18)

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.

**Tags:** production-function
> **Comments:**
> **username_1**: So? As long as the definition is satisfied it is satisfied.  

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## 2 answers

### Answer by username_2 on 2018-02-18. Score: 4

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.


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### Answer by username_3 on 2018-02-18. Score: 0

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.


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