<p>I would say it exhibits no returns to scale. What follows is a counter argument to the idea that it can exhibit returns to scale. A 'return to scale' means that production will change in response to a change in the input. A 'constant return to scale' is a straight-line function (or a portion thereof) including the origin (0, 0), with the input on the horizontal axis and the output on the vertical axis. That is, a directly proportional relationship. A 'decreasing return to scale' means that, as more and more of the input is used, production <em>changes</em> with a decreasing effect. This means that the graph will have a gradient that gets more and more flat as the input increases. An 'increasing return to scale' means that production <em>changes</em> with increasing effect as the input increases - a function who's gradient increases.</p>

<p>In conclusion, if the input has no effect on production, there is no 'return' from the input.</p>

CC BY-SA 3.0
2016-11-10T10:17:01.290Z
2016-11-10T10:39:30.720Z
2016-11-10T10:39:30.720Z
ahorn
<p>You want to find a relation between $tF(z)$ and $F(tz)$ for all $t&gt;1$ (or $0$ for CRS). </p>

<p>So since $2t=tF(z)&gt;F(tz)=2$ for all $t&gt;1$, we see decreasing returns to scale.</p>

CC BY-SA 3.0
2016-11-08T17:02:34.120Z
2016-11-08T17:02:34.120Z
Kitsune Cavalry
<p>Suppose we have a production function $f(z)=2$.</p>

<p>I am asked to determine whether the function exhibits increasing, decreasing, constant or no returns to scale.</p>

<p>For $t&gt;0$, $f(tz)=2$.</p>

<p>I'm not sure about the answer: should I say the function exhibits no returns to scale whatsoever or take different values for $t$ ($0&lt;t&lt;1 \implies$decreasing returns to scale, $t=1 \implies$ constant returns to scale, $t&gt;1 \implies$ increasing returns to scale)?</p>

CC BY-SA 3.0
2016-11-08T05:06:57.477Z
You want to find a relation between $tF(z)$ and $F(tz)$ for all $t > 1$ (or 0 for CRS). So since $2t = tF(z) > F(tz) = 2$ for all $t > 1$, we see decreasing returns to scale.
Kitsune Cavalry
CC BY-SA 3.0
2016-11-08T07:13:08.350Z
@KitsuneCavalry If the question was good enough to upvote and answer, then the answer is good enough to post as an answer.
Giskard
<microeconomics><production-function><economies-of-scale>
Returns to scale - Constant Function
Omrane
# Returns to scale - Constant Function

(Asked by: username_0 on 2016-11-08)

Suppose we have a production function $f(z)=2$.

I am asked to determine whether the function exhibits increasing, decreasing, constant or no returns to scale.

For $t>0$, $f(tz)=2$.

I'm not sure about the answer: should I say the function exhibits no returns to scale whatsoever or take different values for $t$ ($0<t<1 \implies$decreasing returns to scale, $t=1 \implies$ constant returns to scale, $t>1 \implies$ increasing returns to scale)?

**Tags:** microeconomics, production-function, economies-of-scale

> **Comments:**
> **username_1**: You want to find a relation between $tF(z)$ and $F(tz)$ for all $t > 1$ (or 0 for CRS). So since $2t = tF(z) > F(tz) = 2$ for all $t > 1$, we see decreasing returns to scale.  
> **username_2**: @username_1 If the question was good enough to upvote and answer, then the answer is good enough to post as an answer.  

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## 2 answers

### Answer by username_1 on 2016-11-08. Score: 5 | Accepted answer

You want to find a relation between $tF(z)$ and $F(tz)$ for all $t>1$ (or $0$ for CRS).

So since $2t=tF(z)>F(tz)=2$ for all $t>1$, we see decreasing returns to scale.


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### Answer by username_3 on 2016-11-10. Score: 1

I would say it exhibits no returns to scale. What follows is a counter argument to the idea that it can exhibit returns to scale. A 'return to scale' means that production will change in response to a change in the input. A 'constant return to scale' is a straight-line function (or a portion thereof) including the origin (0, 0), with the input on the horizontal axis and the output on the vertical axis. That is, a directly proportional relationship. A 'decreasing return to scale' means that, as more and more of the input is used, production *changes* with a decreasing effect. This means that the graph will have a gradient that gets more and more flat as the input increases. An 'increasing return to scale' means that production *changes* with increasing effect as the input increases - a function who's gradient increases.

In conclusion, if the input has no effect on production, there is no 'return' from the input.


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