<p>From your production function: <span class="math-container">$f(K,L)= 1.8(K^{0.6} + L^{0.6})^{2} \Rightarrow f(K,L) = 1.8(K^{1.2} + 2(KL)^{1.2} + L^{1.2})$</span></p>

<p>You are able to see that <span class="math-container">$f(\lambda K, \lambda L) \Rightarrow \lambda^{1.2} f(K,L)$</span>. Say you double both your inputs. Increasing returns to scale tells you that your output will be more than doubled, which is precisely what <span class="math-container">$\lambda^{1.2}$</span> represents. The level of <span class="math-container">$K$</span> and <span class="math-container">$L$</span> does not affect this conclusion.  The point where the level of <span class="math-container">$K$</span> and <span class="math-container">$L$</span> play a "role" is that for levels such that <span class="math-container">$K + L &gt;1$</span> each unit of input results in more than one unit of output (i.e.<span class="math-container">$f(K,L) &gt; 1$</span>) (again note that we are talking about levels here and not changes, which would regard the returns to scale). You can easily see this by plugging in different values into your formula. But, again, this is not to do with the returns to scale of the function so it doesn't pertain the question you are asked. </p>

CC BY-SA 4.0
2020-01-29T17:09:31.173Z
Should it not be $2K^{0.6}L^{0.6}$ instead of $2(KL)^{1.2}$ ?
Bertrand
CC BY-SA 4.0
2019-05-04T15:17:32.860Z
2019-05-04T15:25:44.407Z
2019-05-04T15:25:44.407Z
Ali
<p><a href="https://i.sstatic.net/I8SZE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/I8SZE.png" alt="enter image description here"></a></p>

<p>Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d is wrong. I am unsure between choosing c and d. </p>

<p>Thanks </p>

CC BY-SA 4.0
2019-05-04T14:37:31.343Z
Hint: How did you arrive to the conclusion that the function exhibits increasing returns to scale? Does the level of K + L matter for your conclusion?
Ali
CC BY-SA 4.0
2019-05-04T14:46:35.183Z
@user20105 I deduced increasing returns to scale by doing f(tK, tL) which gives me t^1.2 f(K,L) since t^1.2 is greater than t, I concluded that the returns to scale is increasing.
6.19
CC BY-SA 4.0
2019-05-04T14:48:41.740Z
I am guessing K+L matters because it is a part of the production equation but returns to scale normally relates to their power so I don't really understand what K+L>1 is indicating.
6.19
CC BY-SA 4.0
2019-05-04T14:54:21.173Z
Since $f(\lambda K, \lambda L) \Rightarrow \lambda^{1.2}f(K,L)$, say you double both your inputs. Increasing returns to scale tells you that your output will be more than doubled, which is precisely what $\lambda^{1.2}$ represents. The level of $K + L$ does not affect this conclusion.
Ali
CC BY-SA 4.0
2019-05-04T14:56:07.817Z
@user20105 Thanks a lot for your help. What is the implication of K+L>1 then?
6.19
CC BY-SA 4.0
2019-05-04T15:18:48.127Z
I have added this as an answer but please note that it is always better when asking questions to show your own work and to type in the questions instead of pasting an image!
Ali
<microeconomics><production-function>
Decreasing and increasing returns to scale question
6.19
# Decreasing and increasing returns to scale question

(Asked by: username_0 on 2019-05-04)

[![enter image description here](https://i.sstatic.net/I8SZE.png)](https://i.sstatic.net/I8SZE.png)

Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d is wrong. I am unsure between choosing c and d.

Thanks

**Tags:** microeconomics, production-function
> **Comments:**
> **username_1**: Hint: How did you arrive to the conclusion that the function exhibits increasing returns to scale? Does the level of K + L matter for your conclusion?  
> **username_0**: @user20105 I deduced increasing returns to scale by doing f(tK, tL) which gives me t^1.2 f(K,L) since t^1.2 is greater than t, I concluded that the returns to scale is increasing.  
> **username_0**: I am guessing K+L matters because it is a part of the production equation but returns to scale normally relates to their power so I don't really understand what K+L>1 is indicating.  
> **username_1**: Since $f(\lambda K, \lambda L) \Rightarrow \lambda^{1.2}f(K,L)$, say you double both your inputs. Increasing returns to scale tells you that your output will be more than doubled, which is precisely what $\lambda^{1.2}$ represents. The level of $K + L$ does not affect this conclusion.  
> **username_0**: @user20105 Thanks a lot for your help. What is the implication of K+L>1 then?  
> **username_1**: I have added this as an answer but please note that it is always better when asking questions to show your own work and to type in the questions instead of pasting an image!  

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## 1 answers

### Answer by username_1 on 2019-05-04. Score: 0

From your production function: $f(K,L)= 1.8(K^{0.6} + L^{0.6})^{2} \Rightarrow f(K,L) = 1.8(K^{1.2} + 2(KL)^{1.2} + L^{1.2})$

You are able to see that $f(\lambda K, \lambda L) \Rightarrow \lambda^{1.2} f(K,L)$. Say you double both your inputs. Increasing returns to scale tells you that your output will be more than doubled, which is precisely what $\lambda^{1.2}$ represents. The level of $K$ and $L$ does not affect this conclusion. The point where the level of $K$ and $L$ play a "role" is that for levels such that $K + L >1$ each unit of input results in more than one unit of output (i.e.$f(K,L) > 1$) (again note that we are talking about levels here and not changes, which would regard the returns to scale). You can easily see this by plugging in different values into your formula. But, again, this is not to do with the returns to scale of the function so it doesn't pertain the question you are asked.

> **Comments:**
> **username_2**: Should it not be $2K^{0.6}L^{0.6}$ instead of $2(KL)^{1.2}$ ?  

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