<p><strong>Hint</strong>: find <span class="math-container">$\ln(U(x))$</span> and then use L'Hopital's rule to find the limit as <span class="math-container">$\rho\rightarrow0$</span>. </p>

CC BY-SA 4.0
2019-11-26T19:04:24.637Z
2019-11-26T19:04:24.637Z
Hal_Incandenza
<p><strong>hint:</strong> you are supposed to show the utility function represents the same preferences not that the utility functions are exactly same. Recall that any monotonic transformations of function preserves the original order of preferences. So you only need to show that in the limit one function is monotonic transformation of the other.</p>

CC BY-SA 4.0
2019-11-25T13:18:59.630Z
well actually I tried to use ln to show it but I couldn't find the relation that's what I asked it here, I guess I asked the wrong question
Aisa.Imn
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2019-11-25T12:22:36.060Z
2019-11-25T12:22:36.060Z
1muflon1
<p>This is the question, I have problem with part b, I don't know what function should I use to reach the result
thanks in forward
<a href="https://i.sstatic.net/ZgsW1.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZgsW1.png" alt="enter image description here"></a></p>

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2019-11-25T14:27:19.250Z
Hi, Welcome to Economics SE! we have a policy regarding homework questions where users must demonstrate effort using text, markdown syntax and/or images space provided in the text of his question submission for the site. Using only images as proof of work is insufficient. for more details see:https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions
EconJohn
CC BY-SA 4.0
2019-11-25T18:35:00.527Z
Possible duplicate of [How can I obtain Leontief and Cobb-Douglas production function from CES function?](https://economics.stackexchange.com/questions/361/how-can-i-obtain-leontief-and-cobb-douglas-production-function-from-ces-function)
Herr K.
<microeconomics><utility>
How can I prove $U(x) = [_1_1^+_2_2^]^{(1/)}$ is equal to Cobb-douglas Utility function when $\rightarrow0$
Aisa.Imn
# How can I prove $U(x) = [_1_1^+_2_2^]^{(1/)}$ is equal to Cobb-douglas Utility function when $\rightarrow0$

(Asked by: username_0 on 2019-11-25)

This is the question, I have problem with part b, I don't know what function should I use to reach the result
thanks in forward
[![enter image description here](https://i.sstatic.net/ZgsW1.png)](https://i.sstatic.net/ZgsW1.png)

**Tags:** microeconomics, utility

> **Comments:**
> **username_1**: Hi, Welcome to Economics SE! we have a policy regarding homework questions where users must demonstrate effort using text, markdown syntax and/or images space provided in the text of his question submission for the site. Using only images as proof of work is insufficient. for more details see:https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions  
> **username_2**: Possible duplicate of [How can I obtain Leontief and Cobb-Douglas production function from CES function?](https://economics.stackexchange.com/questions/361/how-can-i-obtain-leontief-and-cobb-douglas-production-function-from-ces-function)  

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## 2 answers

### Answer by username_3 on 2019-11-26. Score: 3

**Hint**: find $\ln(U(x))$ and then use L'Hopital's rule to find the limit as $\rho\rightarrow0$.


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### Answer by username_4 on 2019-11-25. Score: 2

**hint:** you are supposed to show the utility function represents the same preferences not that the utility functions are exactly same. Recall that any monotonic transformations of function preserves the original order of preferences. So you only need to show that in the limit one function is monotonic transformation of the other.

> **Comments:**
> **username_0**: well actually I tried to use ln to show it but I couldn't find the relation that's what I asked it here, I guess I asked the wrong question  

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