<p>To see if the preferences between $u$ and $u'$ are the same, simply look at the $MRS$ of both of them to see if they are equivalent.</p>

<p>i.e. </p>

<p>$$MRS_{u}=\frac{MU_x}{MU_y}=\frac{\left(0.5x^{-0.5}y^{0.5}\right)}{\left(0.5x^{0.5}y^{-0.5}\right)}=\frac{y}{x}$$</p>

<p>$$MRS_{u'}=\frac{\frac{1}{x}}{\frac{1}{y}}=\frac{y}{x}$$</p>

<p>$$\Rightarrow MRS_u=MRS_{u'}$$</p>

<p>$\therefore$ $u$ and $u'$ have the same preferences.</p>

<p>Hope this is helpful</p>

CC BY-SA 3.0
2017-11-21T15:03:01.180Z
Hi. Thank you. Very helpful. I actually just solved it this way before I came on here again to see if there had been any updates. Again thanks!
jjj
CC BY-SA 3.0
2017-11-21T03:59:58.483Z
2017-11-21T03:59:58.483Z
Bensstats
<p>So, I need to determine whether or not $u=x^{0.5}y^{0.5}$ exhibits the same preferences as $u'= log(x) + log (y)$. Any tricks I can use here? I've done the logarithmic transformation so that I now have $(0.5)log (x) + (0.5)log (y)$. My guess is, if I multiply these by $2$ I'll get $log (x) + log (y)$ and thereby proving that u and u' refer to the same preferences, but I'm not sure if this is correct? </p>

<microeconomics><mathematical-economics>
Transformation of Cobb Douglas Utility
jjj
# Transformation of Cobb Douglas Utility

(Asked by: username_0 on 2017-11-19)

So, I need to determine whether or not $u=x^{0.5}y^{0.5}$ exhibits the same preferences as $u'= log(x) + log (y)$. Any tricks I can use here? I've done the logarithmic transformation so that I now have $(0.5)log (x) + (0.5)log (y)$. My guess is, if I multiply these by $2$ I'll get $log (x) + log (y)$ and thereby proving that u and u' refer to the same preferences, but I'm not sure if this is correct?

**Tags:** microeconomics, mathematical-economics


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## 1 answers

### Answer by username_1 on 2017-11-21. Score: 1

To see if the preferences between $u$ and $u'$ are the same, simply look at the $MRS$ of both of them to see if they are equivalent.

i.e.

$$MRS\_{u}=\frac{MU\_x}{MU\_y}=\frac{\left(0.5x^{-0.5}y^{0.5}\right)}{\left(0.5x^{0.5}y^{-0.5}\right)}=\frac{y}{x}$$

$$MRS\_{u'}=\frac{\frac{1}{x}}{\frac{1}{y}}=\frac{y}{x}$$

$$\Rightarrow MRS\_u=MRS\_{u'}$$

$\therefore$ $u$ and $u'$ have the same preferences.

Hope this is helpful

> **Comments:**
> **username_0**: Hi. Thank you. Very helpful. I actually just solved it this way before I came on here again to see if there had been any updates. Again thanks!  

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