<p>$y= (x_1x_2)^2-x_1x_2$</p>

<p>Let $x_1x_2=z$</p>

<p>then $y=z^2-z$ and $y'=2z-1$</p>

<p>If I can prove that y' is monotonically increasing, does that prove y is a homothetic function? if so then how can I prove that y' is monotonically increasing? </p>

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2017-06-09T12:01:30.503Z
I added the specific point of my confusion.
xyz
<mathematical-economics>
How can I show that the following function is homothetic?
xyz
# How can I show that the following function is homothetic?

(Asked by: username_0 on 2017-06-09)

$y= (x\_1x\_2)^2-x\_1x\_2$

Let $x\_1x\_2=z$

then $y=z^2-z$ and $y'=2z-1$

If I can prove that y' is monotonically increasing, does that prove y is a homothetic function? if so then how can I prove that y' is monotonically increasing?

**Tags:** mathematical-economics

> **Comments:**
> **username_0**: I added the specific point of my confusion.  

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