<p>I have a model where I have to compare the values of y(x) and z(x).</p>
<p>But expressions are complex and what I am getting is
<span class="math-container">$x= f(y(x))= \frac{\sin({y(x)}) + \sqrt{(y(x))^3}}{(\frac{y(x)}{1-y(x)}) ^{1/4}}$</span></p>
<p>and <span class="math-container">$x= g(z(x))$</span> is some complex equation just like f(y(x))</p>
<p>Can I compare x-f(y(x)) and x-g(z(x))? Will it be equivalent of comparing y(x) and z(x)?</p>

CC BY-SA 4.0
2021-09-22T11:36:45.653Z
It would be more helpful if you would actually showcase problem, for example if you have x=g(z(x)) for all we know that function could just be x =2+2x where z(x)=2x and g(h) = 2+h, if this would be the case you can just solve for x in terms of parameters and compare which x value is larger.
1muflon1
CC BY-SA 4.0
2021-09-22T11:59:42.787Z
@1muflon1 I have edited the question. Hope it give some sense to the problem I am asking
Elina Gilbert
CC BY-SA 4.0
2021-09-22T13:13:34.417Z
Can yo define what each of the functions are? Without any structure, the answer to your questions is “not in general”, but for some types of functions such tricks can be used. So you need to provide more context.
Regio
CC BY-SA 4.0
2021-09-24T14:01:54.897Z
If you have the actual functions, but they are too complex for you to reasonably calculate, try using Mathematica.
BB King
CC BY-SA 4.0
2021-09-25T15:04:31.670Z
@BB King I tried that and it still gave me the answers in complex hypergeometric function equations
Elina Gilbert
<inequality><comparative-statics>
Comparison of two variables
Elina Gilbert
# Comparison of two variables

(Asked by: username_0 on 2021-09-22)

I have a model where I have to compare the values of y(x) and z(x).

But expressions are complex and what I am getting is
$x= f(y(x))= \frac{\sin({y(x)}) + \sqrt{(y(x))^3}}{(\frac{y(x)}{1-y(x)}) ^{1/4}}$

and $x= g(z(x))$ is some complex equation just like f(y(x))

Can I compare x-f(y(x)) and x-g(z(x))? Will it be equivalent of comparing y(x) and z(x)?

**Tags:** inequality, comparative-statics

> **Comments:**
> **username_1**: It would be more helpful if you would actually showcase problem, for example if you have x=g(z(x)) for all we know that function could just be x =2+2x where z(x)=2x and g(h) = 2+h, if this would be the case you can just solve for x in terms of parameters and compare which x value is larger.  
> **username_0**: @username_1 I have edited the question. Hope it give some sense to the problem I am asking  
> **username_2**: Can yo define what each of the functions are? Without any structure, the answer to your questions is “not in general”, but for some types of functions such tricks can be used. So you need to provide more context.  
> **username_3**: If you have the actual functions, but they are too complex for you to reasonably calculate, try using Mathematica.  
> **username_0**: @username_3 I tried that and it still gave me the answers in complex hypergeometric function equations  

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## 0 answers

