<p>From your formula for <span class="math-container">$x$</span> when <span class="math-container">$y=0$</span>, you should be able to find <span class="math-container">$U$</span> in terms of <span class="math-container">$M$</span> and <span class="math-container">$p_x$</span> when <span class="math-container">$y=0$</span>.  Similarly, <span class="math-container">$U$</span> in terms of <span class="math-container">$M$</span> and <span class="math-container">$p_y$</span> when <span class="math-container">$x=0$</span>.  The key then is to find the critical price ratio at which, to maximise <span class="math-container">$U$</span>, the switch needs to occur from <span class="math-container">$y=0$</span> to <span class="math-container">$x=0$</span>.</p>

<p>Can you take it from there?</p>

CC BY-SA 4.0
2020-04-01T11:32:35.760Z
Sorry, I'm still struggling with this one, unfortunately, after finding the utility when y=0 and then x=0, U=2m/px and U=m/py respectively. I'm unfamiliar with the term critical price ratio. Thank you for your help so far :)
L W
CC BY-SA 4.0
2020-04-01T11:46:15.633Z
If you equate those two formulae for $U$ you obtain a condition under which utility is the same when $y=0$ or when $x=0$.  You can then cancel $M$ and rearrange to obtain what I call the critical price ratio.  One side of this ratio, utility is maximised with $y=0$; the other side, with $x=0$.
Adam Bailey
CC BY-SA 4.0
2020-04-01T12:01:19.640Z
Okay so I have 2py=px and then to establish which one provides high utility? how? Or am I supposed to use that in the demand function? sorry for being so lost
L W
CC BY-SA 4.0
2020-04-01T12:04:18.433Z
The demand function for $x$ will need to be in two parts: if $p_x/p_y\geq 2$ then ... and if $p_x/p_y\leq2$ then ...
Adam Bailey
CC BY-SA 4.0
2020-04-01T12:17:02.957Z
To conclude it is safe to say in terms of demand functions that if the price ratio is less than 2 the demand function in terms of x is x=m/px and if price ratio is greater than 2 the demand function is x=0?
L W
CC BY-SA 4.0
2020-04-01T12:31:28.320Z
Yes, that's correct.
Adam Bailey
CC BY-SA 4.0
2020-04-01T11:06:53.400Z
2020-04-01T11:06:53.400Z
Adam Bailey
<p>I have a max utility function, therefore;
<strong>U(x,y)= max(2x,y)</strong>
and I am trying to find the demand function x = x(x , y , ), note this function cannot be differentiated. I am familiar that the utility function states that it is best to have x=0 and all of the good y, or vice versa. So I've been trying to solve with the budget line making one x=0 and then again y=0 but I am unsure what to do from this point?</p>

<p>Working so far:
p1x+p2y=M
when y=0
x=m/p1
U= 2m/p1</p>

<p>&amp;
when x=0
y=m/p2
U= m/p2</p>

<p>So now I have two equations in terms of U</p>

CC BY-SA 4.0
2020-04-01T10:59:07.357Z
Yeah, I actually do know what it is :) excuse my non-formal language, I'm asking what the demand function for x is for that given utility function... thanks
L W
CC BY-SA 4.0
2020-04-01T11:05:30.723Z
I get that, but you wrote "it is best to have x=0 and all of the good y, or vice versa." Surely it is very easy to check which one is better for any given M,p1,p2?
Giskard
CC BY-SA 4.0
2020-04-01T11:17:50.970Z
Hint: Does x=m/p1 or x=0 lead to higher utility?
Herr K.
CC BY-SA 4.0
2020-04-01T11:33:25.430Z
I can get the utility of when y=0 and x=0 I'm just getting stuck on showing which has greater utility
L W
CC BY-SA 4.0
2020-04-01T11:41:51.607Z
yep, done that, rather so I have two equations in terms of U
L W
<microeconomics><utility><demand>
Max Utility Function and Finding associated demand curve
L W
# Max Utility Function and Finding associated demand curve

(Asked by: username_0 on 2020-04-01)

I have a max utility function, therefore;
**U(x,y)= max(2x,y)**
and I am trying to find the demand function x = x(x , y , ), note this function cannot be differentiated. I am familiar that the utility function states that it is best to have x=0 and all of the good y, or vice versa. So I've been trying to solve with the budget line making one x=0 and then again y=0 but I am unsure what to do from this point?

Working so far:
p1x+p2y=M
when y=0
x=m/p1
U= 2m/p1

&
when x=0
y=m/p2
U= m/p2

So now I have two equations in terms of U

**Tags:** microeconomics, utility, demand
> **Comments:**
> **username_0**: Yeah, I actually do know what it is :) excuse my non-formal language, I'm asking what the demand function for x is for that given utility function... thanks  
> **username_1**: I get that, but you wrote "it is best to have x=0 and all of the good y, or vice versa." Surely it is very easy to check which one is better for any given M,p1,p2?  
> **username_2**: Hint: Does x=m/p1 or x=0 lead to higher utility?  
> **username_0**: I can get the utility of when y=0 and x=0 I'm just getting stuck on showing which has greater utility  
> **username_0**: yep, done that, rather so I have two equations in terms of U  

---

## 1 answers

### Answer by username_3 on 2020-04-01. Score: 1

From your formula for $x$ when $y=0$, you should be able to find $U$ in terms of $M$ and $p\_x$ when $y=0$. Similarly, $U$ in terms of $M$ and $p\_y$ when $x=0$. The key then is to find the critical price ratio at which, to maximise $U$, the switch needs to occur from $y=0$ to $x=0$.

Can you take it from there?

> **Comments:**
> **username_0**: Sorry, I'm still struggling with this one, unfortunately, after finding the utility when y=0 and then x=0, U=2m/px and U=m/py respectively. I'm unfamiliar with the term critical price ratio. Thank you for your help so far :)  
> **username_3**: If you equate those two formulae for $U$ you obtain a condition under which utility is the same when $y=0$ or when $x=0$.  You can then cancel $M$ and rearrange to obtain what I call the critical price ratio.  One side of this ratio, utility is maximised with $y=0$; the other side, with $x=0$.  
> **username_0**: Okay so I have 2py=px and then to establish which one provides high utility? how? Or am I supposed to use that in the demand function? sorry for being so lost  
> **username_3**: The demand function for $x$ will need to be in two parts: if $p_x/p_y\geq 2$ then ... and if $p_x/p_y\leq2$ then ...  
> **username_0**: To conclude it is safe to say in terms of demand functions that if the price ratio is less than 2 the demand function in terms of x is x=m/px and if price ratio is greater than 2 the demand function is x=0?  
> **username_3**: Yes, that's correct.  

---

