<p><span class="math-container">$u(x_1,x_2)=x_1(x_2)^2$</span></p>
<p>I want to calculate the demand function <span class="math-container">$x_1(m,p_1,p_2)$</span> and <span class="math-container">$x_2(m,p_1,p_2)$</span>.</p>
<p><span class="math-container">$MRS(x_1,x_2)=-\frac{x_2}{2x_1}$</span>, from <span class="math-container">$\frac{x_2}{2x_1}=\frac{p_1}{p_2}$</span> we get <span class="math-container">$x_1=\frac{x_2p_2}{2p_1}$</span> and <span class="math-container">$x_2=\frac{2x_1p_1}{p_2}$</span>.</p>
<p>We have <span class="math-container">$m=x_1p_1+x_2p_2$</span>, <span class="math-container">$x_1=\frac{m-x_2p_2}{p_1}$</span>.</p>
<p>Now I tried inserting the equations into each other but didn't really get anywhere, it says <span class="math-container">$x_1(m, p_1, p_2)=\frac{m}{3p_1}$</span> and <span class="math-container">$x_2(m, p_1, p_2)=\frac{2m}{3p_2}$</span> in the solution sketch but I have no idea how to get to that.</p>

CC BY-SA 4.0
2021-09-06T11:24:24.777Z
Try a bit harder here: $x_2=\frac{2x_1p_1}{p_2}$ and $x_1=\frac{m-x_2p_2}{p_1}$ (you can use either equation to perform a substitution)
Giskard
CC BY-SA 4.0
2021-09-06T12:14:43.857Z
Ok, $x_1=\frac{2(\frac{m-x_2p_2}{p_1})p_1}{p_2}=\frac{2(m-x_2p_2)}{p_2}$? I also got this earlier when I tried but what now?
Linn1
CC BY-SA 4.0
2021-09-06T12:41:15.460Z
Oh I accidentally wrote $x_1$ instead of $x_2$ on the left of the equation but I still can't get any further
Linn1
CC BY-SA 4.0
2021-09-06T13:18:17.003Z
Ohhh I got it now I'm stupid
Linn1
<microeconomics>
Calculating demand function with MRS
Linn1
# Calculating demand function with MRS

(Asked by: username_0 on 2021-09-06)

$u(x\_1,x\_2)=x\_1(x\_2)^2$

I want to calculate the demand function $x\_1(m,p\_1,p\_2)$ and $x\_2(m,p\_1,p\_2)$.

$MRS(x\_1,x\_2)=-\frac{x\_2}{2x\_1}$, from $\frac{x\_2}{2x\_1}=\frac{p\_1}{p\_2}$ we get $x\_1=\frac{x\_2p\_2}{2p\_1}$ and $x\_2=\frac{2x\_1p\_1}{p\_2}$.

We have $m=x\_1p\_1+x\_2p\_2$, $x\_1=\frac{m-x\_2p\_2}{p\_1}$.

Now I tried inserting the equations into each other but didn't really get anywhere, it says $x\_1(m, p\_1, p\_2)=\frac{m}{3p\_1}$ and $x\_2(m, p\_1, p\_2)=\frac{2m}{3p\_2}$ in the solution sketch but I have no idea how to get to that.

**Tags:** microeconomics
> **Comments:**
> **username_1**: Try a bit harder here: $x_2=\frac{2x_1p_1}{p_2}$ and $x_1=\frac{m-x_2p_2}{p_1}$ (you can use either equation to perform a substitution)  
> **username_0**: Ok, $x_1=\frac{2(\frac{m-x_2p_2}{p_1})p_1}{p_2}=\frac{2(m-x_2p_2)}{p_2}$? I also got this earlier when I tried but what now?  
> **username_0**: Oh I accidentally wrote $x_1$ instead of $x_2$ on the left of the equation but I still can't get any further  
> **username_0**: Ohhh I got it now I'm stupid  

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## 0 answers

