<p>Consumer 1 has utility <span class="math-container">$u_1=min\{x_1,y_1\}$</span>, Consumer 2 has utility <span class="math-container">$u_1=min\{x_1,2y_1\}$</span>, their endowments are <span class="math-container">$w_1=(a,0)$</span> and <span class="math-container">$w_1=(b,0)$</span> and in this case <span class="math-container">$a=b$</span>.</p>
<p>I know the offer curves look like this<a href="https://i.sstatic.net/I0jgh.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/I0jgh.png" alt="enter image description here" /></a></p>
<p>But there's no clear explanation. To find the offer curves I know that we must find UMP and then consider 3 cases when <span class="math-container">$P_x/P_y&gt;0$</span>, <span class="math-container">$P_x/P_y&lt;0$</span> and <span class="math-container">$P_x/P_y-=0$</span> to draw them. But sadly I'm not finding enough material in regards to this and every case confuses me. Could someone give an explanation what are the steps we take to derive this?</p>

CC BY-SA 4.0
2021-04-28T21:45:34.343Z
Yes, you need to consider the three cases of solutions as functions of endowments/prices and then think through how those solutions change (e.g. the offer curve will exist further away from the origin for person 1 as their endowment increases). After a bit of visualization of those you should slowly figure it out. The nice thing about Leontief preferences are the simplicity of the offer curves. (side note: very nice figures!)
Brennan
CC BY-SA 4.0
2021-04-28T23:49:48.770Z
@Brennan I understand that but can it be done mathematically, in a general case, not just Leontief. Like you start with UMP that for ex for the first consumer $x^*=a$ how could I turn this into one of these graphs. Just from what I remember ok the slope line is one of the offer curves and basically you follow from there, but it's not always the case (that I understand from different $w$). To me it feels with every case you need a new method on how to solve it. I tried reading Mas Colell chapter on it but it feels insufficient. And I'm so sorry for my rambling, I'm just lost :\
Maybeline Lee
<competitive-equilibrium><edgeworth-box>
Leontif case for Edgeworth box
Maybeline Lee
# Leontif case for Edgeworth box

(Asked by: username_0 on 2021-04-28)

Consumer 1 has utility $u\_1=min\{x\_1,y\_1\}$, Consumer 2 has utility $u\_1=min\{x\_1,2y\_1\}$, their endowments are $w\_1=(a,0)$ and $w\_1=(b,0)$ and in this case $a=b$.

I know the offer curves look like this[![enter image description here](https://i.sstatic.net/I0jgh.png)](https://i.sstatic.net/I0jgh.png)

But there's no clear explanation. To find the offer curves I know that we must find UMP and then consider 3 cases when $P\_x/P\_y>0$, $P\_x/P\_y<0$ and $P\_x/P\_y-=0$ to draw them. But sadly I'm not finding enough material in regards to this and every case confuses me. Could someone give an explanation what are the steps we take to derive this?

**Tags:** competitive-equilibrium, edgeworth-box
> **Comments:**
> **username_1**: Yes, you need to consider the three cases of solutions as functions of endowments/prices and then think through how those solutions change (e.g. the offer curve will exist further away from the origin for person 1 as their endowment increases). After a bit of visualization of those you should slowly figure it out. The nice thing about Leontief preferences are the simplicity of the offer curves. (side note: very nice figures!)  
> **username_0**: @Brennan I understand that but can it be done mathematically, in a general case, not just Leontief. Like you start with UMP that for ex for the first consumer $x^*=a$ how could I turn this into one of these graphs. Just from what I remember ok the slope line is one of the offer curves and basically you follow from there, but it's not always the case (that I understand from different $w$). To me it feels with every case you need a new method on how to solve it. I tried reading Mas Colell chapter on it but it feels insufficient. And I'm so sorry for my rambling, I'm just lost :\  

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## 0 answers

