<p>For perfect complements like <span class="math-container">$u(x,y) = \min( g(x_1), h(x_2))$</span> the points at which kinks occur are such that <span class="math-container">$g(x_1)= h(x_2)$</span>. In this case that would be <span class="math-container">$x= \sqrt(y)$</span> so in this case indifference curves would look like:</p>
<p><a href="https://i.sstatic.net/eGAhw.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/eGAhw.png" alt="enter image description here" /></a></p>
<p>The picture above plots two indifference curves and the dashed line gives you all kinks of every indifference curve. Normally the kinks would lie on <span class="math-container">$45^°$</span> line because usually complements are given by functions where respective slopes of <span class="math-container">$x$</span> and <span class="math-container">$y$</span> are linear (e.g. <span class="math-container">$\min (\alpha x, \beta y ))$</span> but here you have case where you have <span class="math-container">$\sqrt(y)$</span>, so the  <span class="math-container">$x$</span> has to be consumed with exponentially increasing quantities <span class="math-container">$y$</span>.</p>

CC BY-SA 4.0
2020-11-12T19:33:11.933Z
2020-11-12T19:43:43.967Z
2020-11-12T19:43:43.967Z
1muflon1
<p>What would be the I.C of this function? <span class="math-container">$u(x,y)=\min(x,√y)$</span></p>
<p>I understand since it is a perfect complements case it should be &quot;L&quot; shaped but I wanted a more detailed graph.</p>

CC BY-SA 4.0
2020-11-12T19:34:42.427Z
Does this answer your question? [What would the indifference curve of min{√x,y} looks like?](https://economics.stackexchange.com/questions/30807/what-would-the-indifference-curve-of-min%e2%88%9ax-y-looks-like)
Bayesian
<microeconomics><perfect-complements>
Perfect complements indifference curve
Maybeline Lee
# Perfect complements indifference curve

(Asked by: username_0 on 2020-11-12)

What would be the I.C of this function? $u(x,y)=\min(x,√y)$

I understand since it is a perfect complements case it should be "L" shaped but I wanted a more detailed graph.

**Tags:** microeconomics, perfect-complements

> **Comments:**
> **username_1**: Does this answer your question? [What would the indifference curve of min{√x,y} looks like?](https://economics.stackexchange.com/questions/30807/what-would-the-indifference-curve-of-min%e2%88%9ax-y-looks-like)  

---

## 1 answers

### Answer by username_2 on 2020-11-12. Score: 1 | Accepted answer

For perfect complements like $u(x,y) = \min( g(x\_1), h(x\_2))$ the points at which kinks occur are such that $g(x\_1)= h(x\_2)$. In this case that would be $x= \sqrt(y)$ so in this case indifference curves would look like:

[![enter image description here](https://i.sstatic.net/eGAhw.png)](https://i.sstatic.net/eGAhw.png)

The picture above plots two indifference curves and the dashed line gives you all kinks of every indifference curve. Normally the kinks would lie on $45^°$ line because usually complements are given by functions where respective slopes of $x$ and $y$ are linear (e.g. $\min (\alpha x, \beta y ))$ but here you have case where you have $\sqrt(y)$, so the $x$ has to be consumed with exponentially increasing quantities $y$.


---

