<p>Consider the utility function <span class="math-container">$u(x, y)= -|x-5|-|y-5|$</span>.</p>
<p>Indifference map for <span class="math-container">$u$</span> is as follows :
<a href="https://i.sstatic.net/w0Vo6.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/w0Vo6.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-01-16T09:27:12.033Z
2021-01-16T09:27:12.033Z
Amit
<p>How do you define monotonicity? The definition of monotonicity in economics is usually:</p>
<p><span class="math-container">$x\geq y$</span> implies that <span class="math-container">$U(x)\geq U(y)$</span>.</p>
<p>Then a solution could be:</p>
<p><span class="math-container">$U(x_1,x_2)=x_1-x_2$</span></p>
<p><a href="https://i.sstatic.net/gr8Jd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gr8Jd.png" alt="enter image description here" /></a></p>
<p>However, if you use the mathematical definition of monotonic function, then here is one of the solutions:</p>
<p><a href="https://i.sstatic.net/odGTP.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/odGTP.png" alt="enter image description here" /></a>.</p>
<p>You need to add the coordinates by yourself.</p>

CC BY-SA 4.0
2021-01-14T17:27:33.003Z
2021-01-14T17:27:33.003Z
High GPA
<p><em>Draw the indifference curves for a preference relation which is neither monotonous
or strictly convex, yet convex.</em></p>
<p>My solution was to draw a circle but I'm pretty sure that is wrong.</p>

CC BY-SA 4.0
2021-01-13T12:21:12.410Z
That might work on "not monotonous" depending on what that means (related to satiation?),  but a circle might be seen a strictly convex, so some adjustment might be needed, such as a rectangle
Henry
<microeconomics>
Can anyone solve this indifference curve question?
Frederik Ingemann Olsen
# Can anyone solve this indifference curve question?

(Asked by: username_0 on 2021-01-13)

*Draw the indifference curves for a preference relation which is neither monotonous
or strictly convex, yet convex.*

My solution was to draw a circle but I'm pretty sure that is wrong.

**Tags:** microeconomics

> **Comments:**
> **username_1**: That might work on "not monotonous" depending on what that means (related to satiation?),  but a circle might be seen a strictly convex, so some adjustment might be needed, such as a rectangle  

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## 2 answers

### Answer by username_2 on 2021-01-16. Score: 3

Consider the utility function $u(x, y)= -|x-5|-|y-5|$.

Indifference map for $u$ is as follows :
[![enter image description here](https://i.sstatic.net/w0Vo6.png)](https://i.sstatic.net/w0Vo6.png)


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### Answer by username_3 on 2021-01-14. Score: 1

How do you define monotonicity? The definition of monotonicity in economics is usually:

$x\geq y$ implies that $U(x)\geq U(y)$.

Then a solution could be:

$U(x\_1,x\_2)=x\_1-x\_2$

[![enter image description here](https://i.sstatic.net/gr8Jd.png)](https://i.sstatic.net/gr8Jd.png)

However, if you use the mathematical definition of monotonic function, then here is one of the solutions:

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

You need to add the coordinates by yourself.


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