<p><span class="math-container">$u_1(x, y) = -(x-1)^2 - (y-1)^2$</span> </p>

<p><span class="math-container">$u_2(x, y) = -|x-1| - |y-1|$</span></p>

<p>are examples of utility functions that are concave, and therefore represent the preferences that are convex. Also, these preferences are not monotonic.</p>

CC BY-SA 4.0
2019-06-19T12:07:16.627Z
2019-06-19T12:07:16.627Z
Amit
<p>I need an example of a </p>

<ul>
<li><p>Convex, non-monotonic preference</p></li>
<li><p>Non-convex, monotonic preference</p></li>
</ul>

<p>I figured that an example of non-convex, monotonic utility preference could be <span class="math-container">$U(x,y)=x^2+y^2$</span>.
For convex, non-monotonic preference, I cannot think of a standard example. As far as my understanding goes, lexicographic preferences are convex, but I don't think these are non monotonic. 
Please help me figure out the examples so that I can conceptually understand monotonicity and convexity.   </p>

CC BY-SA 4.0
2019-06-16T09:01:16.563Z
$-(x-1)^2 -(y-1)^2$ is an example of convex, non- monotonic preference
Amit
CC BY-SA 4.0
2019-06-16T13:51:16.827Z
@Amit Also post answers you think are correct as answers.
Giskard
CC BY-SA 4.0
2019-06-16T20:31:04.873Z
It's an example of an utility function that represents convex, non-monotonic preferences, actually.
Pedro Cavalcante
<microeconomics><preferences><self-study>
Preference: Convexity and Monotonicity
S.Rana
# Preference: Convexity and Monotonicity

(Asked by: username_0 on 2019-06-16)

I need an example of a

* Convex, non-monotonic preference
* Non-convex, monotonic preference

I figured that an example of non-convex, monotonic utility preference could be $U(x,y)=x^2+y^2$.
For convex, non-monotonic preference, I cannot think of a standard example. As far as my understanding goes, lexicographic preferences are convex, but I don't think these are non monotonic.
Please help me figure out the examples so that I can conceptually understand monotonicity and convexity.

**Tags:** microeconomics, preferences, self-study

> **Comments:**
> **username_1**: $-(x-1)^2 -(y-1)^2$ is an example of convex, non- monotonic preference  
> **username_2**: @username_1 Also post answers you think are correct as answers.  
> **username_3**: It's an example of an utility function that represents convex, non-monotonic preferences, actually.  

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## 1 answers

### Answer by username_1 on 2019-06-19. Score: 4

$u\_1(x, y) = -(x-1)^2 - (y-1)^2$

$u\_2(x, y) = -|x-1| - |y-1|$

are examples of utility functions that are concave, and therefore represent the preferences that are convex. Also, these preferences are not monotonic.


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