<p>Well there are utility functions with thick indifference curves, e.g., take any utility function <span class="math-container">$u(x,y)$</span> and run it through the integer part function so <span class="math-container">$\lfloor u(x,y) \rfloor$</span>. Resulting preference will have thick indifference curves.</p>
<p>As to whether</p>
<blockquote>
<p>we can represent or not the thick preferences</p>
</blockquote>
<p>depends on your exact definition of thick preferences. It is not difficult to alter the lexicographic preference so that on a small range it becomes &quot;thick&quot;. E.g., alter the order by making all bundles where <span class="math-container">$x&lt;1$</span> equivalent.</p>

CC BY-SA 4.0
2022-11-12T18:59:48.913Z
Thank you very much for your answer and time.
Tatanik501
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2022-11-12T17:20:43.757Z
2022-11-12T17:25:48.647Z
2022-11-12T17:25:48.647Z
Giskard
<p>From microeconomics,
<span class="math-container">$u$</span> is strictly quasi-concave if for all <span class="math-container">$x\ne y\in\mathbb{R}^2_+$</span> and <span class="math-container">$t \in (0,1)$</span>, if <span class="math-container">$u(x)\ge u(y)$</span>, then <span class="math-container">$u(tx + (1-t)y)&gt;u(y)$</span>.
You may also check the figure below.</p>
<p><a href="https://i.sstatic.net/PQg6V.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PQg6V.jpg" alt="enter image description here" /></a></p>
<p><strong>Here preferences are convex and utility is quasi-concave.
I wonder if we can represent or not the thick preferences by a utility function?
Thanks.</strong></p>

CC BY-SA 4.0
2022-11-16T14:36:12.187Z
What does “thick preferences” mean?
Nicolas Torres
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2022-11-16T16:59:08.337Z
http://www.econ.ucla.edu/sboard/teaching/econ11_09/econ11_09_lecture2.pdf   you may check the page 8.
Tatanik501
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2022-11-17T04:02:35.370Z
Thanks. I actually find this interesting. +1
Nicolas Torres
CC BY-SA 4.0
2022-11-17T07:31:17.647Z
I find confusing much more than interesting though :)
Tatanik501
<microeconomics><preferences>
Can "thick preferences" be represented by a utility function?
Tatanik501
# Can "thick preferences" be represented by a utility function?

(Asked by: username_0 on 2022-11-12)

From microeconomics,
$u$ is strictly quasi-concave if for all $x\ne y\in\mathbb{R}^2\_+$ and $t \in (0,1)$, if $u(x)\ge u(y)$, then $u(tx + (1-t)y)>u(y)$.
You may also check the figure below.

[![enter image description here](https://i.sstatic.net/PQg6V.jpg)](https://i.sstatic.net/PQg6V.jpg)

**Here preferences are convex and utility is quasi-concave.
I wonder if we can represent or not the thick preferences by a utility function?
Thanks.**

**Tags:** microeconomics, preferences
> **Comments:**
> **username_1**: What does “thick preferences” mean?  
> **username_0**: http://www.econ.ucla.edu/sboard/teaching/econ11_09/econ11_09_lecture2.pdf   you may check the page 8.  
> **username_1**: Thanks. I actually find this interesting. +1  
> **username_0**: I find confusing much more than interesting though :)  

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## 1 answers

### Answer by username_2 on 2022-11-12. Score: 1 | Accepted answer

Well there are utility functions with thick indifference curves, e.g., take any utility function $u(x,y)$ and run it through the integer part function so $\lfloor u(x,y) \rfloor$. Resulting preference will have thick indifference curves.

As to whether

> we can represent or not the thick preferences

depends on your exact definition of thick preferences. It is not difficult to alter the lexicographic preference so that on a small range it becomes "thick". E.g., alter the order by making all bundles where $x<1$ equivalent.

> **Comments:**
> **username_0**: Thank you very much for your answer and time.  

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