<p>Here is the lexicographic preference be given,
<a href="https://i.sstatic.net/EKBFN.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/EKBFN.png" alt="enter image description here" /></a></p>
<p>And here is the choice space,
<a href="https://i.sstatic.net/pAEOu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/pAEOu.png" alt="enter image description here" /></a>
I'm really struggled with determining this proof, can someone help to solve the problem or give some hint? Thanks so much!</p>
<p>(p.s. there is no typo or other mistakes in this question and lexicographic preference)</p>

CC BY-SA 4.0
2023-01-22T13:44:16.227Z
That is not the usual definition of lexicographic preferences; whoever gave this problem has probably made a typo here. See page 6 [here](https://books.openbookpublishers.com/10.11647/obp.0204.04.pdf) for the standard definition.
Michael Greinecker
CC BY-SA 4.0
2023-01-22T15:13:32.343Z
These are certainly not lexicographic preferences as usually defined. Anyways, they are representable by $u(n,x)=-3n+x$.
Michael Greinecker
<mathematical-economics>
When the choice space is X=N*[-1,1], how do you determine whether the following lexicographic preference can be represented by a utility function
user43317
# When the choice space is X=N*[-1,1], how do you determine whether the following lexicographic preference can be represented by a utility function

(Asked by: username_0 on 2023-01-22)

Here is the lexicographic preference be given,
[![enter image description here](https://i.sstatic.net/EKBFN.png)](https://i.sstatic.net/EKBFN.png)

And here is the choice space,
[![enter image description here](https://i.sstatic.net/pAEOu.png)](https://i.sstatic.net/pAEOu.png)
I'm really struggled with determining this proof, can someone help to solve the problem or give some hint? Thanks so much!

(p.s. there is no typo or other mistakes in this question and lexicographic preference)

**Tags:** mathematical-economics

> **Comments:**
> **username_1**: That is not the usual definition of lexicographic preferences; whoever gave this problem has probably made a typo here. See page 6 [here](https://books.openbookpublishers.com/10.11647/obp.0204.04.pdf) for the standard definition.  
> **username_1**: These are certainly not lexicographic preferences as usually defined. Anyways, they are representable by $u(n,x)=-3n+x$.  

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## 0 answers

