<p>It depends on the function. A non-monotonic function with satiation:
<span class="math-container">$$
U(x_1,x_2) = 0.
$$</span>
A non-monotonic function without (global) satiation:
<span class="math-container">$$
U(x_1,x_2) = \left \lfloor{x_1}\right \rfloor  + \left \lfloor{x_2}\right \rfloor .
$$</span></p>

CC BY-SA 4.0
2019-10-22T03:48:59.623Z
Does non-satiation imply monotonicity always?
Frodo Baggins
CC BY-SA 4.0
2019-10-22T06:05:28.023Z
I wouldn't have asked these questions had I not first tried myself. You may be experienced in this field, but I am a novice. So, if you don't want to answer that fine, but I would politely remind you not to impede others from asking pertinent questions.
Frodo Baggins
CC BY-SA 4.0
2019-10-22T08:08:02.753Z
@FrodoBaggins What exactly have you tried? Could you edit some of your efforts into your questions? Into this one and also any other questions you may want to ask. It would help us understand better where you get stuck. If it is the mathematical notation that you find difficult I recommend reading a math textbook on analysis.
Giskard
CC BY-SA 4.0
2019-10-22T08:10:51.543Z
You have already asked six questions in four days. I think you may be better served by thinking more about them. As it says in the [faq](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions): "The purpose of this site is not to provide complete answer keys to homework questions"
Giskard
CC BY-SA 4.0
2019-10-22T15:04:29.937Z
I haven't asked homework questions, but merely conceptual questions. Plus, there is no limit on the number of questions anyone can ask in the forum.
Frodo Baggins
CC BY-SA 4.0
2019-10-22T16:02:44.033Z
Thank you for your response. So are you going to edit in your attempts into the questions? You wrote that you tried to solve these before asking.
Giskard
CC BY-SA 4.0
2019-10-22T22:52:42.573Z
Actually I figured the answer, so I am not going to post. Thanks
Frodo Baggins
CC BY-SA 4.0
2019-10-18T06:04:37.453Z
2019-10-18T06:04:37.453Z
Giskard
<p>A non-monotonic function with local non-satiation:
<span class="math-container">$$u(x, y) = x - y$$</span></p>

CC BY-SA 4.0
2019-10-23T21:53:53.480Z
2019-10-23T21:53:53.480Z
Amit
<p>I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.</p>

CC BY-SA 4.0
2019-10-18T06:01:00.093Z
Defining the exact type of monotonicity and satiation you mean may be helpful.
Giskard
CC BY-SA 4.0
2019-10-18T07:43:30.680Z
Are you asking about local satiation or global satiation? Are you asking about strongly monotonic or weakly monotonic functions and their complements?
Henry
CC BY-SA 4.0
2019-10-18T14:43:23.987Z
I am asking about local-satiation and strongly monotonic functions.
Frodo Baggins
CC BY-SA 4.0
2019-10-19T09:19:48.267Z
Then my answer does not answer your question.
Giskard
<microeconomics><preferences>
Does non-monotonicity imply non-satiation always? Why or why not?
Frodo Baggins
# Does non-monotonicity imply non-satiation always? Why or why not?

(Asked by: username_0 on 2019-10-18)

I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.

**Tags:** microeconomics, preferences
> **Comments:**
> **username_1**: Defining the exact type of monotonicity and satiation you mean may be helpful.  
> **username_2**: Are you asking about local satiation or global satiation? Are you asking about strongly monotonic or weakly monotonic functions and their complements?  
> **username_0**: I am asking about local-satiation and strongly monotonic functions.  
> **username_1**: Then my answer does not answer your question.  

---

## 2 answers

### Answer by username_1 on 2019-10-18. Score: 2

It depends on the function. A non-monotonic function with satiation:
$$
U(x\_1,x\_2) = 0.
$$
A non-monotonic function without (global) satiation:
$$
U(x\_1,x\_2) = \left \lfloor{x\_1}\right \rfloor + \left \lfloor{x\_2}\right \rfloor .
$$

> **Comments:**
> **username_0**: Does non-satiation imply monotonicity always?  
> **username_0**: I wouldn't have asked these questions had I not first tried myself. You may be experienced in this field, but I am a novice. So, if you don't want to answer that fine, but I would politely remind you not to impede others from asking pertinent questions.  
> **username_1**: @FrodoBaggins What exactly have you tried? Could you edit some of your efforts into your questions? Into this one and also any other questions you may want to ask. It would help us understand better where you get stuck. If it is the mathematical notation that you find difficult I recommend reading a math textbook on analysis.  
> **username_1**: You have already asked six questions in four days. I think you may be better served by thinking more about them. As it says in the [faq](https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions): "The purpose of this site is not to provide complete answer keys to homework questions"  
> **username_0**: I haven't asked homework questions, but merely conceptual questions. Plus, there is no limit on the number of questions anyone can ask in the forum.  
> **username_1**: Thank you for your response. So are you going to edit in your attempts into the questions? You wrote that you tried to solve these before asking.  
> **username_0**: Actually I figured the answer, so I am not going to post. Thanks  

---

### Answer by username_3 on 2019-10-23. Score: 0

A non-monotonic function with local non-satiation:
$$u(x, y) = x - y$$


---

