<p>Such a point where utility is a local maxima is called a satiating point.
Think of a good that turns into a bad beyond a certain amount. Most non-tradable consumables goods are of such kind, where beyond a certain point you don't need them, and they may only create inventory or wastage costs.</p>
<p>Usually though, we don't talk much about satiating points, as a utility maximizing individual in making a choice of a consumption bundle will never optimally choose to buy a bundle that had a negative marginal utility for any of the goods in the bundle. Or given an initial endowment, one can reformulate the utility maximizing problem facing the consumer in the way that does not need to consider the satiating point.</p>

CC BY-SA 4.0
2022-04-21T20:59:33.513Z
2022-04-21T20:59:33.513Z
Vishwajeet Agrawal
<p>I'm a calculus teacher trying to construct a realistic example of a smooth utility function <span class="math-container">$U(x,y)$</span> that has a local maximum at some point <span class="math-container">$(x_0,y_0)$</span>. This requires two goods, X and Y, such that the single-variable functions <span class="math-container">$U(x_0,y)$</span> and <span class="math-container">$U(x,y_0)$</span> have local maxima at <span class="math-container">$y_0$</span> and <span class="math-container">$x_0$</span>, respectively. I can't think of a meaningful example of a good/service where, after acquiring a certain amount, the utility actually decreases as more of the good/service is acquired. This condition seems quite strange, but perhaps there are some standard examples I've never heard of given my thin background in economics.</p>

CC BY-SA 4.0
2022-04-21T20:16:01.670Z
The quantities in the utility function are the amounts of the goods *consumed*, not the amounts of the goods *aquired*. I challenge you to name a food where you have no satiation quantity.
Giskard
CC BY-SA 4.0
2022-04-21T20:20:17.060Z
Also, I am not quite sure what you mean by "*realistic example*".
Giskard
<utility>
What are some examples of goods/services whose utility functions have local maxima?
Jared
# What are some examples of goods/services whose utility functions have local maxima?

(Asked by: username_0 on 2022-04-21)

I'm a calculus teacher trying to construct a realistic example of a smooth utility function $U(x,y)$ that has a local maximum at some point $(x\_0,y\_0)$. This requires two goods, X and Y, such that the single-variable functions $U(x\_0,y)$ and $U(x,y\_0)$ have local maxima at $y\_0$ and $x\_0$, respectively. I can't think of a meaningful example of a good/service where, after acquiring a certain amount, the utility actually decreases as more of the good/service is acquired. This condition seems quite strange, but perhaps there are some standard examples I've never heard of given my thin background in economics.

**Tags:** utility
> **Comments:**
> **username_1**: The quantities in the utility function are the amounts of the goods *consumed*, not the amounts of the goods *aquired*. I challenge you to name a food where you have no satiation quantity.  
> **username_1**: Also, I am not quite sure what you mean by "*realistic example*".  

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## 1 answers

### Answer by username_2 on 2022-04-21. Score: 1

Such a point where utility is a local maxima is called a satiating point.
Think of a good that turns into a bad beyond a certain amount. Most non-tradable consumables goods are of such kind, where beyond a certain point you don't need them, and they may only create inventory or wastage costs.

Usually though, we don't talk much about satiating points, as a utility maximizing individual in making a choice of a consumption bundle will never optimally choose to buy a bundle that had a negative marginal utility for any of the goods in the bundle. Or given an initial endowment, one can reformulate the utility maximizing problem facing the consumer in the way that does not need to consider the satiating point.


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