<p>This is something you can figure out yourself. If you have not yet tried, I encourage you to do so.</p>
<hr />
<p>Draw any set <span class="math-container">$H \in \mathbb{R}^n $</span>. Select any point <span class="math-container">$x$</span> of set. Is the set of all points <span class="math-container">$y$</span> &quot;under&quot; this point <span class="math-container">$x$</span>, that is
<span class="math-container">$$
\left\{y\in \mathbb{R}^n | y &lt;&lt; x \right\},
$$</span>
a subset of <span class="math-container">$H$</span>? <br>
If no, free disposal is violated. <br>
If yes, remove any of these points from <span class="math-container">$H$</span>. The reduced set now violates free disposal.</p>
<p>For a figure of such a set, you can consider the Mercedes logo:
<a href="https://i.sstatic.net/03oKv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/03oKv.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-05-14T17:32:45.303Z
definition: The ability to get rid of units of inputs and outputs free of cost.
Alexa Thomas
CC BY-SA 4.0
2021-05-14T17:33:56.293Z
No math definition?
Giskard
CC BY-SA 4.0
2021-05-14T17:36:02.633Z
y ∈ Y and y'≤ y, then y' ∈ y
Alexa Thomas
CC BY-SA 4.0
2021-05-14T17:37:38.223Z
Then it is not enough if "*all of that negative x axis and negative y axis is still possible*", is it?
Giskard
CC BY-SA 4.0
2021-05-14T17:48:10.587Z
So, given the definition, any further suggestions?
Alexa Thomas
CC BY-SA 4.0
2021-05-14T17:48:54.140Z
Other then the exact solution I've already given? No, no further suggestions.
Giskard
CC BY-SA 4.0
2021-05-15T02:22:13.323Z
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/124273/discussion-between-alexa-thomas-and-giskard).
Alexa Thomas
CC BY-SA 4.0
2021-05-14T17:19:49.707Z
2021-05-14T17:19:49.707Z
Giskard
<p>I saw the figure which satisfies the free disposal assumption in Mas-Colell, Whinston and Green (1995), but wondering if there is a figure that DOES NOT satisfy the free disposal assumption? Any leads will be great.</p>
<p>Thanks!</p>

<microeconomics><production-function>
Production Set: Not satisfying Free Disposal Assumption
Alexa Thomas
# Production Set: Not satisfying Free Disposal Assumption

(Asked by: username_0 on 2021-05-14)

I saw the figure which satisfies the free disposal assumption in Mas-Colell, Whinston and Green (1995), but wondering if there is a figure that DOES NOT satisfy the free disposal assumption? Any leads will be great.

Thanks!

**Tags:** microeconomics, production-function

---

## 1 answers

### Answer by username_1 on 2021-05-14. Score: 4

This is something you can figure out yourself. If you have not yet tried, I encourage you to do so.

---

Draw any set $H \in \mathbb{R}^n $. Select any point $x$ of set. Is the set of all points $y$ "under" this point $x$, that is
$$
\left\{y\in \mathbb{R}^n | y << x \right\},
$$
a subset of $H$?   
If no, free disposal is violated.   
If yes, remove any of these points from $H$. The reduced set now violates free disposal.

For a figure of such a set, you can consider the Mercedes logo:
[![enter image description here](https://i.sstatic.net/03oKv.png)](https://i.sstatic.net/03oKv.png)

> **Comments:**
> **username_0**: definition: The ability to get rid of units of inputs and outputs free of cost.  
> **username_1**: No math definition?  
> **username_0**: y ∈ Y and y'≤ y, then y' ∈ y  
> **username_1**: Then it is not enough if "*all of that negative x axis and negative y axis is still possible*", is it?  
> **username_0**: So, given the definition, any further suggestions?  
> **username_1**: Other then the exact solution I've already given? No, no further suggestions.  
> **username_0**: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/124273/discussion-between-alexa-thomas-and-giskard).  

---

