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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!

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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

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  • $\begingroup$ definition: The ability to get rid of units of inputs and outputs free of cost. $\endgroup$ May 14 '21 at 17:32
  • $\begingroup$ No math definition? $\endgroup$
    – Giskard
    May 14 '21 at 17:33
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    $\begingroup$ y ∈ Y and y'≤ y, then y' ∈ y $\endgroup$ May 14 '21 at 17:36
  • $\begingroup$ Then it is not enough if "all of that negative x axis and negative y axis is still possible", is it? $\endgroup$
    – Giskard
    May 14 '21 at 17:37
  • $\begingroup$ So, given the definition, any further suggestions? $\endgroup$ May 14 '21 at 17:48

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