# Production Set: Not satisfying Free Disposal Assumption

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!

## 1 Answer

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