-1
$\begingroup$

Mas-Colell, Whinston and Green's Microeconomic Theory affirms the budget set is closed. I would like to know why.

enter image description here

The definition of open set in the book is the following:enter image description here

$\endgroup$

closed as off-topic by EnergyNumbers, Giskard, Adam Bailey, Kitsune Cavalry Dec 29 '18 at 16:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • 2
    $\begingroup$ What exactly are you asking? Are you asking what 'closed set' means? $\endgroup$ – Giskard Dec 21 '18 at 17:10
1
$\begingroup$

Loosely speaking closed means that it includes the boundary. The boundary of the budget set is formed by those goods baskets ($x$) that imply spending all available income, i.e., such that $p·x=w.$ It is clear that they belong in the budget set and, hence, it is closed. (To be strict, we'd also need to check that points such as $ \vec 0$ also belong in the budget set. That's easy and I leave it for you to prove).

$\endgroup$
0
$\begingroup$

Hint: a set is closed if its complement is open, and if a bundle $x$ is strictly unaffordable, $p \cdot x > w$, every nearby bundle is also unaffordable.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.