# Non Continuous Walrasian Demand Function

I have a silly question.

I’m trying to solve some exercises that have to do with the walrasian demand function $$x(p,w)$$ and excess demand function $$z$$.

More especifically, I’m asked to show that there is not a price vector ($$p$$ belongs to the simplex) such that $$z(p)=0$$ when $$z$$ is not continuous for all goods. As $$z$$, for a given good $$i$$, is the sum of the walrasian demand and a given endowment, I think that the previous statement is the same as saying that if $$x(p,w)$$ is not continuous then there is not $$p$$ s.t $$z(p)=0$$.

Any hint about why, if $$z$$ or $$x$$ aren’t continuous then $$p$$ doesn’t exist?

• There seems to be something missing, "$\ldots$such that $z(p)$" isn't really a statement about anything. Feb 6 at 21:29
• @Martin what is that excess demand function $z$ you talk about? I just started Advanced Microeconomics. Feb 7 at 0:49
• Sorry for the delay Nicolas. The excess demand function, as defined by Mas Colell on chapter 17, is the good’s walrasian demand function (x)minus the endowment (w). Feb 9 at 9:00
• Michael, I corrected the statement. Thanks! Feb 9 at 9:02
• It is not true that there can be no $p$ such that $z(p)=0$ when $z$ or (equivalently) $x$ is discontinuous. There may not be, but continuity is not a necessary condition. Feb 9 at 10:15