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?

  • $\begingroup$ There seems to be something missing, "$\ldots$such that $z(p)$" isn't really a statement about anything. $\endgroup$ Feb 6, 2023 at 21:29
  • $\begingroup$ @Martin what is that excess demand function $z$ you talk about? I just started Advanced Microeconomics. $\endgroup$ Feb 7, 2023 at 0:49
  • $\begingroup$ 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). $\endgroup$
    – Martin
    Feb 9, 2023 at 9:00
  • $\begingroup$ Michael, I corrected the statement. Thanks! $\endgroup$
    – Martin
    Feb 9, 2023 at 9:02
  • $\begingroup$ 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. $\endgroup$ Feb 9, 2023 at 10:15


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