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In between eq. $(2.F.2)$ and $(2.F.3)$ we read ...Walras's law tells us that $w' = p'\cdot x(p',w')$ Assume now that homogeneity of degree zero does not hold. Then we have, $a>0$ $$x(ap,aw) \neq x(p,w)$$ see definition $2.E.1$ Then we can set $p'=ap,w'=aw$ to examine the case $x(p',w') \neq x(p,w)$. But then Walras' law would imply $$w' = p'\cdot ...

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