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In chapter 3, Section 3.G(Page no.73, 2'nd paragraph) of Microeconomic Theory by Andreu Mas-Colell, Whinston and Green the author argued that unlike the Hicksian demand function that can be derived from the consumers expenditure function (i.e $h(p,u) = \nabla_{p}e(p,u)$) the Walrasian demand function $x(p,w)$ , which is an ordinal concept, cannot be extracted from the indirect utility (which is not invariant to increasing utility transformation) $v(p,w)$ by differentiating it wrt to $p$.

What has ordinality and the ability to transform utility function has to do with finding Walrasian demand function by differentiating it w.r.t prices $p$?

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  • $\begingroup$ If you read the next few sentences, you will see what it takes to obtain the Walrasian demand. $\endgroup$
    – Michael Greinecker
    Commented Oct 13 at 18:21
  • $\begingroup$ What i understood after reading the next lines , is that....changing $p$ will change the budget set (i.e the constraint) for which we again calculate $x(p,w)$, therefore we first normalize $v(p,w)$ wrt to marginal utility of wealth. But in case of $e(p,u)$ changing price changes the objective function (i.e expenditure). Im not able to connect ordinality and utility transformation with this explaination $\endgroup$
    – hr08
    Commented Oct 13 at 19:21
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    $\begingroup$ Multiply your utility function with $2$. This has no effect whatsoever on Walrasian demand but clearly changes the indirect utility function. $\endgroup$
    – Michael Greinecker
    Commented Oct 13 at 20:22

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