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

CC BY-SA 4.0
2024-10-13T18:21:48.207Z
If you read the next few sentences, you will see what it takes to obtain the Walrasian demand.
Michael Greinecker
CC BY-SA 4.0
2024-10-13T19:21:47.690Z
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
hr08
CC BY-SA 4.0
2024-10-13T20:22:09.410Z
Multiply your utility function with $2$. This has no effect whatsoever on Walrasian demand but clearly changes the indirect utility function.
Michael Greinecker
<microeconomics><consumer-theory>
Walrasian demand from indirect utility
hr08
# Walrasian demand from indirect utility

(Asked by: username_0 on 2024-10-13)

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 $p$?

**Tags:** microeconomics, consumer-theory

> **Comments:**
> **username_1**: If you read the next few sentences, you will see what it takes to obtain the Walrasian demand.  
> **username_0**: 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  
> **username_1**: Multiply your utility function with $2$. This has no effect whatsoever on Walrasian demand but clearly changes the indirect utility function.  

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## 0 answers

