<p>Mas-Colell, Whinston, Green chapter 3, especially p. 75 explains this. One possible way is $v(p,w)=e(p,v(p,w))$ where $v$ is the indirect utility function, $p$ the price vector and $w$ the wealth.</p>

CC BY-SA 4.0
2018-11-02T10:03:00.860Z
There is a mistake in Figure 3.G.3 on page 75. Since e(p,u) represents expenditure, it equals to wealth (w). w ≡ e (p, v (p, w)) u(x(p,w))≡ u(h(p,u) ≡ v (p, e (p, u))
z.a.
CC BY-SA 4.0
2018-11-03T00:05:36.763Z
This seems more like a comment on [this answer](https://economics.stackexchange.com/a/5141/68) than an answer to this question.
Brythan
CC BY-SA 3.0
2015-04-15T05:10:40.957Z
2015-04-17T01:37:27.520Z
2015-04-17T01:37:27.520Z
Sander Heinsalu
<p>I have the expenditure function: $$e(p,u)=\left(p_1^{\rho/{\rho-1}}+p_2^{\rho/{\rho-1}}\right)^{{\rho-1}/\rho}u$$
where $u$ is the utility, $p_1,p_2$ prices and $\rho$ a parameter. How do I derive the indirect utility function?</p>

CC BY-SA 3.0
2015-03-15T22:37:21.843Z
Doesn't the textbook, (I assume you are using some source), provide the answer? It is one word. So it is not a matter of "calculation" but a matter of understanding why the two are connected in such a  way.
Alecos Papadopoulos
<microeconomics><utility>
Indirect utility from expenditure function
Guilherme Salome
# Indirect utility from expenditure function

(Asked by: username_0 on 2015-03-15)

I have the expenditure function: $$e(p,u)=\left(p\_1^{\rho/{\rho-1}}+p\_2^{\rho/{\rho-1}}\right)^{{\rho-1}/\rho}u$$
where $u$ is the utility, $p\_1,p\_2$ prices and $\rho$ a parameter. How do I derive the indirect utility function?

**Tags:** microeconomics, utility

> **Comments:**
> **username_1**: Doesn't the textbook, (I assume you are using some source), provide the answer? It is one word. So it is not a matter of "calculation" but a matter of understanding why the two are connected in such a  way.  

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## 1 answers

### Answer by username_2 on 2015-04-15. Score: 3 | Accepted answer

Mas-Colell, Whinston, Green chapter 3, especially p. 75 explains this. One possible way is $v(p,w)=e(p,v(p,w))$ where $v$ is the indirect utility function, $p$ the price vector and $w$ the wealth.

> **Comments:**
> **username_3**: There is a mistake in Figure 3.G.3 on page 75. Since e(p,u) represents expenditure, it equals to wealth (w). w ≡ e (p, v (p, w)) u(x(p,w))≡ u(h(p,u) ≡ v (p, e (p, u))  
> **username_4**: This seems more like a comment on [this answer](https://economics.stackexchange.com/a/5141/68) than an answer to this question.  

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