# Indirect utility from expenditure function

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?

• 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 Mar 15 '15 at 22:37

## 1 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.

• 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. Nov 2 '18 at 10:03
• This seems more like a comment on this answer than an answer to this question. – Brythan Nov 3 '18 at 0:05