# 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

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.