# Calculating the limit of an (unusual?) CES utility function

• June 17th 2013, 07:05 AM
ElBotas
Calculating the limit of an (unusual?) CES utility function
Hi everyone,

I stumbled upon this CES utility function, and I'd like to calculate the limit for $\rho \rightarrow 0$ of this function.
$U = \sum_{t=0}^T \frac{1}{\gamma}(C_t^{-\rho} + \theta X_t^{-\rho})^{-\frac{\gamma}{\rho}}, \theta \neq 0$
I know that with a "standard" CES Utility function of the form
$U = \sum_{t=0}^T \frac{1}{\gamma}(\theta C_t^{-\rho} + (1 - \theta) X_t^{-\rho})^{-\frac{\gamma}{\rho}}$
it is easy to do via L'Hôpital, and the limit is a Cobb-Douglas utility function.
Does anyone have an idea how to find the limit of the first equation ?
Has anyone seen such a CES utility function before?

Thanks a lot

Cheers,
ElBotas