Hi everyone,

I stumbled upon this CES utility function, and I'd like to calculate the limit for $\displaystyle $\rho \rightarrow 0$$ of this function.

$\displaystyle 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

$\displaystyle U = \sum_{t=0}^T \frac{1}{\gamma}(\theta C_t^{-\rho} + (1 - \theta) X_t^{-\rho})^{-\frac{\gamma}{\rho}}$

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