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I do not know whether the following utility functions are used a lot but I was wondering whether there was a common name for this type CES like utility function

$$u(z) = \left[ \left( \sum_{j \in J_1} z_{j}^{\alpha_1}\right)^{\rho/\alpha_1} + \left(\sum_{j \in J_2} z_{j}^{\alpha_2}\right)^{\rho/\alpha_2} \right]^{1/\rho},$$

perhaps it is simply an instance of the CES?

The utility function is defined over two non-overlapping groups $J_1$ and $J_2$ of goods $z_j$. The goods from the two groups are weighted diffrently in the inner CES part by $\alpha_1$ and $\alpha_2$ respectively.

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I believe it can be found as "nested CES"

See for example:

Nested CES

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  • $\begingroup$ I think you are right. Do you have any references for it? $\endgroup$
    – Jesper Hybel
    Commented Dec 16, 2020 at 1:49
  • $\begingroup$ I unfortunately don't have much experience with the function. The following link looks familiar, so it is possible I referenced this in the past: gamsworld.org/mpsge/debreu/ces.pdf $\endgroup$
    – qwerty
    Commented Dec 16, 2020 at 1:58
  • $\begingroup$ That looks interesting (and tedious). I will accept the answer and maybe edit it later to add a reference if I find one. $\endgroup$
    – Jesper Hybel
    Commented Dec 16, 2020 at 2:01

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