Non-Constant Elasticity of Substitution What's the literature on Non-Constant elasticities of substitution? Say, I'm interested in the elasticity between $c_1$ and $c_2$ increasing/decreasing in income/wealth. 

CES utility functions with equal spending weights are similar to

$$ \left(\sum_i c_i^\frac{\epsilon-1}{\epsilon}\right)^\frac{\epsilon}{1-\epsilon}$$

A simple way of getting non-constant elasticities would be to let $\epsilon = \epsilon(Y)$. Then the elasticity of substitution would vary with income:

$$\frac{d \log \frac{c_i}{c_j}}{d \log \frac{p_j}{p_i}} = \epsilon(Y)$$

But I feel that this mixture of preference-parameters and outcome variables is suboptimal.

Is there a common way of modeling these preferences?
Eichenbaum and Fisher (2005) follow Kimball (1995) in allowing for the possibility that the elasticity of demand is increasing in a firm’s price. Which is not exactly what I was looking for, but it's a start.