In the Green Book (page 97) it is stated "the elasticity of marginal utility of consumption (μ) with respect to utility".
What is it? Is it an error ? I always heard of the elasticity of the marginal utility with respect to consumption...
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Mere googling leads me to find a bunch of references about elasticity of marginal utility.
Here Professor Acemoglu defines the elasticity of marginal utility as the inverse of the intertemporal elasticity of substitution (pagg. 17-18).
Here you can find a question analogous to yours together with an answer explained in an easier way than Acemoglu's lecture.
If you are interested in something more empirical, have a look here: it is a paper by David Evans about the empirical estimation of elasticity of marginal utility in OECD countries.
Hope this is enough. If you have other questions, please ask