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It is frequently noted that if utility is given by $u(c)$, then the object $$ \frac{u(c)}{u^\prime (c)} $$ puts the utility in consumption units via the normalisation by $u^\prime(c)$. What is the intuition behind this normalisation? Why are these now consumption units of utility?

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The derivative $u'(c)$ is defined as the limit of fractions of the form $\frac{\Delta u}{\Delta c}$, so $\frac{u(c)}{u'(c)}$ is of the form $\frac{u\,\Delta c}{\Delta u}$, which in terms of units reduces to units of consumption $c$ only.

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  • $\begingroup$ +1. I see how the units cancel out but don't remember when do we actually use $\frac{u(c)}{u'(c)}$. Can you please elaborate a bit on that? $\endgroup$ Dec 22, 2023 at 17:18
  • $\begingroup$ @NicolasTorres I'm afraid I can't, as I don't recall ever having seen this "normalization" being used. Maybe the OP can help. $\endgroup$
    – VARulle
    Dec 27, 2023 at 11:54

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