<p>The derivative <span class="math-container">$u'(c)$</span> is defined as the limit of fractions of the form <span class="math-container">$\frac{\Delta u}{\Delta c}$</span>, so <span class="math-container">$\frac{u(c)}{u'(c)}$</span> is of the form <span class="math-container">$\frac{u\,\Delta c}{\Delta u}$</span>, which in terms of units reduces to units of consumption <span class="math-container">$c$</span> only.</p>

CC BY-SA 4.0
2023-12-22T17:18:43.500Z
+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?
Nicolas Torres
CC BY-SA 4.0
2023-12-27T11:54:03.360Z
@NicolasTorres I'm afraid I can't, as I don't recall ever having seen this "normalization" being used. Maybe the OP can help.
VARulle
CC BY-SA 4.0
2023-11-22T14:25:58.930Z
2023-11-22T14:25:58.930Z
VARulle
<p>It is frequently noted that if utility is given by <span class="math-container">$u(c)$</span>, then the object
<span class="math-container">$$ \frac{u(c)}{u^\prime (c)} $$</span>
puts the utility in consumption units via the normalisation by <span class="math-container">$u^\prime(c)$</span>. What is the intuition behind this normalisation? Why are these now consumption units of utility?</p>

<microeconomics><utility>
Understanding consumption units normalisation by $u^\prime (c) $
Debreu
# Understanding consumption units normalisation by $u^\prime (c) $

(Asked by: username_0 on 2023-11-21)

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?

**Tags:** microeconomics, utility

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## 1 answers

### Answer by username_1 on 2023-11-22. Score: 6

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.

> **Comments:**
> **username_2**: +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?  
> **username_1**: @NicolasTorres I'm afraid I can't, as I don't recall ever having seen this "normalization" being used. Maybe the OP can help.  

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