Editing Prudence (section)

== In economics ==
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Economists describe a [[consumer]] as "prudent" if he or she [[Saving|saves]] more when faced with [[risk]]ier future income. This additional saving is called [[precautionary saving]].

If a risk-averse consumer has a [[utility function]] <math>u(x)</math> over consumption <math>x</math>, and if <math>u(x)</math> is [[Derivative|differentiable]], then the consumer is not prudent unless the third [[derivative]] of utility is positive, that is, <math>
u'''\left(x\right)>0
</math>.<ref>{{cite journal |first=A. |last=Sandmo |year=1970 |title=The Effect of Uncertainty on Saving Decisions |journal=[[Review of Economic Studies]] |volume=37 |issue=3 |pages=353–360 |doi=10.2307/2296725 |jstor=2296725 }}</ref>

The strength of the precautionary saving motive can be measured by '''absolute prudence''', which is defined as
<math>
-\frac{u'''\left(x\right)}{u''\left(x\right)}
</math>. Similarly, '''relative prudence''' is defined as absolute prudence, multiplied by the level of consumption. These measures are closely related to the concepts of absolute and relative [[risk aversion]] developed by [[Kenneth Arrow]] and [[John W. Pratt]].<ref>{{cite journal |first=Miles S. |last=Kimball |year=1990 |title=Precautionary Saving in the Small and in the Large |journal=[[Econometrica]] |volume=58 |issue=1 |pages=53–73 |doi=10.2307/2938334 |jstor=2938334 |s2cid=153558057 |url=http://www.nber.org/papers/w2848.pdf }}</ref>