I'm having trouble seeing why an agent is said to exhibit "prudence" when u'''($\cdot$) > 0. How does having a utility function with a strictly positive third derivative make an agent act "prudently"? Thanks in advance.

  • $\begingroup$ Are you aware that prudence is related to the theory of precautionary savings? $\endgroup$
    – Herr K.
    Feb 25, 2018 at 20:06

1 Answer 1


From the Wikipedia article:

Economists describe a consumer as "prudent" if he or she saves more when faced with riskier future income. This additional saving is called precautionary saving.

For risk averse consumers with thrice differentiable utility $u^{\prime\prime\prime}>0$ is a necessary and sufficient condition for consumers to save more for tomorrow when they are really unsure what is going to happen in the future.

  • 2
    $\begingroup$ A reference for "is a necessary and sufficient condition for consumers" would be nice! $\endgroup$
    – Giskard
    Feb 25, 2018 at 18:06
  • $\begingroup$ This is ratherh close to being a link-only answer. $\endgroup$ Mar 4, 2018 at 20:16

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