<p>From the <a href="https://en.wikipedia.org/wiki/Prudence#In_economics" rel="nofollow noreferrer">Wikipedia</a> article:</p>

<blockquote>
  <p>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.</p>
</blockquote>

<p>For risk averse consumers with thrice differentiable utility  $u^{\prime\prime\prime}&gt;0$ is a <a href="https://www.jstor.org/stable/2296725" rel="nofollow noreferrer">necessary and sufficient condition</a> for consumers to save more for tomorrow when they are really unsure what is going to happen in the future.</p>

CC BY-SA 3.0
2018-02-25T18:06:41.130Z
A reference for "is a necessary and sufficient condition for consumers" would be nice!
Giskard
CC BY-SA 3.0
2018-03-04T20:16:36.957Z
This is ratherh close to being a link-only answer.
Acccumulation
CC BY-SA 3.0
2018-02-25T18:00:47.260Z
2018-02-26T01:40:32.857Z
2018-02-26T01:40:32.857Z
dsmithecon
<p>I'm having trouble seeing <em>why</em> 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. </p>

CC BY-SA 3.0
2018-02-25T20:06:37.027Z
Are you aware that prudence is related to the theory of [precautionary savings](https://en.wikipedia.org/wiki/Precautionary_savings#Theoretical_motivation)?
Herr K.
<macroeconomics><utility><saving><definition>
Intuition Behind the Definition of Prudence?
Freddie Papazyan
# Intuition Behind the Definition of Prudence?

(Asked by: username_0 on 2018-02-25)

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.

**Tags:** macroeconomics, utility, saving, definition

> **Comments:**
> **username_1**: Are you aware that prudence is related to the theory of [precautionary savings](https://en.wikipedia.org/wiki/Precautionary_savings#Theoretical_motivation)?  

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## 1 answers

### Answer by username_2 on 2018-02-25. Score: 5

From the [Wikipedia](https://en.wikipedia.org/wiki/Prudence#In_economics) 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](https://www.jstor.org/stable/2296725) for consumers to save more for tomorrow when they are really unsure what is going to happen in the future.

> **Comments:**
> **username_3**: A reference for "is a necessary and sufficient condition for consumers" would be nice!  
> **username_4**: This is ratherh close to being a link-only answer.  

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