<p>I assume that the agent is an expected utility maximizer with Bernoulli index <span class="math-container">$u$</span>, where <span class="math-container">$b$</span> and <span class="math-container">$y$</span> are fixed constants. Then, just take expectations of <span class="math-container">$u$</span> and try to write the right-hand side as function of the mean and variance of <span class="math-container">$M$</span>.</p>

<p>For the risk aversion part, recall that an expected-utility maximizer is risk averse if his Bernoulli index <span class="math-container">$u$</span> is concave. </p>

CC BY-SA 4.0
2018-12-09T05:27:53.093Z
2018-12-09T05:27:53.093Z
MJRS
<p>Show that u=a+bM-yM^2 represents a risk averter's utility function who is interested only in the mean and the variance of the state distribution of Income M.  Can anybody send me the full solution. thanx</p>

CC BY-SA 4.0
2018-12-09T11:55:45.227Z
can anybody send me the full solution? thanx
rashid
<microeconomics><econometrics><mathematical-economics>
Advance Microeconomics
rashid
# Advance Microeconomics

(Asked by: username_0 on 2018-12-09)

Show that u=a+bM-yM^2 represents a risk averter's utility function who is interested only in the mean and the variance of the state distribution of Income M. Can anybody send me the full solution. thanx

**Tags:** microeconomics, econometrics, mathematical-economics

> **Comments:**
> **username_0**: can anybody send me the full solution? thanx  

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## 1 answers

### Answer by username_1 on 2018-12-09. Score: 2

I assume that the agent is an expected utility maximizer with Bernoulli index $u$, where $b$ and $y$ are fixed constants. Then, just take expectations of $u$ and try to write the right-hand side as function of the mean and variance of $M$.

For the risk aversion part, recall that an expected-utility maximizer is risk averse if his Bernoulli index $u$ is concave.


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