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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

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closed as off-topic by Herr K., Kenny LJ, Giskard, dismalscience, Kenneth Rios Dec 10 '18 at 7:01

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  • $\begingroup$ can anybody send me the full solution? thanx $\endgroup$ – rashid Dec 9 '18 at 11:55
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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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