# Advance Microeconomics [closed]

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

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

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

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.