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 Rios Dec 10 '18 at 7:01
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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.