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
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.