I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility function. Could anyone please help with this?
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$\begingroup$ I think quadratic utility is associated with increasing absolute risk-aversion. The assumption being that there is reduced risk-taking from wealthier folk, because the marginal utility on conducting risk is decreasing. $\endgroup$– EB3112Commented Nov 26, 2020 at 8:23
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Quadratic utility is given by $$u(w) = w - b w^2$$ which has derivative $$u'(w) = 1- 2b w$$ such that for high levels of $w, u'(w)<0$. That is, the utility is not everywhere increasing. This may be weird because even people with high wealth should prefer more to less. The second derivative is $$u'(w) = -2b$$ such that absolute risk aversion is $$\frac{- u''(w)}{u'(w)} = \frac{ 2b}{1- 2b w},$$ which is increasing in wealth. This contradicts evidence that wealthier people take more financial risks instead of less.