Quadratic utility: monotonicity and risk aversion 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?
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 $w, u'(w)&lt;0$. 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.