Consider the following expression:
where u''(w) is the second derivative of u evaluated at w
Appartently this is negative if we assume decreasing absolute risk aversion. That is if we assume that:
is a decreasing function.
We also know the following:
--all parameters are positive and
I would appreciate if someone could explain to me why the above expression is negative, given all the assumptions I listed. This is from a question on tax evasion and risk aversion. I thought it may have something to do with u(w) being more concave at different w's because of the condition on a(w), but I really cant get anything formal down. Thanks.