Consider the following expression:

$\displaystyle

ps[1-t-st]u''([1-t-st]y+stx)-(1-p)u''(y-tx)

$

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:

$\displaystyle a(w)=-u''(w)/u'(w)$ is a decreasing function.

We also know the following:

--all parameters are positive and

$\displaystyle

p<1;

t<1;

x<y;

u''(w)<0;

u'(w)>0;

$

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.