Hello, I'm trying to understand how the range of w is determined. Per the non satiation property, U'(w) =1+2dw must be greater than 0. This implies that w>-1/2d. But according to the notes, the range of w is defined as, -inf<w<-1/2d Both of the above ranges take into account that d<0. So why should the ranges in the above two differ?
Hi, You are correct that if U'(w) > 0 , this implies that 2dw > -1. However, because U''(w) < 0 (risk averse), 2d < 0 and so d is negative. Therefore, because when dividing by a negative number you reverse the inequality, w < -1/2d . We have the minimum of -inf for w so that results in -inf<w<-1/2d . I hope this helps! Alvin.
