CM2 Ch 2 Quadratic Utility function

[Nolasko]

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?

 

[Alvin Kissoon]

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.