4 An individual has the following utility func tion uw ws w

4. An individual has the following utility func- tion: u(w) = ws where w = wealth.

Solution

1) Ranking: P2, P3, P1
Working:
P1 (.8, 1000, 600): .8 X 1000^.5 + .2 X 600^.5 = 30.197
P2 (.7, 1200, 600): .7 X 1200^.5 + .3 X 600^.5 = 31.59
P3 (.5, 2000, 300): .5 X 2000^.5 + .5 X 300^.5 = 31.02

2) lncertainty equivalent = .7*ln(1200) + .3*ln(600)=6.88
Certainty equivalent for Prospect P2= e^(6.88) = 2.72^6.88 = 976.864

3) P1 will have certainty equivalent that will be lower than the certainty equivalent of P2 because P1 is ranked lower than P2