Roger has the following utility function with respect to wealth:
U = 20W - 0.4W2.
Roger starts with W = 25.
a) Plot the utility function ( Use Excel ).
b) Will Roger buy insurance against a utility loss? Why or why not?
c) He has a 20% chance of losing 20. Calculate his expected loss, his expected wealth and his expected utility given this risk.
If Roger could insure himself fully against the loss and the insurance is actuarially fair.
d) What is the fair premium for his risk?
e) Calculate his utility gain due to insurance.
f) What value for the premium (instead of a fair premium would cause Roger to change his mind about purchasing this policy?