In: Economics
A decision maker (DM) has a house worth $80,000 and $10,000
cash. These are all of his assets. There is a risk of a fire in
which case he will lose the house altogether. DM can insure against
the fire completely for a premium of $9,000. In other words, if he
buys this insurance his assets will be worth $81,000, whether or
not there is an accident. Probability of the fire is 0.1. (a) (10
points) If the decision maker is risk neutral, i.e., DM’s utility
function is u(x) = x, would he buy this insurance policy? (b) (10
points) If the decision maker is an expected utility maximizer and
has utility function px, where x is the value of his total assets,
would he buy this insurance policy?
(c) (10 points) Suppose he can buy partial insurance that covers
80% of the losses for a premium of $7,000. Would he buy this
insurance? Which one does he prefer, 100% insurance for $9,000 or
80% insurance for $7,000? (Assume u(x)=px)