A decision maker (DM) has a house worth $80,000 and $10,000 cash. These are all of...

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)

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Rahul Sunny answered 2 years ago

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