3 Taking out insurance (12 points) Your utility function is U(W) = W1/4 . You are an art collector and terribly afraid of someone stealing your paintings. Your collection and other assets are worth $810,000. In case someone steals your art, you are left with only $10,000. The probability of theft is 20%. (a) Find the expected value and utility without insurance. (2) (b) How much would you maximally be willing to pay to an insurance if they cover you in case of theft? How much of it is due to your aversion to risk and how much is due to expected loss? (4) (c) AllProvince offers insurance for 25 cents per dollar. You have to pay the insurance no matter whether your collection gets stolen or not. How much insurance should you buy? [This number is not nice; round to dollars.] (4) (d) What are the expected profits AllProvince gets out of this insurance contract? (2)