$1000,000. A failure in the temperature, humidity, and air circulation systems can result in an estimated damage of $800,000 in this museum section. The likelihood (probability) of such a damage is 4%. The utility function of the museum administrators, with respect to the value of collections (), is given by () = .

a. Would the museum purchase an insurance policy with a coverage of $100,000 and a premium of $8,000? Would the insurance company make a profit or break even with this type of insurance policy? At which premium would the insurance company make zero profit for such coverage? Would then the museum purchase this policy?

b. What is the maximum premium that the museum would pay for a full-coverage policy? c. What is your answer to (b) if we believe the probability of a damage to the collection is 5%?