Assuming that the landlord has a house worth 2 million yuan, if no risk management has been carried out, the fire probability of the house is 20%. A fire will lead to a loss of 1 million. After managing the risk of the house, the cost is 40,000 yuan, the probability of fire is 5%. Suppose the utility function of landlord is () = () ( is wealth).

(1) If the landlord doesn't buy any insurance, what are the expected utility when managing and not managing the risk? Will the landlord carry out risk management on the house?

(2) Suppose the insurance company thinks that the landlord will carry out risk management on the house, so as to sell fair full insurance to the landlord (the amount of insurance is 1 million and the premium is 50,000). What is the expected utility of the landlord' hen managing and not managing the risk?? Will the landlord carry out risk management on the house?

(3) The insurance company is also rational. After considering the moral hazard, the premium will be increased to 200,000 yuan. Will the landlord buy insurance again?