Nate Jacobs keeps $100,000 cash in a checking account that pays no interest. If he gets injured and is taken to hospital, Nate will pay a cost of $50,000. The chance of this happening is 1/100. He can, however, get health insurance that would completely reimburse to him the $50,000 if he is injured. (a) If his utility function is U = Y1/2, where Y denotes the amount of cash he has, what's the expected utility of not being insured? (b) Assume his utility function is U = Y1/2. If he has to pay a premium for this health 2 A insurance, what's the expected utility of being insured. (Write EU as a function of ) = (c) Assume his utility function is U-Y1/2, What's the insurance premium 7 so that he is indifferent between being insured and not being insured? = (d) What if his utility function is U-Y2. What's the insurance premium so that he is indifferent between being insured and not being insured? (e) What if his utility function is U = Y. What's the insurance premium w so that he is indifferent between being insured and not being insured? (f) If it's a fair insurance, the insurance premium is $500 (that's 100*$50,000). With which utility function above, Nate will strictly prefer being insured than not being insured? Why