Lucy and Henry each have $4321. Each knows that with 0.1 probability, they will lose 85% of their wealth. They both have the option of buying a units of insurance, with each unit costing $0.1. Each unit of insurance pays out $1 in the event the loss occurs. The cost of the insurance policy is paid regardless of whether the loss is incurred. Lucy's utility is given by u(x) = x. Henry's utility is given by u (x) = Vi. Answer the following: (If rounding is needed, only round at the end and write your answer to three decimal places.) ) (0.5 marks) Without insurance, what is the expected value of the loss? b) (0.5 marks) For Henry, facing the "lottery " above without any insurance is as bad as losing how many dollars for sure? c) (1 mark) Find Lucy's utility maximising choice of o. If more than 1 exist, enter the largest a. d) (1 mark) Now suppose insurance costs $0.2. Find Lucy's utility maximising choice of o. If more than 1 exist, enter the largest o. ) (1 mark) What is Henry's utility maximising choice of o with the new price of 0.2? If more than 1 exist, enter the largest a