PLEASE ANSWER 3c WITH WORK

3. Health Insurance. Masomenos, a premier health insurer, was asked by Verycheap Inc. to provide a quote on a health insurance policy for its employees. Masomenos evaluates that Verycheap's employers' projected yearly health expenditures are uniformly distributed between $0 and $4,000. It also estimates that each employer values such health expenditures $400 more than the actual cost. Finally, consider that Masomenos incurs in administrative costs of $100 per insured employee. (a) What price will Masomenos quote? What is the fraction of employees that will buy insurance? What is the expected health expenditures of the healthiest insurance subscriber? (20 points) (b) Now assume that Verycheap decides to subsidize insurance, by paying $100 to every employee that subscribes. What price will Masomenos quote? What is the fraction of employees that will buy insurance? What is the expected health expenditures of the healthiest insurance subscriber? (20 points) (c) Finally, assume that Verycheap's subsidy is ad-valorem, i.e. is expressed as a percentage of the insurance premium. What is the percentage subsidy that generates the same fraction of insured as in part (b)? (20 points)