Calculating willingness to pay for health insurance)

Benjamin and Iris are deciding whether or not to buy health insurance from the individual market. Each of them has the same utility function U = 40(Y)1/4 and the same probability (20%) of becoming ill in the coming year. Benjamin expects his take home pay after taxes (Y), if he is well, to be $40,000 and if he is sick to be $20,000. Iris expects her take home pay after taxes (Y) if she is well to be $100,000 and if she is ill to be $80,000. Since they have the same health risk, their annual insurance premium is $7500 and will be deducted from their take home pay. So Benjamin will take home $32,500 if he buys insurance and Iris will take home $92,500 if she buys insurance

1. Illustrate what is the maximum premium which Benjamin is willing to pay for health insurance? Will he buy insurance when the premium is $7500? Could the health insurance organization charge Benjamin even more which $7500? How much could they charge?

2. Illustrate what is the maximum premium which Iris is willing to pay for health insurance? Will she buy insurance when the premium is $7500? Could the health insurance organization charge Iris even more? How much could they charge?

Now suppose which labour unions lobby Congress to allow the health insurance premium to be deducted from income taxes. Benjamin is in the 10% income tax bracket and Iris is in the 50% tax bracket.

1. With the tax deduction Benjamin pays 90% (1-.10) of the premium. Illustrate what is his out of pocket premium? Will he be willing to purchase insurance now which it is tax deductible?

2. Iris pays 50% (1-50%) of the premium. Illustrate what is her out of pocket premium now? Will she be willing to purchase health insurance now which it is tax deductible?

3. Who gets the largest tax benefit from the tax deduction of health insurance, Benjamin or Iris? (Compute the dollar value of the tax deduction)