Question

                                                                Demand for Health Insurance

Susan is a self-employed consultant, earning $85,000 annually. She does not have health insurance but knows that, in a given year, there is a 5 percent probability (i.e. 0.05) she will develop a serious illlness. If so, she could expect medical bills to be as high as $20,000. Susan derives utility from her income according to the following formula:

U = Y(0.25),(i.e. Y raised to the 0.25 power), where Y is annual income.

1. What is Susan's expected utility? Round to two decimals.

2. What is Susan's maximum willingness to pay for health insurance? Round nearest whole number.

3. What is Susan's risk premium? Round to nearest whole number.

4. Susan is offered an individual, full-coverage health insurance policy for which she would pay $1,700 annual premium. She is in the 22 percent tax break and could deduct the insurance premium for ger taxable income. Would she buy the policy, and would the tax deduction affect or change her decision? explain.

Answer 1

All assuming the income remains same even if ill-

1. Susan's expected utility= 0.95*85000^0.25+0.05*(85000-20000)^0.25=17.02

2. Income correspond to expected utility=17.0193^4=$83,903 hence, maximum willingness to payment=85000-83903=1097

3. Risk premium = willingness to pay-expected loss=1097-0.05*20000=$97

4. Net payment post tax deductible=(1-0.22)*1700=$1326 which is still higher than maximum willingness to pay hence the decision wil not change