Health Economics Second Problem Set (There are 3 worksheets to this assignment) Learning Objectives Upon completion of this problem set, students performing up to expectaion will be able to: 1. analyze and calculate elements of optimal insurance coverage for an individual, including: - expected utility - maximum willingness to pay for health insurance an actuarially fair insurance premium (AFIP) - risk premium 2. explain the affect of marginal income tax rates on the demand for health insurance 3. analyze and calculate a separating equilibrium to address adverse selection (i.e. information asymmetry) in health insurance markets . analyze the effect of employer-sponsored insurance on the supply and demand for labor (i.e. the labor market) and the cause of inefficiencies due to this mechanism of obtaining health insurance. 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 s a 5 percent probability (i.e. 0.05) she will develop a serious illness. 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: = Y(0.25), (i.e. Y raised to the 0.25 power), where Y is annual income. Use this information to answer the questions below . Questions: What is Susan's expected utility? Note: Round to two decimal places (either manually or using Excel's ROUND function). What is Susan's maximum willingness to pay for health insurance? lote: Round to nearest whole number What is Susan's risk premium? Note: Enter a formula to calculate the risk premium (round to nearest whole number). Susan is offered an individual, full-coverage health insurance policy for which she would have to pay a $1,700 annual premium. She is in the 22 percent tax bracket and could deduct the insurance premium from her taxable income. Would she buy the policy and would the tax deduction affect (or change) her decision? Briefly explainInformation Asymmetry A population has two equal-sized members of "healthy" and "unhealthy" individuals. Members of each type have the same, identical, utility function: U = 100Y0.3 (i.e. 100 x Y raised to the 0.3 power), where Y is annual income. Assume each individual, in either group, has disposable income (after normal expenses) of $18,000 a year. If in need of major medical care (and does not have insurance), each individual will have $15,000 in medical expenses. A "healthy" individual has a 2% probability, while an "unhealthy" individual has a 14% probability, of requiring major medical care. Use the information above to answer the questions (a. through f.) below. NOTE: An actuarially fair insurance premium (AFIP) is always calculated as: AFIP = (Medical expenses covered) x (Probability of occurring). Questions: a. Calculate the AFIP of the full-coverage policy for a "healthy" individual. b. Calculate the AFIP of the full-coverage policy for an "unhealthy" individual. . Calculate the AFIP of a deductible policy for a "healthy" individual, for which the deductible is equal to $12,000. 1. Calculate the AFIP of a deductible policy for an "unhealthy" individual, for which the deductible is equal to $12,000. e. Suppose health status ("healthy" or "unhealthy") represents asymmetric information: Each individual knows her or his health status, but insurance companies do not. Now, suppose an insurance company offers only two types of policies: 1) a full-coverage policy with premium equal to the most expensive (regardless of individual type) of the two full-coverage policies that you calculated above, and 2) a deductible policy with premium equal to the least expensive (regardless of individual type of the two deductible policies that you calculated above. e1. In the boxes below, calculate expected utility for a "healthy" individual, for each scenario: (NOTE: Round answers to nearest whole number)e. Suppose health status ("healthy" or "unhealthy") represents asymmetric information: Each individual knows her or his health status, but insurance companies do not. Now, suppose an insurance company offers only two types of policies: 1) a full-coverage policy with premium equal to the most expensive (regardless of individual type) of the two full-coverage policies that you calculated above, and 2) a deductible policy with premium equal to the least expensive (regardless of individual type) of the two deductible policies that you calculated above. e1. In the boxes below, calculate expected utility for a "healthy" individual, for each scenario: (NOTE: Round answers to nearest whole number) No Insurance: Most Expensive Full-Coverage Policy (Option 1): Least Expensive Deductible Policy (Option 2): e2. In the boxes below, calculate expected utility for an "unhealthy" individual, for each scenario: (NOTE: Round answers to nearest whole number) No Insurance: Most Expensive Full-Coverage Policy (Option 1):e1. In the boxes (NOTE: Round answers to nearest whole number) No Insurance: Most Expensive Full-Coverage Policy (Option 1): Least Expensive Deductible Policy (Option 2): e2. In the boxes below, calculate expected utility for an "unhealthy" individual, for each scenario: (NOTE: Round answers to nearest whole number) No Insurance: Most Expensive Full-Coverage Policy (Option 1): Least Expensive Deductible Policy (Option 2): e3. Based on your answers in e1. and e2., which option would a representative member of each group (i.e. "healthy" and "unhealthy") choose? f. Suppose the government mandates that all individuals purchase health insurance. Further, the government requires that all insurance companies offer the same policy: full coverage, with the premium equal to the average of the full-coverage premiums you calculated above (in questions a. and b.). f1. In the boxes below, calculate expected utility for a "healthy" and "unhealthy" individual from purchasing this insurance. "Healthy" "Unhealthy" f2. Are members of each group better or worse off with the mandate than with the market-based solution (i.e. choice in Question e.)? Briefly explain.f2. Are members of each group better or worse off with the mandate than with the market-based solution (i.e. choice in Question e.)? Briefly explain. Now, suppose an insurance company offers only two types of policies: 1) a full-coverage policy with premium equal to the most expensive (regardless of individual type) of the two full-coverage policies that you calculated above, and 2) a deductible policy with premium equal to the least expensive (regardless of individual type of the two deductible policies that you calculated above. e1. In the boxes below, calculate expected utility for a "healthy" individual, for each scenario: (NOTE: Round answers to nearest whole number) No Insurance: Most Expensive Full-Coverage Policy (Option 1): Least Expensive Deductible Policy Option 2) e2. In the boxes below, calculate expected utility for an "unhealthy" individual, for each scenario: (NOTE: Round answers to nearest whole number) No Insurance: Most Expensive Full-Coverage Polic (Option 1): Least Expensive Deductible Policy (Option 2): e3. Based on your answers in e1. and e2., which option would a representative member of each group (i.e. "healthy" and "unhealthy") choose? f. Suppose the government mandates that all individuals purchase health insurance. Further, the government requires that all insurance companies offer the same policy: full coverage, with the premium equal to the average of the full-coverage premiums you calculated above (in questions a. and b.). +e3. Based on your answers in e1. and e2., which option would a representative member of each group (i.e. "healthy" and "unhealthy") choose? f. Suppose the government mandates that all individuals purchase health insurance. Further, the government requires that all insurance companies offer the same policy: full coverage, with the premium equal to the average of the full-coverage premiums you calculated above (in questions a. and b.). f1. In the boxes below, calculate expected utility for a "healthy" and "unhealthy" individual from purchasing this insurance. "Healthy" "Unhealthy" f2. Are members of each group better or worse off with the mandate than with the market-based solution (i.e. choice in Question e.)? Briefly explain.Annual Wage Local Labor Market S Wo: $54,000 D Lo: 35,000 Quantity of Labor Questions: . Suppose all employers in this labor market begin to voluntarily contribute $5,000 annually, per worker, toward health insurance? (NOTE: Give specific values). In the long run, after the labor market has fully adjusted to this charge in the compensation structure, what would be the equilibrium wage and quantity of labor employed? b. Alternatively, suppose workers in this labor market are generally young and therefore place very little value, if any, on health-insurance contributions from employers. How would the equilibrium wage and quantity of labor likely be affected if a law was passed mandating that all employers contribute at least $5,000 a year toward each worker's health insurance? (NOTE: Your need only provide relative effects. comparing to vour villues in a. above)