All that is needed to solve is QUESTION 5 & itssub-parts...
Asymmetric Information and SeparatingEquilibrium
A population has two equal-sized members of \"healthy\"and \"unhealthy\" individuals. Members of each type have the same,identical, utility function: U = 20Y0.5 (i.e. 20 x Y raised to the0.5 power), where Y is annual income.
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Assume each individual, in either group, has disposableincome (after normal expenses) of $19,000 a year. If in need ofmajor medical care (and does not have insurance), each individualwill have $15,000 in medical expenses. A \"healthy\" individual has a6% probability, while an \"unhealthy\" individual has a 18%probability, of requiring major medical care.
Use the information above to answer the questions (1through 5) below.
NOTE: An actuarially fair insurance premium (AFIP) isalways calculated as: AFIP = (Medical expenses covered) x(Probability of occurring).
1. Calculate the AFIP of the full-coverage policy for a\"healthy\" individual.
2. Calculate the AFIP of the full-coverage policy for an\"unhealthy\" individual. Â
3. Calculate the AFIP of a deductible policy for a\"healthy\" individual, for which the deductible is equal to$12,000.
4. Calculate the AFIP of a deductible policy for an\"unhealthy\" individual, for which the deductible is equal to$12,000.
5. Suppose health status (\"healthy\" or \"unhealthy\")represents asymmetric information: Each individual knows her or hishealth status, but insurance companies donot. Â
Now, suppose an insurance company offers only two typesof policies: 1) a full-coverage policy with premium equal to themost expensive (regardless of insurance type) of the twofull-coverage policies.
a. In the boxes below, calculate expected utility for a\"healthy\" individual, for each scenario:
No Insurance:
Most Expensive Full-Coverage Policy (Option1):
Least Expensive Deductible Policy (Option2):
b. In the boxes below, calculate expected utility for an\"unhealthy\" individual, for each scenario:
No Insurance:
Most Expensive Full-Coverage Policy (Option1):
Least Expensive Deductible Policy (Option2):
c. Based on your answers in 5a. and 5b., which optionwould a representative member of each group (i.e. \"healthy\" and\"unhealthy\") choose?
d. In the box below, enter the insurance company'sexpected economic profit from selling the desired policy (from theindividual's perspective) to a member of each group.
Expected Profit from \"Healthy\":
Expected Profit from \"Unhealthy\":
