Question

I was able to get questions 1 - 4 answer and only need question 5 and its sub-parts.

Asymmetric Information and Separating Equilibrium

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 the 0.5 power), where Y is annual income.

                          

Assume each individual, in either group, has disposable income (after normal expenses) of $19,000 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 6% probability, while an "unhealthy" individual has a 18% probability, of requiring major medical care.

Use the information above to answer the questions (1 through 5) below.

NOTE: An actuarially fair insurance premium (AFIP) is always 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.  

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 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 insurance type) of the two full-coverage policies.

a. In the boxes below, calculate expected utility for a "healthy" individual, for each scenario:

No Insurance:

Most Expensive Full-Coverage Policy (Option 1):

Least Expensive Deductible Policy (Option 2):

b. In the boxes below, calculate expected utility for an "unhealthy" individual, for each scenario:

No Insurance:

Most Expensive Full-Coverage Policy (Option 1):

Least Expensive Deductible Policy (Option 2):

c. Based on your answers in 5a. and 5b., which option would a representative member of each group (i.e. "healthy" and "unhealthy") choose?

d. In the box below, enter the insurance company's expected economic profit from selling the desired policy (from the individual's perspective) to a member of each group.

Expected Profit from "Healthy":

Expected Profit from "Unhealthy":

Answer 1