Asymmetric Information and Insurance

(50 points)Assume that the typical individual in Wisconsin has an annual income of $45,000 a year and the annual cost of medical care if he contracts a chronic condition is $25,000.The probability of needing medical care is .2 for individuals who do not have any pre-existing condition (low-risk), and .4 for individuals who have a pre-existing condition (high-risk).Assume that 70% of the population are high-risk and 30% are low-risk.People are risk averse, and their utility function is U = sqrt(I).

a. (6 points)What is the expected utility for low-risk individuals? What is the expected utility for high-risk individuals?[Round to the second decimal]

You don't need to have answered question a. to answer questions b. through e.

GotchaCoveredis an insurance company that provides health insurance in Wisconsin.The Affordable Care Act of 2010 mandated that (i) insurance companies charge the same premiums to people regardless of their health status, and (ii) all people buy health insurance.

Given the proportion of low-risk and high-risk people, in 2018GotchaCoveredoffered a fair and full policy with C=25,000 and P=6,500 (which everyone was required to buy).The (expected) utility for both low-risk individuals and high-risk individuals under the policy is 196.21.

(b. 4 points)Is this insurance policy fair for low-risk individuals?

c. (6 points)Is this policy Pareto efficient?

d. (4 points)Without using math, explain why the expected utility for low-risk individuals and high-risk individuals under this policy is the same.

The Tax Cuts and Jobs Act eliminated the individual mandate.Therefore, in 2019, individuals could decide whether or not to purchase a health insurance policy.

e. (10 points)Illustrate the insurance company's decision using a decision tree.

f. (4 points)Given your answer to parta., do you expect low-risk individuals to purchase health insurance in 2019? Explain.

g. (6 points)WillGotchaCoveredcontinue to offer a policy with C=25,000 and P=6,500?

GotchaCoveredhires an economic consultant who suggests thatGotchaCoveredoffer a menu of health insurance policies.The economic consultant argues that ifGotchaCovereddesigns the policies carefully, both low-risk and high-risk will buy a policy fromGotchaCovered.The economic consultant suggests thatGotchaCoveredoffer a policy with C=3,500 and P=700 (Policy A) and a policy with C=25,000 and P=10,000 (Policy B).

It turns out that the consultant is right, and both groups (low-risk and high-risk) accept the policies.

h. (6 points)Which group will accept Policy A? Which group will accept Policy B?

i. (4 points)Is this policy a Pareto improvement compared to the full and fair policy described in partb.?