This problem set will explore Adverse Selection and Moral Hazard. We recommend you review the learning materials and Wikipedia articles listed in the readings. Please search ""Adverse Selection in wikipedia Adverse Selection Problem

Its March 2020 and people are coming down with a strange virus. Right now, only 2% of the population have visible symptoms; they require hospitalization, and are known to have the virus. Another 10% have it but do not know it they are asymptomatic. The remaining 88% of the population do not have it.

At this point, there is not yet a test to determine whether an asymptomatic person has the virus. Hospitalization costs $35-45,000 (with an average of $40k). In the US, anyone who has the virus cannot buy insurance because they already have the condition. These unlucky few must pay out-of-pocket.

Asymptomatic patients have a 50% chance of needing hospitalization. Uninfected patients have a 10% chance of eventually needing hospitalization. Others who do contract the virus do not require hospitalization, and will convalesce at home, not requiring insurance. Both of these groups want to get insurance as soon as possible.

Q. No Insurance Case & Infected Case: What is the expected cost to someone who has the virus, visible symptoms, and needs hospitalization? Answer (numbers/vale)

Q. No Information Case: Assuming that both uninfected and asymptomatic patients want to buy insurance, how much would an insurance company in a competitive market charge for expected costs? Neither the insurance firms nor the prospective patients know who is infected but asymptomatic or uninfected. Answer: (No decimals)

Full information case: Suppose a test becomes available that can tell definitively whether an asymptomatic person has the virus. It can also tell that a person is uninfected. Assume the government will pay for the test so neither patients nor insurance firms need to pay for it. What are the prices of insurance offered in the market?

Q. For asymptomatic infected patients, the price is: (No decimals)

Q. For uninfected patients, the price is: (No decimals)

Asymmetric information case: Suppose that, before the test becomes available, asymptomatic patients themselves can determine whether they have the virus because they cannot taste strawberries. People who can taste strawberries dont have the virus. Otherwise, there are no outwardly visible signs, and people who can and cannot taste strawberries can easily lie, so both can claim that their taste is fine. Assume the asymmetric conditions hold for all remaining questions.

Q. Since asymptomatic patients can easily lie about their taste buds, insurance firms still have no data about who is uninfected and who is asymptomatic. From their perspective, what is the expected cost of offering insurance to uninfected and asymptomatic patients? Answer: (No decimals)

Q. At the expected average insurance cost in Question 4, what can be said about the insurance contract that the uninfected patients will purchase? (Choose best answer):

1. They will actually buy a contract for $5,400

2. They will actually buy a contract for $5,520

3. They will not pay $5,520 and will exit the market

4. They will actually buy a contract for $4,000

5. They will actually buy a contract for $4,200

The choice of the uninfected patients is best described as... (Choose best answer):

1. Moral Hazard

2. Signaling

3. Lemons Market

4. Private Insurance Market

Screening: It becomes known that the asymptomatic cases will mature into symptomatic cases within 14 days. Which of the following is the likely new insurance offered in the market by the insurance firms (Choose best answer):

1. A single contract priced at $4,000

2. A single contract priced at $5,520

3. A single contract priced at $20,000

4. A $20,000 and a $4,000 contract where the high-priced contract only provides coverage after 14 days

5. A $20,000 and a $4,000 contract where the low priced contract only provides coverage after 14 days

Signaling: Suppose that uninfected patients have a 1% chance of becoming infected and symptomatic in 10 days, in which case they are on their own for coverage [expected costs would be (1%)(40,000)=$400]. A new test is developed that will prove the presence or absence of the virus. It costs $20, and the government will not pay for it. Which option best describes the choice of patients in the market (choose best answer):

1. Uninfected patients pay out-of-pocket to take the test

2. Asymptomatic patients pay out-of-pocket to take the test

3. Both uninfected patients and asymptomatic patients pay to take the test

4. The insurance firms pay to test patients so they can offer $4,000 and $20,000 contracts

5. The insurance firms pay to test patients so they can offer a $5,520 contract

6. The insurance firms pay to test patients so they can offer $4,000, $5,520 and $20,000 contracts