It's 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.

Question:

1. No Insurance Case & Infected Case: What is the expected cost to someone who has the virus, visible symptoms, and needs hospitalization?
2. 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.
3. 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?