Assume that only one health condition ever afflicts people for which one treatment is available, costing $100,000. The condition is very bad, so all consumers would be willing to pay for the treatment even if they did not have insurance. Consumers differ in their risk of being afflicted by the condition. Specifically, “healthy types” have a 1% chance of being afflicted, while “sickies” have an 11% probability, with an equal number of each type in the population.

For each of the following scenarios, calculate the premium (or premiums) for full insurance you would expect in a competitive market, and explain which consumers would be expected to purchase full insurance. Assume all consumers are risk-averse and only full insurance policies are available. Assume also that everyone (consumers and insurers) know the information above.

Scenario 1: Neither consumers nor insurers know anybody’s risk type.

Scenario 2: Consumers all know their own risk type, but insurers do not know the risk type of individual consumers.

Scenario 3: All consumers and insurers know everyone’s risk type.

Scenario 4: Same as Scenario 3, except “community rating” laws prevent insurers from charging different premiums to different consumers, and “guaranteed issues” laws prevent insurers from denying coverage to anyone. (I.e. full insurance must be offered to everyone at the same premium, regardless of their risk type.)

Scenario 5: Same as Scenario 4, but consumers are legally required to purchase full insurance.

Which scenarios lead to efficient outcomes in the insurance market? Why might someone prefer one efficient outcome over another?