In a group of people 10% are unhealthy but don't know it. Of these 50% will likely need to be hospitalized. Of the 90% that are healthy, 10% will likely need be hospitalized. The cost of hospitalization is $50000.
What price of insurance should be offered in the market given:
Neither patients nor the insurance company know who is healthy or un-healthy.
Both patients and the insurance company know who is healthy or not healthy.
Patients know who is healthy or un-healthy but the insurers don't.
I think the answer to 1. is
(0.1 x 0.5 x 50000) + (0.9 x .1 x 50000) = 7000
but I am not sure how to get 2. and 3.
Any guidance would be appreciated.