There is a town with exactly 1,000 residents. 75% of the residents make healthy choices, and 25% of the residents consistently make unhealthy choices, but the health insurance company in town cannot tell who is healthy and who is unhealthy. A healthy person has an average of $600 in medical expenses each year and is willing to pay $800 for insurance. An unhealthy person has an average of $1,600 in medical expenses each year and is willing to pay $2,000 for insurance. The health insurance provider can offer insurance at only one price.

a. In equilibrium, what is the minimum price of insurance?

b. In equilibrium, who will buy insurance?