(6 points) There are fifty low-risk people in a town and fifty high-risk people. A low-risk person has an average of $1,000 in medical expenses each year and is willing to pay $1,200 for medical insurance (this person is risk averse). A high-risk person has an average of $2,000 in medical expenses each year and is willing to pay $2,400 for medical insurance. Insurance companies are unable to tell who is high-risk and who is low-risk.

a) Show that an insurance company would lose money if it offered medical insurance at a price of $1,600.

b) Show that if the insurance company offered medical insurance at a price of $2,200, low-risk people would not be insured. Calculate total surplus if the price is $2,200.

c) Now suppose the government in this town passes a law that requires everyone to purchase medical insurance and sets the price of insurance at $1,600. Calculate total surplus under this law.