Healthcare problem

Consider an insurance company. Risk level varies across insurance buyers with expected losses of $0, $1,000, $2,000, $3,000, and $4,000. Each risk class has the same probability 20%. The monetary surplus from purchasing insurance is k = $1,000. Sellers of insurance compete away the surplus to insurance buyers.

(a) Suppose that insurance is mandatory, and that its cost is covered through the tax system, what is the average price of insurance?

(b) Suppose that the insurance company can perfectly classify insurance buyers into respective category. What is the average price of insurance?

(c) Suppose that neither the insurance company nor the insurance buyer knows the risk level. What is the average price of insurance?

(d) Suppose that the insurance buyer knows his type, while the insurance company does not have the resources to find out. What is the average price of insurance?