Assume that everybody earns $100 which is spent on consumption c. Individuals face a probability s of becoming sick. If sick, they cannot work and earn $0. Individuals can purchase insurance from private firms. The insurance pays $100 if they get sick. The price of insurance is p.

Assume that there are three types of people (50 people of each type) that differ in the probability of getting sicks and their utility function over consumption c, and they are not observable:

Type I: s1 = 60% and U1(c) = c 1/2

Type II: s2 = 20% and U2(c) = c 1/2

Type III: s3 = 10% and U3(c) = c

a) Calculate how much each type is willing to pay for insurance w.

d) What is the equilibrium price of insurance? Who gets insured in equilibrium?

e) Should the government intervene in this market?

f) Assume instead that the probability of getting sick for type I individuals drops to s1 = 40%. What is the equilibrium price of insurance? Who gets insured in equilibrium?