1) This question is on health insurance. There are two types of customers: low-risk and high-risk. Half the population is high-risk and half the population is low-risk. Each person has wealth 400. The low-risk people get sick with probability 0.1 and the high-risk people get sick with probability 0.5. If they get sick their medical bill is 300. So without insurance they have wealth M=100 if they are sick, and M=400 otherwise. Their utility from wealth is . People know if they are high-risk or low-risk.

a.What is the expected value of the wealth of the low-risk and high-risk people?

i.Low-risk: E[V]=

ii.High-risk: E[V]=

b. How much would fair-insurance cost for each type (if their type was known)?

i.Price of fair insurance for low-risk: =

ii.Price of fair insurance for high-risk: =

c. What is the expected utility of the low-risk and high-risk people without insurance?

i.Low-Risk:E[U]=

ii.High-Risk: E[U]=

d.Are these people risk-averse, risk-loving, or risk-neutral?

e.Which types would be willing to buy insurance at price ?

f.Which types would be willing to buy insurance at price ?