Understanding demand for health insurance is a key to formulating good health policy. In this question you will model how much people are willing to pay for a COVID-19 insurance plan. The plan only applies to this one disease. Here are our starting assumptions:

- the consumer has an income of $49 next year

- if they get sick they will have to pay $40 for tests and medicine

- they live in Florida so they have a 20% chance of getting sick

(a) Suppose the utility function is U(W)=W. Calculate the expected utility assuming that health insurance is not an option.

(b) What is the actuarily fair price of insurance for this consumer?

(c) Suppose a health insurance plan is offered that would cost $13 but cover any expenses in case the consumer got sick. Would they buy the plan?

(d) Calculate the risk premium that the consumer is willing to pay for health insurance.