Risk and Uncertainty

Suppose Rita has log utility in wealth,u(w) = ln(w), and has an initial wealth of

$40,000. There is a 25% chance that she will be healthy this year and her wealth wont be affected by illness. However, there is a 50% chance that she will have a minor illness at some point and a 25% chance that she will experience a major illness. In the case of a minor illness, she will lose $5,000 of her wealth, but a major illness will cost her $30,000.

1. What is the expected value of Ritas wealth when she is faced with possible illness, ()?
2. What is her utility at that level of wealth, u[E(w)]?
3. What is her expected level of utility when faced with potential illness, E[u(w)]?
4. Show whether Rita is risk averse, risk neutral, or risk loving.
5. What is her certainty equivalent wealth when faced with potential illness?
6. What is the risk premium (Markowitz) associated with her potential illness? Interpret this.
7. Suppose that she can purchase a health insurance policy that removes the risk entirely (her wealth will remain at $40,000 with certainty). What is the most she will be willing to pay for the insurance policy?