This is one of the questions form a practice worksheet for my final, but i have been having a difficult time.

Suppose there is 30% chance that a risk averse person with current wealth of $150,000 will suffer property damage of $30,000 due to a fire. This person has a utility function of U = ln(W ).

• a. What is the actuarially fair price for insurance in this case?
• b. Assuming this person does not buy insurance, what is the expected level of wealth? What is the expected level of utility?
• c. What is the maximum premium this consumer is willing to pay for full coverage of $30,000? Verify your answer by calculating E(U) when fully insured.
• d. Suppose this person can purchase full coverage at the actuarially fair rate. Is the consumer better off by doing so?
• f. Would this person be better off, compared to the part (d) outcome, if he purchased insurance to cover half the loss at a fair price?