8.4 Suppose there is a 50–50 chance that a risk-averse individual with a current wealth of $20,000 will contact a debilitating disease and suffer a loss of $10,000.

a. Calculate the cost of actuarially fair insurance in this situation and use a utility-of-wealth graph (such as shown in Figure 8.1) to show that the individual will prefer fair insurance against this loss to accepting the gamble uninsured.

b. Suppose two types of insurance policies were available:
(1) A fair policy covering the complete loss.
(2) A fair policy covering only half of any loss incurred.
Calculate the cost of the second type of policy and show that the individual will generally regard it as inferior to the first.