24. There are three types of individuals: e Super healthy: probability of getting sick is 0.1; correspond to 1/10 of the popu- lation e Average: probability of getting sick is 0.2; correspond to 8/10 of the population e Poor health: probability of getting sick is 0.3; correspond to 1/10 of the population Individuals have initial wealth W, = 8. If they get sick, they incur a monetary cost of 6. Other than that cost, the sickness does not affect their utility. The utility function over final wealth is u(W) = log,(W) (that is, log base 2: log,(2) = 1,log,(4) = 2,log,(8) = 3). There is a competitive market for full insurance. Thus, full insurance will be offered at the actuarially fair value (that is, the expected profit of insurance companies is zero). Individuals may choose to purchase insurance or not. What is the insurance premium 12 in this market? Hint: if your calculator does not have log base 2, computations using the natural logarithm should lead to the same results in this question. Solution: b