II - Reducing Risk

Consider a household with $160,000 worth of valuables, such as jewelry. This household faces a 0.2 probability of burglary, which means it loses $70,000 worth of valuables. Suppose it can buy an insurance policy for $15,000 that would fully reimburse the amount of loss from burglary. The household's utility is given byU(X) = 4X^0.5.

1. Should the household buy this insurance policy?
2. What is the actuarially fair price for the insurance policy?
3. What is the most the household is willing to pay for this insurance policy that fully covers it against the loss?