An entrepreneur has initial wealth of $88. Her initial wealth is invested in two buildings, each of which is worth $40. Her remaining $8 in initial wealth is invested in cash. Each building has a 25% chance of being destroyed and a 75% chance of not suffering any damage. Because the buildings are located far away from each other, these risks are statistically independent. Since the entrepreneur has $8 in cash, she can use some or all of this money to purchase actuarially fair insurance policies to cover her risks. Note that the price for an actuarially fair insurance policy equals the expected value of the payoff (indemnity) provided by the insurance policy. 1. (8 points) Given the entrepreneur's cash resources, if she covers 60% of the first building's potential loss, what is the maximum level of coverage (in terms of proportion of potential loss) that she can purchase against the risk that the second building will be destroyed? 2. (8 points) Given the entrepreneur's cash resources, what is the maximum level of coverage (in terms of proportion of potential loss) for each building that will result in the same premium being paid for each policy? == 3. (8 points) Suppose the entrepreneur's utility function is U(W) = W. Show that the entrepreneur is better off if she insures both buildings at the same level of coverage (for a total premium of $8) than she would be if she implemented the risk management strategy implied in Part 1 of this problem. 4. (8 points) Explain why the expected utility of having the same level of coverage on both buildings is higher than the expected utility of having different levels of coverage.