Assume a consumer has initial wealth of $10,000, utility of wealth U(W) = W, and her wealth is subject to the following loss distribution:

Loss Amount (Ls) Probability (ps)

$0 50%

$1,000 25%

$9,000 25%

A. Determine the expected utility of wealth, assuming the consumer is uninsured.

B. Calculate the actuarially fair price for a full (100%) coverage insurance policy.

C. Show that it is optimal for this consumer to purchase a full coverage insurance policy at its actuarially fair price by comparing expected utility in the absence of insurance with expected utility in the presence of insurance.

D. If only full coverage insurance policies are available in the market, what is the maximum price that this consumer is willing to pay for such a policy?

E. Suppose this consumer may choose one of the following four risk management strategies: 1) Policy A fully covers all losses for a price of $3,125; 2) Policy B has a $1,000 deductible and costs $2,500; 3) Policy C covers 80% of all losses for a price of $2,500; and 4) Self-insure. Which of these four strategies will this consumer choose? Explain why.