Mr. Casadesus's current wealth consists of his home, which is worth $50,000, and $20,000 in savings, which are earning 7% in a savings and loan account. His (one-year) homeowner's insurance is up for renewal, and he has the following estimates of the potential losses on his house owing to fire, storm, and so on, during the period covered by the renewal:

Table 1:

Value of Loss ($) Probability 0 .98 5.000 .01 10.000 .005 50,000 .005

His insurance agent has quoted the following premiums:

Table 2: Amount of Insurance coverage ($) Premium ($) 30.0 30 + AVL1 40.0 27 + AVL2 50.0 24 + AVL3

where AVL = actuarial value of loss = expected value of the insurer's loss.

Mr. Casadesus expects neither to save nor to dissave during the coming year, and he does not expect his home to change appreciably in value over this period. His utility for wealth at the end of the period covered by the renewal is logarithmic; that is, U(W) = ln(W).

(a) Calculate the AVL from the insurer's viewpoint, since the insurer sets the premiums (b) Calculate the premium for each amount of coverage. (c) Calculate the end of period wealth of Mr. Casadesus if he chooses one of the amounts of insurance coverage in Table 2 or no insurance.

(d) Calculate the expected utility of the end of period wealth for all the amounts of insurance coverage in Table 2 or no insurance. Will Mr. Casadesus, who maximizes expected utility of end of period wealth, renew the insurance policy for the full value of the home, for $40,000, for $30,000 or will he opt cancel it?