(Our thanks to David Pyle, University of California, Berkeley, for providing this problem.) 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) homeowners insurance is up for renewal, and he has the following estimates of the potential losses on his house owing to fire, storm, etc., during the period covered by the renewal:
His insurance agent has quoted the following premiums:
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, i.e., U(W) = ln(W).
a) Given that the insurance company agrees with Mr. Casadesus's estimate of his losses, should he renew his policy (1) for the full value of his house, (2) for $40,000, or (3) for $30,000, or (4) should he cancel it?
b) Suppose that Mr. Casadesus had $320,000 in a savings account. Would this change his insurance decision?
c) If Mr. Casadesus has $20,000 in savings, and if his utility function is
U( W) = - 200,000 W
should he renew his home insurance? And if so, for what amount of coverage?
Note: Insurance covers the first x dollars of loss. For simplicity, assume that all losses occur at the end of the year and that the premium is paid at the beginning of the year.]