Consider again the bank’s customer loan decision problem in Problem 49. Suppose now that the bank’s utility function of profit x (in dollars) is U(x) =1-e -x/150000 . Find the strategy that maximizes...

Consider again the bank’s customer loan decision problem in Problem 49. Suppose now that the bank’s utility function of profit x (in dollars) is U(x) =1-e^-x/150000. Find the strategy that maximizes the bank’s expected utility in this case. How does this optimal strategy compare to the optimal decision with an EMV criterion? Explain any difference in the two optimal strategies.

Problem 49

A customer has approached a bank for a $100,000 1-year loan at a 12% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Without additional information, the bank believes that there is a 4% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the bank will lose $100,000. At a cost of $1000, the bank can thoroughly investigate the customer’s credit record and supply a favorable or unfavorable recommendation. Past experience indicates that in cases where the customer did not default on the approved loan, 80% received a favorable recommendation on the basis of the credit investigation. Furthermore, in cases where the customer defaulted on the approved loan, 25% received a favorable recommendation on the basis of the credit investigation.

a.  What course of action should the bank take to maximize its expected profit?


b.  Compute and interpret the expected value of sample information (EVSI) in this decision problem. c.  Compute and interpret the expected value of perfect information (EVPI) in this decision problem.