# Consider again the bank’s customer loan decision problem in Problem 51. Suppose now that the…

Consider again the bank’s customer loan decision problem in Problem 51. 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 between the two optimal strategies.

Problem 51

A customer has approached a bank for a \$100,000 oneyear 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, the probability of receiving a favorable recommendation on the basis of the credit investigation was 0.80. Furthermore, in cases where the customer defaulted on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 0.25.

a. What strategy should the bank follow to maximize its expected profit?

b. Calculate and interpret the expected value of sample information (EVSI) for this decision problem.

c. Calculate and interpret the expected value of perfect information (EVPI) for this decision problem.

d. How sensitive are the results to the accuracy of the credit record recommendations? Are there any “reasonable” values of the error probabilities that change the optimal strategy?