A manufacturer must decide whether to extend credit to a retailer who would like to open an account with the firm. Past experience with new accounts indicates that 45% are high risk, 35% are moderate risk and 20% are low risk customers. If credit is extended the manufacturer can expect to lose $60,000 with a high risk customer, make $50,000 with a moderate risk customer and make $100,000 with a low-risk customer. If the manufacturer decides not to extend credit to a customer, the manufacturer neither makes nor loses money. Prior to making a credit extension decision the manufacturer can obtain a credit report on the customer at a cost of $2000. The credit agency will rate the retailer as belonging to low, medium or high risk categories. The credit agency admits that its ratings are not perfect. In particular they will rate a low risk customer as moderate risk with probability 0.10 and as a high risk customer with probability 0.05. Furthermore they will rate a moderate risk customer as low risk with probability 0.06 and as a high risk customer with probability 0.07. Finally the rating procedure will rate a high risk customer as low risk with probability of 0.01 and as medium risk with probability 0.05.

Draw the decision diagram and find the strategy that maximizes the manufacturer’s expected net earnings.

Compute the EVSI and EVPI for this decision problem.

Re-evaluate the tree using an exponential utility function with R=$5000 and determine the expected value of the utility and its certainty equivalent. Did the decision change?