Exam 9: Decision Making Under Uncertainty

Exhibit 9-1A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 \ 0 0.15 \ 5,000 0.10 \ 10,000 0.15 \ 15,000 0.30 \ 20,000 -Refer to Exhibit 9-1. Suppose the farmer is uncertain about the reliability of the National Weather Service forecast. If he thinks the probability of a freeze occurring could be anywhere between 40% and 80%, would that change his decision?

The expected value of perfect information (EVPI) is a largely irrelevant concept since perfect information is almost never available at any price.

Exhibit 9-1A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 \ 0 0.15 \ 5,000 0.10 \ 10,000 0.15 \ 15,000 0.30 \ 20,000 -Refer to Exhibit 9-1. Suppose the farmer is not risk-neutral, but instead his behavior can be modeled using an exponential utility function with a risk tolerance parameter of 100,000. What is the most he would be willing to pay for insulation in that case?

The expected value of information (EVI) is the difference between the EMV obtained with free sample information and the EMV obtained without any information.

Probabilities on the branches of a chance node may be ____ events that have occurred earlier in the decision tree.

Exhibit 9-2A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000. -Refer to Exhibit 9-2. What should the credit union do? What is their expected profit?

A utility function for risk averse individuals is ____ and/or ____.

The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.

Which of the following are probabilities that are conditioned on information that is obtained?

Expected monetary value (EMV) is: