Exam 9: Decision Making Under Uncertainty

Exhibit 9-2 A 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.Suppose that an actual (not perfectly reliable)credit report has the following characteristics based on historical data; 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 80%,while 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 25%.Given this information,what are the posterior probabilities that default will and will not occur,given the credit report

For each possible decision and each possible outcome,the payoff table lists the associated monetary value.

The solution procedure for solving decision trees is called:

Exhibit 9-1 A 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 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 monetary value (EMV)criterion represents the long-run average of uncertain outcomes,so it should only be used for recurring decisions.

Exhibit 9-1 A 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 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

Exhibit 9-1 A 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 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.Construct a risk profile and from that determine the probability that no additional cost is incurred if the decision to insulate at a cost of $20,000 is made.​​

The denominator of Bayes' rule:

For a risk averse decision maker,the certainty equivalent is less than the expected monetary value (EMV).

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

Exhibit 9-1 A 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 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.Construct a decision tree to help the farmer make his decision.What should he do Explain your answer.

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

The strategy region graph is a type of sensitivity analysis chart that:

Exhibit 9-2 A 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

All problems related to decision making under uncertainty have three common elements:

Exhibit 9-2 A 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.Construct a decision tree to help the credit union decide whether or not to make the loan.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Exhibit 9-2 A 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.Should the credit union purchase the report if it costs $150

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

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

In general,the expected monetary value (EMV)of a decision will be equal to one of the possible payoffs.