Deck 9: Decision Making Under Uncertainty

Question 1

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

A)Prior probabilities
B)Posterior probabilities
C)Marginal probabilities
D)Objective probabilities

Answer 1

B

Question 2

The denominator of Bayes' rule:

A)is the same as the simple probability of an outcome O.
B)decomposes the probability of the new information I into all possibilities.
C)is sometimes called the law of complementary probabilities.
D)is unique for each possible outcome.

Answer 2

B

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

A)is useful in determining whether the optimal decision changes over the range of the input variable.
B)ranks the sensitivity of the EMV to the input variables.
C)reflects how the value of information changes over a range of probabilities.
D)None of these

Question 8

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

A)the mean, median, and mode
B)the set of decisions, the cost of each decision and the profit that can be made from each decision
C)the set of possible outcomes, the set of decision variables and the constraints
D)the set of decisions, the set of possible outcomes, and a value model that prescribes results

Question 9

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

A)decreasing, linear
B)decreasing, convex
C)increasing, linear
D)increasing, concave

Question 10

Expected monetary value (EMV) is:

A)the average or expected value of the decision if you knew what would happen ahead of time
B)the weighted average of possible monetary values, weighted by their probabilities
C)the average or expected value of the information if it was completely accurate
D)the amount that you would lose by not picking the best alternative

Question 11

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

Question 12

The solution procedure for solving decision trees is called:

A)sensitivity analysis
B)policy iteration
C)risk profiling
D)folding back

Question 13

Bayes' rule is used to:

A)update the prior probabilities once new information is observed.
B)turn the given conditional probabilities (i.e. likelihoods) around.
C)update the posterior probabilities once new information is observed.
D)All of the above are uses for Bayes' rule.

Question 14

Bayes' rule is used for updating the probability of an uncertain outcome after observing the results of a test or study.

Question 15

Prior probabilities are sometimes called likelihoods, the probabilities that are influenced by information about the outcome of an earlier uncertainty.

Question 16

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

Question 17

The risk profile shows the probability distribution of monetary outcomes in both graphical and tabular form.

Question 18

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

A)marginal due to
B)conditional on
C)averaged with
D)increased by

Question 19

Which of the following statements is true concerning decision tree conventions?

A)Time proceeds from right to left.
B)The trees are composed of circles, triangles and ovals.
C)The nodes represent points in time.
D)Probabilities of outcomes are shown to the right of the end nodes.

Question 20

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

Question 21

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. Should the credit union purchase the report if it costs $150?

Question 22

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. The bank can thoroughly investigate the customer's credit record and obtain a favorable or unfavorable recommendation. If the credit report is perfectly reliable, what is the most the credit union should be willing to pay for the report?

Question 23

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:

Refer to Exhibit 9-1. Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop.

Question 24

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. 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.

Question 25

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. 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?

Question 26

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:

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?

Question 27

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:

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.

Question 28

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:

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

Question 29

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?

Question 30

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:

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?