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Exam 5: Extension: Decision Theory

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Question 1

True/False

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Among decision environments, uncertainty implies that states of nature have wide-ranging probabilities associated with them.

A) True
B) False

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Question 2

Multiple Choice

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Option A has a payoff of $10,000 in environment 1 and $20,000 in environment 2. Option B has a payoff of $5,000 in environment 1 and $27,500 in environment 2. Once the probability of environment 1 exceeds ______, option A becomes the better choice.

A) .40
B) .45
C) .50
D) .57
E) .60

F) A) and B)
G) A) and E)

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E

Question 3

Multiple Choice

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The term "sensitivity analysis" is most closely associated with:

The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services, and she has estimated demand in three categories, low, medium, and high. $\begin{array} { | l | l | l | l | } \hline { \begin{array} { l } \text { NUMBER } \\\text { OF } \\\text { BEAUTICIANS }\end{array} } & { \text { DEMAND } } \\\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \\\hline \text { One } & 50 & 75 & 100 \\\hline \text { Two } & 0 & 100 & 100 \\\hline \text { Three } & - 100 & 70 & 300 \\\hline\end{array}$ If she uses the maximax criterion, how many beauticians will she decide to hire?

Expected monetary value gives the long-run average payoff if a large number of identical decisions could be made.

Consider the following decision scenario: $\begin{array} { | l | l | l | l | l | } \hline { \text { Alternative } } & { \text { State of Nature } } & & \\\hline & \# 1 & \# 2 & \# 3 & \# 4 \\ \hline \text { A } & 1 & 0 & 1 & 6 \\\hline \text { B } & 1 & 5 & 4 & 2 \\\hline \text { C } & 3 & 2 & 2 & 3 \\\hline\end{array}$ If you feel that P(#1) = .4, P(#2) = .3, P(#3) = .2, and P(#4) = .1, what is your expected value of perfect information?

One local hospital has just enough space and funds currently available to start either a cancer or heart research lab. If administration decides on the cancer lab, there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year, and an 80 percent chance of getting nothing. If the cancer research lab is funded the first year, no additional outside funding will be available the second year. However, if it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, the hospital's management decides to go with the heart lab, then there is a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year and a 50 percent change of getting nothing. If the heart lab is funded the first year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent chance for getting $50,000 and a 40 percent chance for getting nothing in the following year. For both the cancer and heart research labs, no further possible funding is anticipated beyond the first two years. What is the expected value for the optimum decision alternative?

The local operations manager for the Internal Revenue Service must decide whether to hire one, two, or three temporary tax examiners for the upcoming tax season. She estimates that net revenues (in thousands of dollars) will vary with how well taxpayers comply with the new tax code just passed by Congress, as follows: $\begin{array} { | l | l | l | l | } \hline { \begin{array} { l } \text { NUMBER } \\\text { OF } \\\text { EXAMINERS }\end{array} } & { \text { COMPLIANCE } } \\\hline & \text { LOW } & \text { NORMAL } & \text { HIGH } \\\hline \text { One } & 50 & 50 & 50 \\\hline \text { Two } & 100 & 60 & 20 \\\hline \text { Three } & 150 & 70 & - 10 \\\hline\end{array}$ If she uses the minimax regret criterion, how many new examiners will she decide to hire?

Option A has an expected value of $2,000, a minimum payoff of -$4,000, and a maximum payoff of $18,000. Option B has an expected value of $2,200, a minimum payoff of -$1,000, and a maximum payoff of $6,000. Option C has an expected value of $1,900, a minimum payoff of $100, and a maximum payoff of $2,000. In this situation, a risk-averse decision maker would pay __________ for his risk aversion, and a risk-seeking decision maker would pay __________ for his risk seeking.

Consider the following decision scenario: $\begin{array} {r} { \text { State of Nature } } \\\begin{array} { | l | l | l | } \hline & \text { Yes } & \text { No } \\\hline \text { Small } & \$ 10 ^ { * } & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Med.-Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Ex-Large } & 60 & 20 \\\hline\end{array}\end{array}$ *PV for profits ($000) The maximin strategy would be:

The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows: $\begin{array} { | l | l | l | l | } \hline { \text { ALTERNATIVE } } & { \text { PRECIPITATION } } \\\hline& \text { LOW } & \text { NORMAL } & \text { HIGH } \\\hline \text { Do Nothing } & - 100 & 100 & 300 \\\hline \text { Expand } & 350 & 500 & 200 \\\hline \text { Build New } & 750 & 300 & 0 \\\hline\end{array}$ If he uses the maximax criterion, which alternative will he decide to select?

A manager is quite concerned about the recent deterioration of a section of the roof on a building that houses her firm's computer operations. According to her assistant there are three options which merit consideration: A, B, and C. Moreover, there are three possible future conditions that must be included in the analysis: I, which has a probability of occurrence of .5; II, which has a probability of .3; and III, which has a probability of .2. If condition I materializes, A will cost $12,000, B will cost $20,000, and C will cost $16,000. If condition II materializes, the costs will be $15,000 for A, $18,000 for B, and $14,000 for C. If condition III materializes, the costs will be $10,000 for A, $15,000 for B, and $19,000 for C. (A) Draw a decision tree for this problem. (B) Using expected monetary value, which alternative should be chosen?

Decision trees, with their predetermined analysis of a situation, are really not useful in making health care decisions since every person is unique.

The term "suboptimization" is best described as the:

Sensitivity analysis is required because:

Consider the following decision scenario: $\begin{array} {r} { \text { State of Nature } } \\\begin{array} { | l | l | l | } \hline & \text { Yes } & \text { No } \\\hline \text { Small } & \$ 10 ^ { * } & 30 \\\hline \text { Medium } & 20 & 40 \\\hline \text { Med.-Large } & 30 & 45 \\\hline \text { Large } & 40 & 35 \\\hline \text { Ex-Large } & 60 & 20 \\\hline\end{array}\end{array}$ *PV for profits ($000) If yes and no are equally likely, which alternative has the largest expected monetary value?

The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, medium, or high, as follows: $\begin{array} { | l | l | l | l | } \hline \text { Bus } & { \text { DEMAND } } \\\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \\ \hline \text { Small } & 50 & 60 & 70 \\\hline \text { Medium } & 40 & 80 & 90 \\\hline \text { Large } & 20 & 50 & 120 \\\hline\end{array}$ If he feels the chances of low, medium, and high demand are 30 percent, 30 percent, and 40 percent respectively, what is the expected annual profit for the bus that he will decide to purchase?

In a decision-making setting, if the manager has to contend with limits on the amount of information he or she can consider, this __________ can lead to a poor decision.

Consider the following decision scenario: $\begin{array} { | l | l | l | l | l | } \hline { \text { Alternative } } & { \text { State of Nature } } & & \\\hline & \# 1 & \# 2 & \# 3 & \# 4 \\ \hline \text { A } & 1 & 0 & 1 & 6 \\\hline \text { B } & 1 & 5 & 4 & 2 \\\hline \text { C } & 3 & 2 & 2 & 3 \\\hline\end{array}$ If you feel that P(#1) = .4, P(#2) = .3, P(#3) = .2, and P(#4) = .1, what is your expected payoff under certainty?

Consider the following decision scenario: $\begin{array} { | l | l | l | l | l | } \hline { \text { Alternative } } & { \text { State of Nature } } & & \\\hline & \# 1 & \# 2 & \# 3 & \# 4 \\ \hline \text { A } & 1 & 0 & 1 & 6 \\\hline \text { B } & 1 & 5 & 4 & 2 \\\hline \text { C } & 3 & 2 & 2 & 3 \\\hline\end{array}$ If you feel that P(#1) = .4, P(#2) = .3, P(#3) = .2, and P(#4) = .1, which alternative will you select?