Decision Analysis – Practice Problems
DMUO ‐ 2015
Dr. Gunjan Malhotra
[email protected]
;
[email protected]
Question 1.
•
Bob’s bike shop is considering three options for its facility next year.
Bob can expand his current shop, move to a larger facility, or make
no change. With a good market, the annual payoff would be
$56,000 if he expands, $70,000 if he moves, and $30,000 if he does
nothing. With an average market, his payoffs will be $21,000,
$35,000, and $10,000, respectively. With a poor market, his payoff
will be ‐$29,000, ‐$45,000, and $5,000 respectively.
(a) Which option should Bob choose if he uses the maximax
criterion?
(b) Which option should Bob choose if he uses the maximin criterion?
(c) Which option should Bob choose if he uses the equally likely
criterion?
(d) Which option should Bob choose if he uses the criterion of realism
with α =0.6?
(e) Which option should Bob choose if he uses the minimax regret
criterion?
Answer 1.
(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.6) Alternatives Maximum Choice Minimum Choice Average Choice Realism Choice
Expand $56,000 -$29,000 $16,000 $22,000
Move $70,000 Best -$45,000 $20,000 Best $24,000 Best
No change $30,000 $5,000 Best $15,000 $20,000
Regret Outcomes (e) Minimax Alternatives Good Average Poor Maximum Choice
Expand $14,000 $14,000 $34,000 $34,000 Best Move $0 $0 $50,000 $50,000 No change $40,000 $25,000 $0 $40,000
Question 2.
•
Bob (in continuation to the previous question)
has gathered some additional information. The
probabilities of good, average, and poor markets
are 0.25, 0.45, and 0.3, respectively.
•
(a) Using EMVs, what option should Bob choose?
What is the maximum EMV?
•
(b) Using EOL, what option should Bob choose?
What is the minimum EOL?
•
(c) Compute the EVPI and show that it is the
same as the minimum EOL.
Answer 2.
Alternatives EMV Choice Expand $14,750
Move $19,750 Best No change $13,500
Expected Value WITH Perfect Information (EVwPI) = $34,750 Best Expected Monetary Value (EMV) = $19,750 Expected Value OF Perfect Information (EVPI) = $15,000
Alternatives EOL Choice Expand $20,000
Move $15,000 Best No change $21,250
Question 3.
•
Jeff Park sells newspapers on Sunday mornings in an area
surrounded by three busy churches. Assume that Jeff’s demand can
either be for 100, 200, or 300 newspapers, depending on traffic and
weather. Jeff has the option to order 100, 200, or 300 newspapers
from his supplier. Jeff pays$1.25 for each newspaper he orders and
sells each for $2.00.
•
(a) How many papers should Jeff order if he chooses the maximax
criterion?
•
(b) How many papers should Jeff order if he chooses the maximin
criterion?
•
(c) How many papers should Jeff order if he chooses the equally
likely criterion?
•
(d) How many papers should Jeff order if he chooses the criterion
of realism α =0.4?
•
(e) How many papers should Jeff order if he chooses the minimax
regret criterion?
Answer 3.
(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.4) (e) Minimax Alternative s Maximu m Choic e Minimu m Choic
e Average Choice Realism Choice
Maximu m Choic e 100 $75 $75 Best $75 $75 Best $150 200 $150 -$50 $83 Best $30 $125 Best 300 $225 Best -$175 $25 -$15 $250
Question 4.
•
Jeff Park (in continuation to question 3) has done
some research and discovered that the
probabilities for demands of 100, 200, and 300
newspapers are 0.4, 0.35, and 0.25, respectively.
•
(a) Using EMVs, how many paper should Jeff
order?
•
(b) Using EOL, how many paper should Jeff
order?
•
(c) Compute Jeff’s EVwPI and EVPI.
Answer 4.
Alternatives EMV Choice
100 $75 Best 200 $70
300 -$5
Expected Value WITH Perfect Information (EVwPI) = $139 Best Expected Monetary Value (EMV) = $75 Expected Value OF Perfect Information (EVPI) = $64
Alternatives EOL Choice
100 $64 Best 200 $69
Question 5.
• Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following payoff (profit) table: • (a) what is the maximax decision? • (b) what is the maximin decision? • (c) what is the equally likely decision? • (d) what is the criterion of realism decision, using α = 0.8? • (e) what is the minimax regret decision?Size Good Market ($) Fair Market ($) Poor Market ($)
Small 50,000 20,000 ‐10,000
Medium 80,000 30,000 ‐20,000
Large 1,00,000 30,000 ‐40,000
Answer 5.
(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.8) (e) Minimax Alternative s Maximu m Choic e Minimum Choic
e Average Choice Realism Choice
Maximu m Choic e Small $50,000 -$10,000 Best $20,000 $38,000 $250,000 Medium $80,000 -$20,000 $30,000 $60,000 $220,000 Large $100,000 -$40,000 $30,000 $72,000 $200,000 Very large $300,000 Best
Question 6.
• Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, ken has been able to increase his annual salary by a factor of over 100. At the present time, ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives, outcomes, and payoffs (profits) are shown in the following table: • (a) Ken has always been very optimistic decision maker. Which alternative is best from Ken’s point of view? • (b) Although ken is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob attributes his success to his pessimistic attitude about business and the oil industry. Which alternative is best from Bob’s point of view? • (c) The Lubricant is an expensive oil newsletter to ken subscribes. In the latest issue, the newsletter describes how the demand for oil products will be extremely high. Apparently, the American consumer will continue to use oil products even if the price of these products doubles. Indeed, one of the articles in the Lubricant states that the chance of a favourable market for oil products is 70%. If ken uses these probabilities in determining the best decision, which alternative is best?Equipment Favorable market ($) Unfavorable market ($)
Sub 100 300,000 ‐200,000
Oiler J 250,000 ‐ 100,000
Answer 6.
Outcomes
(a) Maximax
(b) Maximin
(c) EMV
Alternatives Fav mkt Unfav mkt Maximum Choice Minimum Choice EMV Choice
Sub 100
$300,000 -$200,000 $300,000 Best -$200,000
$150,000 Best
Oiler J
$250,000 -$100,000 $250,000
-$100,000
$145,000
Question 7.
•
A group of medical professionals is considering constructing a private
clinic. If patient demand for the clinic is high, the physicians could realize a
net profit of $100,000. If the demand is low, they could lose $40,000. Of
course, they don’t have to proceed at all, in which case there is no cost. In
the absence of any market data, the best the physicians can guess is that
there is a 50‐50 chance that demand will be good.
•
(a) construct a decision tree to help analyze this problem. What should the
medical professionals do?
•
(b) The physicians have been approached by a market research firm that
offers to perform a study of the market at a fee of $5,000. The market
researchers claim that their experience enables them to use Bayes’
theorem to make the following statements of probability:
• Probability of high demand given a positive study result = 0.82 • Probability of low demand given a positive study result = 0.18 • Probability of high demand given a negative study result = 0.11 • Probability of low demand given a negative study result = 0.89 • Probability of a positive study result = 0.55•
Expand the decision tree in part (a) to reflect the options now open with
the market study. What should the medical professionals do now?
Answer 7.
•
(a) EMV if we construct the clinic = 0.5 * $100,000 + 0.5 * (‐$40,000) =
$30,000. EMV if we do nothing = $0. Therefore, construct clinic.
•
•
(b) Excel: Construct clinic if result is positive. Do not construct clinic if
result is negative. EMV = $36,140
•
•
(c) EVSI = $11,140. Thus, the physicians would pay up to $11,140 more for
the survey. Note: Since EVSI should be calculated assuming no cost to
gather the sample information, $5,000 had to be added back to $36,140.
•
•
(d) EVwPI = $50,000. Best EMV = $30,000. EVPI = $20,000. Efficiency =
55.70%.
•
•
Answer 7.
0.82 High demand
(a) Construct clinic; EMV = $30,000 $95,000
(b) Conduct study. Construct clinic if positive result Construct $1,00,000 $95,000 Do not construct clinic if negative result.
EMV = $36,140 $0 $69,800 0.18
(c) EVSI = $11,140 0.55 Low demand
(d) EVwPI = $50,000 Positive result -$45,000
Best EMV = $30,000 1 -$40,000 -$45,000 EVPI = $20,000 $0 $69,800 Efficiency = 55.70% Not Construct -$5,000 $0 -$5,000 Study 0.11 -$5,000 $36,140 High demand $95,000 Construct $1,00,000 $95,000 $0 -$29,600 0.89 0.45 Low demand Negative result -$45,000 2 -$40,000 -$45,000 $0 -$5,000 1 Not Construct $36,140 -$5,000 $0 -$5,000 0.50 High demand $1,00,000 Construct $1,00,000 $1,00,000 $0 $30,000 0.50 Low demand No Study -$40,000 1 -$40,000 -$40,000 $0 $30,000 Not Construct $0 $0 $0 Problem 7
Question 8.
• Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50‐mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because there will be a five‐ year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry has done some analysis about the profitability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $60,000 if the market is good, but he will lose $40,000 if the market is bad. The small shop will return a $30,000 profit in a good market and a $10,000 loss in a bad market. At the present time, he believes that there is a 59% chance that the market will be good. Jerry also has the option of hiring his old marketing professor for $5,000 to conduct a marketing research study. If the study is conducted, the results could be either favorable or unfavorable. It is estimated that there is a 0.6 probability that the survey will be favorable. Furthermore, there is a 0.9 probability that the market will be good, given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of 0.12 of a good market if the marketing research results are not favorable. • (a) Develop a decision tree for Jerry and help him to decide what he should do. • (b) How much is the marketing professor’s information worth? What is the efficiency of this information>Answer 8.
•
(a) Conduct survey. If results are favorable,
build large shop. If the results are unfavorable,
don't build any shop.
•
•
(b) EVSI = $11,000. EVwPI = $35,400. Best
EMV = $19,000. EVPI = $16,400. Efficiency =
67.07%.
•
Answer 8.
0.59 Good m arket
(a) Conduc t s urvey $60,000
If favorable, build large s hop Large shop $60,000 $60,000 If unfavorable, don't build any s hop
EVSI = $11,000 $0 $19,000 0.41 Bad m arket (b) EVwPI = $35,400 -$40,000 Bes t EMV = $19,000 -$40,000 -$40,000 EVPI = $16,400 Effic ienc y = 67.07% 0.59 Good m arket No survey $30,000 1 Sm all shop $30,000 $30,000 $0 $19,000 $0 $13,600 0.41 Bad m arket -$10,000 -$10,000 -$10,000 No s hop $0 $0 $0 0.90 Good m arket $55,000 Large shop $60,000 $55,000 $0 $45,000 0.10 2 Bad m arket $25,000 -$45,000 -$40,000 -$45,000 0.90 0.60 Good m arket Favorable $25,000 1 Sm all shop $30,000 $25,000 $0 $45,000 $0 $21,000 0.10 Bad m arket -$15,000 -$10,000 -$15,000 No s hop -$5,000 $0 -$5,000 Survey 0.12 -$5,000 $25,000 Good m arket $55,000 Large shop $60,000 $55,000 $0 -$33,000 0.88 Bad m arket -$45,000 -$40,000 -$45,000 0.12 0.40 Good m arket Unfavorable $25,000 3 Sm all shop $30,000 $25,000 $0 -$5,000 $0 -$10,200 0.88 Bad m arket -$15,000 -$10,000 -$15,000 No s hop -$5,000 $0 -$5,000 Problem 8
Question 9.
Rob Johnson is a product manager for Diamond Chemical. The
firm is considering whether to launch a new product line that
will require building a new facility. The technology required to
produce the new product is yet untested. If Rob decides to build
the new facility and the process is successful, Diamond Chemical
will realize a profit of $650,000. If the process does not succeed,
the company will lose $800,000. Rob estimates that there is a
0.6 probability that the process will succeed.
Rob can also decide to build a pilot plant for $50,000 to
test the new process before deciding to build the full – scale
facility. If the pilot plant succeeds, Rob feels the chance of the
full‐scale facility succeeding is 85%. If the pilot plant fails, Rob
feels the chance of the full‐scale facility succeeding is only 20%.
The probability that the pilot plant will succeed is estimated at
0.6. Structure this problem with a decision tree and advise Rob
what to do.
Answer 9.
•
Build the pilot plant. If the pilot plant
succeeds, build facility. If the pilot plant fails,
don't build facility. Expected profit = $209,500.
•
Answer 9.
0.85 Facility works
Build the pilot plant. $6,00,000 If pilot plant succeeds, build facility. Build facility $6,50,000 $6,00,000
If pilot plant fails, don't build facility.
Expected profit = $209,500 $0 $3,82,500 0.15 0.60 Facility fails Pilot works -$8,50,000 1 -$8,00,000 -$8,50,000 $0 $3,82,500 Don't build -$50,000 $0 -$50,000 Build pilot 0.20 -$50,000 $2,09,500 Facility works $6,00,000 Build facility $6,50,000 $6,00,000 $0 -$5,60,000 0.80 0.40 Facility fails Pilot fails -$8,50,000 2 -$8,00,000 -$8,50,000 $0 -$50,000 Don't build -$50,000 1 $0 -$50,000 $2,09,500 0.60 Facility works $6,50,000 Build facility $6,50,000 $6,50,000 $0 $70,000 0.40 Facility fails -$8,00,000 -$8,00,000 -$8,00,000 Do nothing $0 $0 $0 Problem 9
Question 10.
•
Rob Johnson (see problem 9) has some revised
information concerning the accuracy of the pilot
plant probabilities. According to his new
information, the probability that the pilot plant
will be successful, given that the full‐scale facility
will work, is 0.8. The probability that the pilot
plant will fail, given that the full‐scale facility will
fail, is 0.85. Calculate the posterior probabilities
and reevaluate the decision tree from Problem 9.
Does this new information affect Diamond
Chemical’s original decisions?
Answer 10.
•
(a)
•
(b) Build the pilot plant. If the pilot plant succeeds,
build facility. If the pilot plant fails, don't build facility.
Expected profit = $244,300.
•
Prior Probabilities P(Facility works) = 0.60 P(Facility fails) = 0.40 Conditional probabilitiesP(Pilot works | Facility works) = 0.80 P(Pilot fails | Facility works) = 0.20 P(Pilot works | Facility fails) = 0.15 P(Pilot fails | Facility fails) = 0.85
Posterior probabilities GIVEN pilot works
Outcome P(Pilot works | Outcome) Prior prob Jt prob Post. prob Facility works 0.80 0.60 0.48 0.89 Facility fails 0.15 0.40 0.06 0.11 P(Pilot works) = 0.54
Posterior probabilities GIVEN pilot fails
Outcome P(Pilot fails | Outcome) Prior prob Jt prob Post. prob Facility works 0.20 0.60 0.12 0.26 Facility fails 0.85 0.40 0.34 0.74
Question 11.
•
Shamrock Oil owns a parcel of land that has the potential to be an
underground oil field. It will cost $500,000 to drill for oil. If oil does
exist on the land, Shamrock will realize a payoff of $4,000,000 (not
including drilling costs). With current information, Shamrock
estimates that there is a 0.2 probability that oil is present on the
site. Shamrock also has the option of selling the land as is for
$400,000, without further information about the likelihood of oil
being present. A third option is to perform geological tests at the
site, which would cost $100,000. There is a 30% chance that the
test results will be positive, after which Shamrock can sell the land
for $650,000 or drill the land, with a 0.65 probability that oil exists.
If the test results are negative, Shamrock can sell the land for
$50,000 or drill the land, with 0.05 probability that oil exists. Using
a decision tree, recommend a course of action for Shamrock Oil.
Answer 11.
•
Test the land. If the test result is positive, drill
for oil. If the test result is negative, sell the
land. Expected profit = $565,000.
•
•
Answer 11.
Test land. If test is positive, drill. If test is negative, sell. Expected profit = $565,000. Sell land $400 $400 $400 Sell land $550 0.3 $650 $550 Positive 2 0.65 $0 $2,000 Oil $3,400 Drill Land $4,000 $3,400 -$500 $2,000 0.35
Test land Dry
-$600 -$100 $565 $0 -$600 2 $565 Sell land -$50 0.7 $50 -$50 Negative 1 0.05 $0 -$50 Oil $3,400 Drill land $4,000 $3,400 -$500 -$400 0.95 Dry -$600 $0 -$600 0.2 Oil $3,500 Drill Land $4,000 $3,500 -$500 $300 0.8 Dry -$500 $0 -$500 Problem 11
Question 12.
•
Shamrock Oil (see Problem 11) has some revised
information concerning the accuracy of the
geological test probabilities. According to this
new information, the probability that the test will
be positive, given that the oil is present in the
ground, is 0.85. The probability that the test will
be negative, given that oil is not present, is 0.75.
Calculate the posterior probabilities and
reevaluate the decision tree from problem 11.
Does this information affect Shamrock Oil’s
original decision?
Answer 12.
•
(a)
•
(b) Test the land. If the test result is positive, drill
for oil. If the test result is negative, sell the land.
Expected profit = $427,300.
Prior Probabilities P(Oil well) = 0.20 P(Dry well) = 0.80 Conditional probabilitiesP(Positive test | Oil well) = 0.85 P(Negative test | Oil well) = 0.15 P(Positive test | Dry well) = 0.25 P(Negative test | Dry well) = 0.75
Posterior probabilities GIVEN positive test
Outcome P(Positive test | Outcome) Prior prob Jt prob Post. prob
Oil well 0.85 0.20 0.17 0.46
Dry well 0.25 0.80 0.20 0.54
P(Positive test) = 0.37
Posterior probabilities GIVEN negative test
Outcome P(Negative test | Outcome) Prior prob Jt prob Post. prob
Oil well 0.15 0.20 0.03 0.05
Dry well 0.75 0.80 0.60 0.95
Answer 12.
Test land. If test is positive, drill. If test is negative, sell. Expected profit = $427,300. Sell land $400 $400 $400.00 Sell land $550 0.37 $650 $550 Positive 2 0.46 $0 $1,240 Oil $3,400 Drill Land $4,000 $3,400 -$500 $1,240 0.54
Test land Dry
-$600 -$100 $427.30 $0 -$600 2 $427.30 Sell land -$50 0.63 $50 -$50 Negative 1 0.05 $0 -$50 Oil $3,400 Drill land $4,000 $3,400 -$500 -$400 0.95 Dry -$600 $0 -$600 0.2 Oil $3,500 Drill Land $4,000 $3,500 -$500 $300.00 0.8 Dry -$500 $0 -$500 Problem 12
Question 13
•
Shamrock Oil (see Problem 11) has decided to rely on utility
theory to assist in the decision concerning the oil field. The
following table describes its utility function; all monetary values
are in thousands of dollars:
•
(a) Redo problem 11 using this information.
•
(b) How can you best describe Shamrock Oil’s attitude toward
risk? Justify your answer.
Monetary Value ($) Utility ‐600 0.00 ‐500 0.03 ‐50 0.10 400 0.15 550 0.17 3400 0.90 3500 1.00Answer 13.
•
(a) Test the land. If the test result is positive, drill for oil. If the
test result is negative, sell the land. Expected utility = 0.246.
•
•
Test land. If test is positive, drill. If test is negative, sell. Expected utility = 0.246. Sell land 0.150 0.150 Sell land 0.170 0.30 0.170 Positive 2 0.65 0.585 Oil 0.900 Drill Land 0.90 0.585 0.35
Test land Dry
0.000 0.246 0.00 2 0.246 Sell land 0.100 0.70 0.100 Negative 1 0.05 0.100 Oil 0.900 Drill land 0.90 0.045 0.95 Dry 0.000 0.00 0.20 Oil 1.000 Drill Land 1.000 0.224 0.80 Dry 0.030 0.030 Problem 13 (a)
Answer 13.
•
(b) Shamrock Oil is a risk seeker.
Dollar Utility -$600 0.00 -$500 0.03 -$50 0.10 $400 0.15 $550 0.17 $3,400 0.90 $3,500 1.00 Risk seeker. Problem 13 (b) 0.00 0.25 0.50 0.75 1.00 -$600 $0 $600 $1,200 $1,800 $2,400 $3,000 $3,600 U til it y Monetary value Utility CurveQuestion 14.
Jim Sellers is thinking about producing a new type of electric razor for men. If the market is good, he would get a return of $100,000, but if the market for this new type of razor is poor, he would lose $60,000. Because Ron Bush is a close friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested two options to Jim. The first alternative is a sophisticated questionnaire that would be administered to a test market. It will cost $5,000. The second alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron has suggested that it would be a good idea for Jim to conduct either the questionnaire or the pilot before making the decision concerning whether to produce the new razor. But Jim is not sure if the value of either option is worth the cost. For the sake of solving this problem, assume that Jim has the following probability estimates available: the probability of a successful market without performing the questionnaire or pilot study is 0.5, the probability of a successful market given a positive questionnaire result is 0.78, the probability of a successful market given a negative questionnaire result is 0.27, the probability of the successful market given a positive pilot study result is 0.89, and the probability of a successful market given a negative pilot study result is 0.18. Further, the probability of a positive questionnaire result is 0.45 and the probability of a positive pilot study result is also 0.45. (a) Draw the decision tree for this problem and identify the best decision for Jim. (b) What is the value of the questionnaire’s information? What is its efficiency? (c) What is the value of the pilot study’s information? What is its efficiency?Answer 14.
•
(a)Conduct the survey questionnaire. If the
response is positive, produce razor. If the
response is negative, do not produce razor.
Expected return = $24,160.
•
•
(b) EVPI = $30,000. EVSI = $9,160. Efficiency =
30.53%.
•
•
(c) EVPI = $30,000. EVSI = $17,080. Efficiency =
56.93%.
Answer 14.
0.78 Good market
(a) Conduct questionnaire. $95,000
If positive, produce razor. Produce $1,00,000 $95,000
If negative, do not produce razor.
Expected return = $24,160. $0 $59,800 0.22
EVPI = $30,000 0.45 Poor market
Positive result -$65,000
(b) EVSI = $9,160 1 -$60,000 -$65,000
Efficiency = 30.53% $0 $59,800
(c) EVSI = $17,080 Not Produce
Efficiency = 56.93% -$5,000 $0 -$5,000 Questionnaire 0.27 -$5,000 $24,160 Good market $95,000 Produce $1,00,000 $95,000 $0 -$21,800 0.73 0.55 Poor market Negative result -$65,000 2 -$60,000 -$65,000 $0 -$5,000 Not Produce -$5,000 $0 -$5,000 0.89 Good market $80,000 Produce $1,00,000 $80,000 $0 $62,400 0.11 0.45 Poor market Positive pilot -$80,000 1 -$60,000 -$80,000 $0 $62,400 1 Not Produce $24,160 -$20,000 $0 -$20,000 Pilot study 0.18 -$20,000 $17,080 Good market $80,000 Produce $1,00,000 $80,000 $0 -$51,200 0.82 0.55 Poor market Negative pilot -$80,000 2 -$60,000 -$80,000 $0 -$20,000 Not Produce -$20,000 $0 -$20,000 0.5 Good market $1,00,000 Produce $1,00,000 $1,00,000 $0 $20,000 0.5 Poor market Neither test -$60,000 1 -$60,000 -$60,000 $0 $20,000 Not produce $0 $0 $0 Problem 14
Question 15.
•
Jim Sellers (see problem 14) has been able to
estimate his utility for a number of different
values, and he would like to use these utility
values in making his decision. The utility values
are U (‐$80,000) = 0, U(‐$65,000) = 0.5, U(‐
$60,000) = 0.55, U($80,000) = 0.9, U ($95,000) =
0.95, and U($100,000) = 1.
•
(a) Solve Problem 14(a) again using utility values.
•
(B) Is Jim a risk avoider or risk seeker? Justify your
answer.
Answer 15.
•
(a) Conduct the survey questionnaire. If the survey response is positive,
produce razor. If the survey response is negative, do not produce razor.
Expected utility = 0.823.
•
0.78 Good m arketConduc t ques tionnaire. 0.950
If pos itive, produc e raz or. Produc e 0.950
If negative, do not produc e raz or.
Expec ted utility = 0.823. 0.851 0.22
0.45 Poor m arket
Pos itive res ult 0.500
1 0.500 0.851 Not Produc e 0.800 0.800 Ques tionnaire 0.27 0.823 Good m arket 0.950 Produc e 0.950 0.622 0.73 0.55 Poor m arket
Negative res ult 0.500
2 0.500 0.800 Not Produc e 0.800 0.800 0.89 Good m arket 0.900 Produc e 0.900 0.801 0.11 0.45 Poor m arket
Pos itive pilot 0.000
1 0.000 0.00 0.801 1 Not Produc e 0.823 0.700 0.700 Pilot s tudy 0.18 0.745 Good m arket 0.900 Produc e 0.900 0.162 0.82 0.55 Poor m arket Negative pilot 0.000 2 0.000 0.700 Not Produc e 0.700 0.700 0.50 Good m arket 1.000 Produc e 1.000 0.775 0.50 Poor m arket Neither tes t 0.550 2 0.550 0.810 Not produc e 0.810 0.810 Pr oble m 15 (a)