Decision Analysis – Practice Problems
DMUO ‐ 2015
Dr. Gunjan Malhotra
[email protected];
[email protected] 9/8/2015
IMT, Ghaziabad, INDIA
1
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 Alternatives Maximum Choice Minimum Choice Expand $56,000 -$29,000 Move $70,000 Best -$45,000 No change $30,000 $5,000 Best
(c) Equally Likely (d) Hurwicz (0.6) Average Choice Realism Choice $16,000 $22,000 $20,000 Best $24,000 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 Expand Move No change
EMV $14,750 $19,750 $13,500
Choice Best
Expected Value WITH Perfect Information (EVwPI) = $34,750 Best Expected Monetary Value (EMV) = $19,750 Expected Value OF Perfect Information (EVPI) = $15,000 Alternatives Expand Move No change
EOL Choice $20,000 $15,000 Best $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. (c) Equally Likely
(d) Hurwicz (0.4)
(a) Maximax (b) Maximin (e) Minimax Alternative Maximu Choic Minimu Choic Maximu Choic s m e m e Average Choice Realism Choice m 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 $69 300 $144
Question 5. •
• • • • •
Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following payoff (profit) table: Size
Good Market ($)
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
Very Large 3,00,000 25,000 (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?
‐1,60,000
Answer 5. (a) Maximax (b) Maximin Alternative Maximu Choic Choic s m e Minimum e Small $50,000 -$10,000 Best Medium $80,000 -$20,000 Large $100,000 -$40,000 Very large $300,000 Best $160,000
(c) Equally Likely
(d) Hurwicz (0.8)
Average Choice Realism $20,000 $38,000 $30,000 $60,000 $30,000 $72,000
(e) Minimax Maximu Choic Choice m e $250,000 $220,000 $200,000
$55,000 Best $208,000 Best $150,000 Best
Question 6. •
• •
•
Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, ken has been able to increase his annual salary by a factor of over 100. At the present time, ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives, outcomes, and payoffs (profits) are shown in the following table: Equipment
Favorable market ($)
Unfavorable market ($)
Sub 100
300,000
‐200,000
Oiler J
250,000
‐ 100,000
Texan
75,000
‐18,000
(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?
Answer 6. Outcomes Alternatives Fav mkt Unfav mkt Sub 100 $300,000 -$200,000 Oiler J $250,000 -$100,000 Texan $75,000 -$18,000
(a) Maximax (b) Maximin (c) EMV Maximum Choice Minimum Choice EMV Choice $300,000 Best -$200,000 $150,000 Best $250,000 -$100,000 $145,000 $75,000 -$18,000 Best $47,100
• DECISION TREES
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. Problem 7
0.82 High demand
(a) Construct clinic; EMV = $30,000 (b) Conduct study. Construct clinic if positive result Do not construct clinic if negative result. EMV = $36,140 (c) EVSI = $11,140 0.55 (d) EVwPI = $50,000 Positive result Best EMV = $30,000 1 EVPI = $20,000 $0 $69,800 Efficiency = 55.70%
$95,000 Construct
$1,00,000 $0
$69,800
$95,000
0.18 Low demand -$45,000 -$40,000 -$45,000
Not Construct -$5,000 $0
-$5,000
Study -$5,000
0.11 High demand
$36,140
$95,000 Construct
$1,00,000 $0
-$29,600
0.45 Negative result
0.89 Low demand -$45,000
2 $0
$95,000
-$40,000 -$45,000
-$5,000
1
Not Construct
$36,140
-$5,000 $0
-$5,000
0.50 High demand $1,00,000 Construct $0
$1,00,000 $1,00,000 $30,000
0.50 Low demand
No Study
-$40,000 1
$0
-$40,000
-$40,000
$30,000 Not Construct $0 $0
$0
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. Problem 8
0.59 Good market
(a) Conduc t s urvey
$60,000
Large shop
If favorable, build large s hop If unfavorable, don't build any s hop EVSI = $11,000 (b) EVwPI = Bes t EMV = EVPI = Effic ienc y =
$0
$60,000
$60,000
0.41 Bad market
$19,000
$35,400 $19,000 $16,400 67.07%
-$40,000 -$40,000
-$40,000
0.59 Good market
No survey
$30,000 1
$0
Small shop
$30,000
$30,000
$19,000 $0
0.41 Bad market
$13,600
-$10,000 -$10,000
-$10,000
No shop $0 $0
$0
0.90 Good market $55,000
Large shop $0
$60,000 $45,000
$55,000
0.10 Bad market
2 $25,000
-$45,000 -$40,000
-$45,000
0.90 Good market
0.60 Favorable
$25,000 1
$0
Small shop
$30,000
$25,000
$45,000 $0
$21,000
0.10 Bad market -$15,000 -$10,000
-$15,000
No shop -$5,000 $0
-$5,000
Survey -$5,000
0.12 Good market
$25,000
$55,000
Large shop $0
$60,000 -$33,000
$55,000
0.88 Bad market -$45,000 -$40,000
0.12 Good market
0.40 Unfavorable
$25,000
3 $0
-$45,000
Small shop
$30,000
$25,000
-$5,000 $0
-$10,200
0.88 Bad market -$15,000 -$10,000
-$15,000
No shop -$5,000 $0
-$5,000
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. Problem 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
0.60 Pilot works
-$8,50,000 1
$0
0.15 Facility fails -$8,00,000
-$8,50,000
$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 $0
-$5,60,000
0.40 Pilot fails
$6,00,000
0.80 Facility fails -$8,50,000
2 $0
$6,50,000
-$8,00,000
-$8,50,000
-$50,000 Don't build -$50,000
1
$0
-$50,000
$2,09,500 0.60 Facility works $6,50,000 Build facility $0
$6,50,000 $70,000
$6,50,000
0.40 Facility fails -$8,00,000 -$8,00,000
-$8,00,000
Do nothing $0 $0
$0
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)
Prior Probabilities P(Facility works) = P(Facility fails) = Conditional probabilities P(Pilot works | Facility works) = P(Pilot fails | Facility works) = P(Pilot works | Facility fails) = P(Pilot fails | Facility fails) =
Posterior probabilities GIVEN pilot works Outcome P(Pilot works | Outcome) Facility works 0.80 Facility fails 0.15 Posterior probabilities GIVEN pilot fails Outcome P(Pilot fails | Outcome) Facility works 0.20 Facility fails 0.85
0.60 0.40 0.80 0.20 0.15 0.85
Prior prob 0.60 0.40 P(Pilot works) =
Jt prob 0.48 0.06 0.54
Post. prob 0.89 0.11
Prior prob 0.60 0.40 P(Pilot fails) =
Jt prob 0.12 0.34 0.46
Post. prob 0.26 0.74
• (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. •
Answer 10.
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. Problem 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 Positive
$650
$550
2 $0
0.65
$2,000
Oil $3,400 Drill Land -$500
$4,000 $2,000
Test land
$3,400
0.35 Dry -$600
-$100
$565
$0
-$600
2 $565
Sell land -$50 0.7 Negative
$50
-$50
1 $0
0.05
-$50
Oil $3,400 Drill land -$500
$4,000 -$400
$3,400
0.95 Dry -$600 $0
-$600
0.2 Oil $3,500 Drill Land -$500
$4,000 $300
$3,500
0.8 Dry -$500 $0
-$500
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)
Prior Probabilities P(Oil well) = P(Dry well) = Conditional probabilities P(Positive test | Oil well) = P(Negative test | Oil well) = P(Positive test | Dry well) = P(Negative test | Dry well) =
Posterior probabilities GIVEN positive test Outcome P(Positive test | Outcome) Oil well 0.85 Dry well 0.25 Posterior probabilities GIVEN negative test Outcome P(Negative test | Outcome) Oil well 0.15 Dry well 0.75
0.20 0.80 0.85 0.15 0.25 0.75
Prior prob 0.20 0.80 P(Positive test) =
Jt prob 0.17 0.20 0.37
Post. prob 0.46 0.54
Prior prob 0.20 0.80 P(Negative test) =
Jt prob 0.03 0.60 0.63
Post. prob 0.05 0.95
• (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.
Answer 12. Problem 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 Positive
$650
$550
2 $0
0.46
$1,240
Oil $3,400 Drill Land -$500
$4,000 $1,240
Test land
$3,400
0.54 Dry -$600
-$100
$427.30
$0
-$600
2 $427.30
Sell land -$50 0.63 Negative
$50
-$50
1 $0
0.05
-$50
Oil $3,400 Drill land -$500
$4,000 -$400
$3,400
0.95 Dry -$600 $0
-$600
0.2 Oil $3,500 Drill Land -$500
$4,000 $300.00
$3,500
0.8 Dry -$500 $0
-$500
Question 13 • Shamrock Oil (see Problem 11) has decided to rely on utility theory to assist in the decision concerning the oil field. The following table describes its utility function; all monetary values are in thousands of dollars: Monetary Value ($)
Utility
‐600
0.00
‐500
0.03
‐50
0.10
400
0.15
550
0.17
3400
0.90
3500
1.00
• (a) Redo problem 11 using this information. • (b) How can you best describe Shamrock Oil’s attitude toward risk? Justify your answer.
Answer 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. •
Problem 13 (a)
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 Positive
0.170 2
0.65
0.585
Oil 0.900 Drill Land
0.90 0.585
Test land
0.35 Dry 0.000
0.246
0.00
2 0.246
Sell land 0.100 0.70 Negative
0.100 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
Answer 13. • (b) Shamrock Oil is a risk seeker. Problem 13 (b) Utility Curve 1.00 0.75
Utility
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
0.50 0.25 0.00 -$600
$0
$600
$1,200
$1,800
Monetary value Risk seeker.
$2,400
$3,000
$3,600
Question 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. Problem 14
0.78 Good market
(a) Conduct questionnaire. If positive, produce razor. If negative, do not produce razor. Expected return = $24,160. EVPI = $30,000 (b) EVSI = Efficiency =
$9,160 30.53%
(c) EVSI = Efficiency =
$17,080 56.93%
$95,000 Produce
$1,00,000
$0
$59,800
0.45 Positive result
0.22 Poor market -$65,000
1 $0
$95,000
-$60,000
-$65,000
$59,800 Not Produce -$5,000 $0
-$5,000
Questionnaire -$5,000
0.27 Good market
$24,160
$95,000 Produce
$1,00,000
$0
-$21,800
0.55 Negative result
0.73 Poor market -$65,000
2 $0
$95,000
-$60,000
-$65,000
-$5,000 Not Produce -$5,000 $0
-$5,000 0.89 Good market $80,000
Produce
$1,00,000
$0
$62,400
0.45 Positive pilot
0.11 Poor market -$80,000
1 $0
$80,000
-$60,000
-$80,000
$62,400
1
Not Produce
$24,160
-$20,000 $0
-$20,000
Pilot study -$20,000
0.18 Good market
$17,080
$80,000 Produce
$1,00,000
$0
-$51,200
0.55 Negative pilot
0.82 Poor market -$80,000
2 $0
$80,000
-$60,000
-$80,000
-$20,000 Not Produce -$20,000 $0
-$20,000
0.5 Good market $1,00,000 Produce $0
$1,00,000 $20,000
$1,00,000
0.5 Poor market
Neither test
-$60,000 1
$0
-$60,000
-$60,000
$20,000 Not produce $0 $0
$0
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.
Pr oblem
•
15
(a)
0.78 Good m arket
Conduc t ques tionnaire. If pos itive, produc e raz or. If negative, do not produc e raz or. Expec ted utility = 0.823.
0.950 Produc e
0.950 0.851
0.45 Pos itive res ult
0.22 Poor m arket 0.500
1
0.500
0.851 Not Produc e 0.800 0.800 Ques tionnaire 0.27 Good m arket
0.823
0.950 Produc e
0.950 0.622
0.55
0.73 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
0.45 Pos itive pilot
0.000 1
0.00
0.11 Poor m arket 0.000
0.801
1
Not Produc e
0.823
0.700 0.700 Pilot s tudy 0.18 Good m arket
0.745
0.900 Produc e
0.900 0.162
0.55 Negative pilot
0.82 Poor m arket 0.000
2
0.000
0.700 Not Produc e 0.700 0.700 0.50 Good m arket 1.000 Produc e 0.775 Neither
1.000 0.50 Poor m arket
tes t
0.550 2
0.550
0.810 Not produc e 0.810 0.810
Answer 15. • (b) Jim is a risk avoider. Problem 15 (b) Utility Curve 1.00 0.75
Utility
Dollar Utility -$80,000 0.00 -$65,000 0.50 -$20,000 0.70 -$5,000 0.80 $0 0.81 $80,000 0.90 $95,000 0.95 $1,00,000 1.00
0.50 0.25 0.00 -$80,000
-$40,000
$0
$40,000
Monetary value Risk avoider.
$80,000
