Deck 13: The Value of Information

Question 1

A price cut would increase the firm's profits by $2 million if demand is weak but would decrease profit by $3 million if demand proves to be strong.The firm's best assessment is a 0.3 probability of strong demand.The firm conducts market research that clearly indicates that demand is weak.The expected value of this information from market research is _____.

A)$0
B)$0.5 million
C)$1.5 million
D)$1.4 million
E)$2 million

Answer 1

C

Question 2

A bank has categorized its credit card accounts as high risk or low risk.The overall default rate on all the bank's credit card accounts is 0.20.In the past,of the accounts that defaulted,50 percent were correctly identified by the bank as high risk.What is the default risk for a high-risk credit card account?

A)0.50
B)0.15
C)0.40
D)0.25
E)There is not enough information to determine the answer.

Answer 2

E

Question 3

A firm wants to launch a new luxury product only if demand for the product is strong.The probability that demand is strong is estimated to be 0.6.With a perfect market survey,what is the probability that the test will show that demand is strong?

A)0.6
B)0.4
C)0.24
D)0.5
E)0.2

Answer 3

A

Question 4

The expected value of test information is:

A)zero if the new information does not change the firm's decisions.
B)the difference between the actual outcome with test information and without it.
C)the sum of the expected value with the information and without it.
D)the expected value of the decision taken using the test.
E)the same as the expected value of the decision taken without the test.

Question 5

In a large metropolitan area,one out of ten drivers on the road on Saturday after midnight is intoxicated.Half of all accidents during this time period involve drunk drivers.Finally,the overall accident rate on Saturday after midnight is 3 accidents per 100 cars on the road.For a drunk driver,the risk of accident is _____.

A)1/10
B)1/2
C)3/100
D)3/20
E)1/100

Question 6

Suppose that the chance of having both a favorable survey and an unsuccessful product launch is 0.2.In addition,the frequency of favorable market surveys for all new product launches is 0.5.Then the chance of a successful product launch given a favorable survey is:

A)0.8
B)0.5
C)0.4
D)0.6
E)0.3

Question 7

Joint probability refers to:

A)the decision maker's prior probability.
B)the accuracy of new test information.
C)a long-run frequency.
D)the product of a prior probability and a conditional probability.
E)the chance that at least one of the two events will occur.

Question 8

A firm's expected profit without information is $50,000,while its expected value with test information is $75,000.If the cost of the test is $40,000,then the expected value of information [EVI] is _____.

A)$85,000
B)$35,000
C)$25,000
D)$10,000
E)$40,000

Question 9

Revision of an event's probability depends on:

A)purely subjective assessments.
B)prior probabilities and the accuracy of new information.
C)the sum of the prior probability and the conditional probability.
D)the expected value of information.
E)a consensus among experts' opinions.

Question 10

If Pr(a)= 0.4,Pr(b)= 0.3,and Pr(ba)= 0.5,then Pr(a&b)is _____.

A)0.35
B)0.5
C)0.2
D)0.6
E)0.14

Question 11

Kevin goes trick-or-treating on Halloween.His neighbor gives him 3 small bags with two candies in each of them.One bag has two Snickers bars,one has a Tootsie Roll and a Snickers bar,and the third bag has two Tootsie Rolls.Kevin opens one of the bags and sees a Snickers bar.What are the odds that the other candy in the bag is also a Snickers bar?

A)2/5
B)5/7
C)1/2
D)3/4
E)2/3

Question 12

You are offered a favorable bet on a coin toss,heads or tails.If you correctly call the result,you gain $20.If your call is incorrect,you lose $10.What is the expected value of information if you could perfectly predict the coin toss?

A)$5
B)$10
C)$15
D)$20
E)$25

Question 13

A decision-maker should acquire new information:

A)only if it can be acquired at a low cost.
B)only if its expected value is greater than its cost.
C)whenever the information will have an impact on the manager's decision.
D)only if the information is falsifiable.
E)only if the expected value without the information is positive.

Question 14

The owner of a DVD rental store notes that 1 out of every 50 DVDs that are rented are not returned on time.He also calculates that 1 out of every 100 DVDs that are returned late are action movies.What is the probability that an action movie will be returned late?

A)0.006
B)0.03
C)0.1
D)0.0002
E)0.01

Question 15

If Pr(a)= 0.5 and Pr(b)= 0.3,then the value of Pr(a&b)_____.

A)is equal to 0.8
B)is equal to 0.375
C)is equal to 0.15
D)is equal to 0.2
E)cannot be determined without more information

Question 16

The test result B has no value in predicting outcome A if:

A)Pr(A|B)= 1.
B)Pr(A&B)= Pr(A)Pr(B).
C)Pr(A|B)= Pr(B|A).
D)Pr(A)> Pr(A|B).
E)Pr(A|B)= 0.

Question 17

Information is considered to be valueless if:

A)it has a positive expected value.
B)it drastically alters decisions made by the firm.
C)the prior probability is unchanged.
D)it changes the revised probability to unity.
E)it is incomplete.

Question 18

Using Bayes Theorem Pr(ab)can be expressed as:

A)Pr(b|a)/Pr(b)+ Pr(a).
B)Pr(a&b)/Pr(b).
C)Pr(b|a)/Pr(b).
D)Pr(a&b)/Pr(a).
E)Pr(a|b)/Pr(a).

Question 19

When there is perfect information on the outcome of an event,the revised probability of the event will be:

A)equal to zero.
B)the same as the prior probability.
C)equal to one.
D)higher than the prior probability.
E)smaller than the prior probability.

Question 20

A prior probability refers to:

A)the probability of the outcome before new information is obtained.
B)the conditional probability of the outcome after the new information is obtained.
C)the probability that the information source is accurate.
D)the probability assessment that combines both current and new information.
E)the probability that the outcome will not occur.

Question 21

Suppose that two independent geologists begin with different prior assessments concerning the chance of oil and natural gas at a particular site.They both observe the results of a seismic test.Will they agree concerning their revised probabilities? In what instance,would their revised probabilities be identical?

Question 22

When investing in a venture with increasing probabilities of success,the firm's optimal-stopping strategy is to:

A)invest until the total cost of its investment equals the potential profit.
B)invest once and continue investing if the probability of success increases.
C)invest until the venture is successful or not invest at all.
D)continue to invest until sunk costs are recovered.
E)invest until the break-even point.

Question 23

A firm is considering the development of a new technology with a declining probability of success in each research stage.The firm's researchers have estimated the probabilities at 0.35,0.25,0.15,0.07,and 0.01 for the various stages.The profit the firm would receive for successful development is $100 million,while the cost of research in each period is $10 million.How many investment stages should the firm undertake before abandoning the project?

Question 24

A company is trying to decide whether to build a large plant or a small plant to supply future sales of a new product.However,it is uncertain about the market response to the product;whether demand will be strong or weak.According to the firm's marketing department,the probability of strong demand is 0.3 and of weak demand is 0.7.The table below lists the firm's profits (in millions of dollars)depending on plant capacity and the market response:
(a)The company must make its plant decision now,before it will know what the market response will be.Which plant size maximizes its expected profit?

Question 25

With declining probabilities of success,the optimal-stopping strategy is to:

A)continue to invest until the venture becomes successful.
B)continue investing till sunk cost of investment is equal to zero.
C)not invest in the project at all.
D)discontinue investing when the expected profit is zero.
E)invest once to earn the highest profit and then discontinue investing.

Question 26

A high-tech firm is pursuing research and development (R&D)to commercialize the next generation of DVD players (using very high-definition DVDs).Two R&D approaches are available: laser technology and digital technology.Either way,the firm will receive the same expected profit if successful.Development costs are $100 million and $125 million,and probabilities of success are 0.3 and 0.5,for the respective approaches.Which R&D method should the firm pursue first?

Question 27

Given two methods for developing a new product,a firm should undertake:

A)the method with the greater chance of success.
B)the method with the lower investment cost.
C)the methods in order of greatest probability-to-cost ratio.
D)the method with the greater probability-to-cost ratio.
E)both methods simultaneously.

Question 28

With respect to a decision-maker's optimal strategy,what is the difference between situations of perfect and imperfect information?

Question 29

Briefly describe the potential pitfalls associated with making intuitive predictions.

Question 30

Explain how Bayes Theorem is used to revise probabilities.

Question 31

The following table shows the probabilities of A,B,X,and Y.Compute the joint probability table.Then calculate Pr(BY)and Pr(XB).

Question 32

Explain how ascending and descending probabilities of success in research affect investment strategies.

Question 33

A petrochemical company must decide whether to fill a specialty order for one of its customers.Its cost (and therefore profit)depends on the quality of the raw material it has on hand to make the chemical.The firm expects to earn $50,000 from the order if the material is high quality (H)but will lose $30,000 if it is low quality (L).The firm's engineers estimate these probabilities to be 0.32 and 0.68 respectively.Before making its decision,the firm can test the material with one of two outcomes,"favorable" or "unfavorable." A favorable test increases the chance of H to 0.5,while an unfavorable result reduces it to 0.2.The likelihood of a favorable test is 0.4.Determine the expected value of this test.

Question 34

The use of intuitive prediction in forecasting:

A)puts the wrong weights on different kinds of information.
B)provides approximately correct decisions most of the time.
C)is objective and reliable.
D)gives statistically significant results.
E)is consistent with probabilistic prediction.

Question 35

Assuming a uniform distribution of purchase offers between $100,000 and $200,000,the expected maximum offer from 9 potential buyers is _____.

A)$150,000
B)$160,000
C)$188,888
D)$180,000
E)$190,000

Question 36

Suppose that the firm's expected profit without test information is $75,000.There exists a perfectly reliable test that produces a positive result with a probability of 0.75 and a negative result otherwise.In light of a positive result,the firm's expected profit is $120,000;after a negative result,its expected profit is $40,000.Find the expected value of information [EVI].

Question 37

Buyer A has offered $20,000 for a painting you are trying to sell.You are about to approach Buyer B whose best offer,you believe,might be anywhere between $16,000 and $24,000,with all values in between being equally likely.After hearing B's price,you will pick the higher of the two offers.What is the price that you expect to get for the painting?

A)$20,000
B)$21,333
C)$22,000
D)$22,680
E)$23,700

Question 38

How is a uniform distribution defined?

A)All the values in the distribution are equally likely.
B)The values in the distribution are distributed with equal intervals.
C)The distribution takes the shape of a bell-shaped curve.
D)The values in the distribution are contingent on a previous result.
E)All the values in the distribution are based on subjective estimates.

Question 39

Firm X is currently selling a consumer good at a standard price,but is also considering cutting its price.The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will grow at a steady pace (G)or whether it will experience a recession (R).The table below shows the firm's possible profit results (in $ millions).Finally,the firm judges that there is a 70% chance of growth and a 30% chance of a recession.
(a)Firm X must make its decision now (before knowing the future course of the economy).Which pricing policy maximizes its expected profit?

Question 40

A real estate broker is attempting to sell a warehouse.She estimates that an offer from a typical potential buyer will be centered on $5.5 million plus or minus $0.5 million and that any offers will be uniformly distributed within this range.The broker has located four potential buyers.What will be the best price,on average,that she can expect to receive?

Question 41

In a medical study of 5,000 middle-aged men,it was found that (i)10% suffered heart disease, (ii)20% got little or no exercise,and (iii)Of those suffering from heart disease,60% had a history of little or no exercise.Based on this information,determine the risk of heart disease for a middle-aged man who does not exercise.

Question 42

A firm hires an economist to conduct market research and determine demand for a new product.If the test is correct and the firm launches the product,it earns a profit of $600,000.If the firm launches the product when there is weak demand,it incurs a loss of $250,000.

What is the firm's expected profit from an accurate and inaccurate test respectively? What can you conclude about the quality of the market research?

Question 43

A company is about to launch a new product and is considering one of two prices: high or low.However,the company is uncertain about the market response to the product - whether demand will be strong or weak.According to the firm's marketing department,the probability of strong demand is 0.6 and of weak demand is 0.4.The following table lists the firm's economic profit (in millions of dollars)at the two prices under strong and weak demand:
(a)Suppose the company is risk neutral and must commit to a price before knowing what the market response will be.Should it launch the product? If so,at what price?

Question 44

In the late 1990s,many local affiliates of the three TV networks (ABC,CBS,and NBC)left their current partner to join a rival network that was seeking new stations (The networks pay their affiliates to carry programs,which is a major source of revenue for the stations).Why would the affiliates leave their current partner for a new network?

Question 45

Stake Gold Mines has the option to purchase a parcel of land adjacent to its current mining operations in a Western state.The seller's best and final price is $3 million.If the land has commercial mineral deposits,Stake Gold estimates its value at $5 million.If there are no deposits,the estimated value is $2 million.A preliminary look at the land leads Stake Gold to believe that the chance of mineral deposits is 50:50.
(a)Given this information,should Stake Gold purchase the land? For a fee of $200,000,the seller has agreed to let Stake Gold collect extensive mineral samples on the site.Based on past experience,if there are minerals present,the samples will provide a favorable indication 80% of the time.If no minerals are present,the samples will (falsely)give a favorable reading 40% of the time.Determine Pr(M|F)and Pr(M|U).(Here,M denotes mineral deposits,NM denotes no mineral deposits,F denotes favorable samples,and U denotes unfavorable samples. )

Question 46

A middle manager is an avid runner and keeps an informal diary of her daily 5-mile training runs.Most of the time,she spends 10 minutes or more stretching before running,believing that this will help prevent minor muscle injuries.In fact,she estimates that 64% of days over the last year,she has stretched and avoided any muscle problems,that is,the relevant joint probability is Pr(Stretch & Healthy)= 0.64.
(a)Is she correct in concluding that there is a positive association between stretching and being injury free? Now suppose she does some additional thinking and recalls many days when she hadn't bothered to stretch and fortunately still avoided any muscle pulls.Her guess is that Pr(No Stretch & Healthy)= 0.20.Determine Pr(Stretch|Healthy).Does this indicate that stretching reduces the risk of injury?

Question 47

(a)Suppose that buyers' offers are independently and uniformly distributed between $32 million and $56 million.Construct a table showing expected maximum prices with 1 to 7 buyers.

Question 48

In making sequential risky investments,what is the firm's optimal stopping rule? Provide a brief explanation as to why it makes sense.

Question 49

Describe how a decision-maker's attitude toward risk affects her strategy for acquiring information.

Question 50

Oliver undergoes a standard medical test while at his regular checkup.The test is 90% reliable in detecting a form of cancer (C)that is found in 2% of the population.In particular,Pr(+|C)= 0.90.The test is also 90% reliable in screening out cancer,that is,Pr(-|H)= 0.90.
(a)If Oliver tests positive,how likely is it that he actually has cancer? If he tests negative,what is his cancer risk?

Question 51

A firm is contemplating the channel of distribution for a newly launched product.Since there is strong demand for the product,its expected profit of $500,000 are unaffected by the channel of distribution.If the firm opts to sell via a distributor,the probability of success is 2/5 and the cost incurred will be $10,000.If the firm opts for direct marketing,the probability of success is 3/5 and the cost incurred will be $20,000.Which method should the firm pursue first?

Question 52

The Professional Beach Volleyball League is accepting bids for televising the national championship playoffs.Competition is stiff,and the league expects bids to be higher this year than last.League officials have estimated that the bid of a particular network might range between $10 million and $20 million,with all values in between considered equally likely.Furthermore,the values of network bids are considered to be (probabilistically)independent of each other.
(a)If the three major television networks bid,what is the expected value of the winning bid?