Deck 13: The Value of Information

Question 1

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) $7.50

Answer 1

A

Question 2

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

Answer 2

E

Question 3

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 backed by extensive data.
E) only if the expected value without the information is negative.

Answer 3

B

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

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 .3 probability that demand will be weak. The expected value of perfect information from market research is:

A) $0.
B) $.6 million.
C) $.9 million.
D) $1.4 million.
E) $2.1 million.

Question 6

If Pr(a) = .4, Pr(b) = .3, and Pr(ba) = .5, then Pr(a&b) is:

A) )35.
B) )5.
C) )2.
D) )6.
E) )14.

Question 7

An event's revised 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 8

Information is considered to be valueless if it:

A) has a negative expected value.
B) drastically alters decisions made by the firm.
C) leaves the prior probability unchanged.
D) it changes the revised probability to zero.
E) it comes from an imperfect test.

Question 9

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 chance of two events both happening.
E) the chance that at least one of the two events will occur.

Question 10

A prior probability refers to:

A) the chance of an outcome before new information is obtained.
B) the conditional chance of an outcome after new information is obtained.
C) the probability that the information source is accurate.
D) a probability assessment that combines both current and new information.
E) the chance of an outcome based on purely subjective information.

Question 11

Suppose that the chance of having both a favorable survey and a successful product launch is .3. In addition, the frequency of favorable market surveys for all new product launches is .5. Then the chance of a successful product launch given a favorable survey is:

A) )8
B) )5
C) )4
D) )6
E) )3

Question 12

If Pr(a) = .5 and Pr(b) = .3, then the value of Pr(a&b):

A) equals .8.
B) equals .375.
C) equals .15.
D) equals .2.
E) cannot be determined without more information.

Question 13

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

A) 0.
B) the same as the prior probability.
C) 1.0.
D) 100% greater than the prior probability.
E) smaller than the prior probability.

Question 14

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) likely to produce inaccurate and biased results.
E) is consistent with probabilistic prediction.

Question 15

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

A) Pr(A $\mid$ B) = 1.
B) Pr(A&B) = Pr(A)Pr(B).
C) Pr(A $\mid$ B) = Pr(B $\mid$ A).
D) Pr(A) > Pr(A $\mid$ B).
E) Pr(A $\mid$ B) = 0.

Question 16

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 .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) )50.
B) )15.
C) )40.
D) )25.
E) There is not enough information to determine the answer.

Question 17

In a 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) )10.
B) )15.
C) )50.
D) )03
E) )05

Question 18

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 is:

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

Question 19

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

A) Pr(b $\mid$ a)/Pr(b) + Pr(a).
B) Pr(a&b)/Pr(b).
C) Pr(b $\mid$ a)/Pr(b).
D) Pr(a&b)/Pr(a).
E) Pr(a $\mid$ b)/Pr(a).

Question 20

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 .6. With a perfect market survey, what is the probability that the test will show that demand is strong?

A) )6
B) )4
C) )24
D) )5
E) )2

Question 21

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 22

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) = .90. The test is also 90% reliable in screening out cancer, that is, Pr(-|H) = .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 23

Explain how Bayes Theorem is used to revise probabilities.

Question 24

Which of the following is true of an English auction with private values?

A) The bid value can exceed the reservation price of the buyer who wins.
B) A typical buyer shades his/her bid below the true private value.
C) A buyer's optimal bid strategy depends on the bidding behavior of other buyers.
D) The final price is approximately equal to the second highest buyer value.
E) Answers c and d are both correct.

Question 25

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) $21,000
C) $21,500
D) $22,000
E) There is not enough information to provide an answer.

Question 26

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 .32 and .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 .5, while an unfavorable result reduces it to .2. The likelihood of a favorable test is .4. Determine the expected value of this test.

Question 27

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 in pursuit of commercial success and then discontinue investing.

Question 28

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 .3 and of weak demand is .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 29

If there is a private-value model with risk-neutral buyers, what can be inferred regarding the expected revenues generated by English and sealed-bid auctions?

Question 30

Firm Z is one of the 5 bidders, each with a value independently drawn from the range $100,000 to $160,000 with all values in between being equally likely. In a sealed-bid auction, Firm Z's equilibrium bidding strategy is:

A) b_i = (.2)(160,000) + .8v_i
B) b_i = (.5)(160,000) + .5v_i
C) b_i = (.25)(100,000) + .75v_i
D) b_i = (.2)(100,000) + .8v_i
E) b_i = (.8)(100,000) + .2v_i

Question 31

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 .35, .25, .15, .07, and .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 32

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) = .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) = .20. Determine Pr(Stretch|Healthy). Does this indicate that stretching reduces the risk of injury?

Question 33

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.

Question 34

In a sealed-bid auction, a firm with a reservation price of $480,000 submits a bid of $400,000. If its probability of winning is .75, then its expected profit from the auction is:

A) $60,000
B) $75,000
C) $80,000
D) $300,000
E) There is not enough information to provide an answer.

Question 35

The winner's curse occurs when:

A) buyers are realistic in their value estimates.
B) the winning bid exceeds the true value of a good.
C) the contract bidder experiences frequent cost overruns.
D) the winning bid is drawn from the left tail of the bid distribution.
E) the firm's bid discount exceeds its (upward) estimation error.

Question 36

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 .6 and of weak demand is .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 37

Briefly describe the potential pitfalls associated with making intuitive predictions.

Question 38

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).
$\begin{array} { | c | c | c | } \hline & \mathbf { X } & \mathbf { Y } \\\hline \mathbf { A } & \mathbf { 3 2 5 } & 455 \\\hline \mathrm { B } & 416 & 104 \\\hline\end{array}$

Question 39

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 40

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 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

What are the conditions suitable for a seller to use an auction? Explain.

Question 43

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

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

Explain with an example the potential benefit of competitive bidding versus bargaining to secure a better price by a seller.

Question 46

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.
$\begin{array} { | c | c | c | c | } \hline & \text { Strong } & \text { Weak } & \text { Total } \\\hline \text { Accurate } & 0.2 & 0.2 & 0.4 \\\hline \text { Inaccurate } & 0.3 & 0.3 & 0.6 \\\hline & 0.5 & 0.5 & 1.0 \\\hline\end{array}$ 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 47

Compare the strategies bidders employ when participating in the English, sealed-bid, and Dutch auctions.