Question 1

Explain how Bayes Theorem is used to revise probabilities.

Accepted Answer

Bayes Theorem offers a logical means for incorporating new information into a decision-maker's probability assessment. Information is (generally) useful in determining a course of action. The usual formulation of Bayes theorem using test result t to predict uncertain event e is: Pr(e|t) = [Pr(t$\mid$e)/Pr(t)]Pr(e).

Question 2

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

Accepted Answer

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

Question 3

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:

Accepted Answer

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

Question 4

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?
(b) The company is considering spending $10 million to test market the product on a national scale. In the process, it will learn the exact market response (strong or weak demand) before having to decide on a final launch and pricing strategy. Should it go ahead with the market test?
(c) Suppose instead that the company can hire a marketing consultant to undertake a limited market survey in the Midwest. The company anticipates that the consultant will come back with one of two possible demand forecasts: favorable (F) or unfavorable (U). In the past, the consultant's forecast accuracy has been as follows: Pr(F|S) = .8 and Pr(U|W) = .6. Compute the revised probabilities, Pr(S|F) and Pr(S|U).

Accepted Answer

From the joint proba

Question 5

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

Accepted Answer

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). 
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 6

A decision-maker should acquire new information:

Accepted Answer

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. 
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.

Question 7

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?

Accepted Answer

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

Question 8

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:

Accepted Answer

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

Question 9

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?

Accepted Answer

A)  $5 
B)  $10 
C)  $15 
D)  $20 
E)  $7.50 
A)  $5 
B)  $10 
C)  $15 
D)  $20 
E)  $7.50

Question 10

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.)
(b) Should Stake Gold pay $200,000 for the right to collect samples?

Accepted Answer

Upon collecting the mineral samples, Sta

Question 11

A prior probability refers to:

Accepted Answer

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. 
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 12

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

Accepted Answer

In an English auction with private value

Question 13

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?

Accepted Answer

A)  $20,000 
B)  $21,000 
C)  $21,500 
D)  $22,000 
E)  There is not enough information to provide an answer. 
A)  $20,000 
B)  $21,000 
C)  $21,500 
D)  $22,000 
E)  There is not enough information to provide an answer.

Question 14

The expected value of test information is:

Accepted Answer

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. 
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 15

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.
 $\begin{array} { | l | c | c | } 
\hline & \text { Growth } & \text { Recession } \
\hline \text { Standard Price } & 20 & - 10 \
\hline \text { Cut Price } & 15 & 0 \
\hline
\end{array}$ (a) Firm X must make its decision now (before knowing the future course of the economy). Which pricing policy maximizes its expected profit?
(b) Now suppose that Firm X can wait and decide its pricing decision after it knows the course of the economy. Determine its best pricing decisions and its overall expected profit.
(c) Firm X has hired a macroeconomic forecaster. The macro forecast is either positive (+) or negative (–). In the past, the forecaster has made positive forecasts prior to 4 of 7 periods of economic growth: Pr(+|G) = 4/7. In turn, he has made negative forecasts prior to 2 of 3 recessions: Pr(–|R) = 2/3. Compute Pr(G|+) and Pr(G|–) 
(d) Suppose the forecasting report can be purchased for $.2 million. Should Firm X buy the report? Explain your answer.

Accepted Answer

After a positive macro forecast, cutting

Question 16

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?
(b) Finally, the manager recalls a small number of instances when she neglected to stretch and, indeed, suffered muscle pulls, leading to the guesstimate: Pr(No Stretch and Muscle Pull) = .02. Write down the appropriate two-by-two joint probability table. Does stretching reduce the risk of injury?

Accepted Answer

The complete joint probability table is:

Question 17

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

Accepted Answer

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. 
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 18

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?

Accepted Answer

In equilibrium, revenue equivalence hold

Question 19

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?

Accepted Answer

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

Question 20

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:

Accepted Answer

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

Explain how Bayes Theorem is used to revise probabilities.

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

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:

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

A decision-maker should acquire new information:

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:

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 prior probability refers to:

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

The expected value of test information is:

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

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?

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:

Introduction to Economic Decision Making

Optimal Decisions Using Marginal Analysis

Demand Analysis and Optimal Pricing

Estimating and Forecasting Demand

Production

Cost Analysis

Perfect Competition

Monopoly

Oligopoly

Game Theory and Competitive Strategy

Regulation, Public Goods, and Benefit-Cost Analysis

Decision Making Under Uncertainty

Asymmetric Information and Organizational Design

Bargaining and Negotiation

Linear Programming

Auctions and Competitive Bidding Available Online

Filters

Exam 13: The Value of Information

Explain how Bayes Theorem is used to revise probabilities.

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

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:

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

A decision-maker should acquire new information:

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:

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 prior probability refers to:

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

The expected value of test information is:

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

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?

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:

Introduction to Economic Decision Making

Optimal Decisions Using Marginal Analysis

Demand Analysis and Optimal Pricing

Estimating and Forecasting Demand

Production

Cost Analysis

Perfect Competition

Monopoly

Oligopoly

Game Theory and Competitive Strategy

Regulation, Public Goods, and Benefit-Cost Analysis

Decision Making Under Uncertainty

Asymmetric Information and Organizational Design

Bargaining and Negotiation

Linear Programming

Auctions and Competitive Bidding Available Online

Filters