Deck 12: Decision Making Under Uncertainty

Question 1

A firm must decide whether to launch a new product before knowing whether sales demand will be strong or weak. In addition, depending on how demand unfolds, the firm has the flexibility to set either a high price or a low price. The best order in which to draw the firm's decision tree is:

A) launch, set price, and observe demand.
B) observe demand, launch, and set price.
C) launch, observe demand, and set price.
D) set price, observe demand, and launch.
E) set price, launch, and observe demand.

Answer 1

C

Question 2

When taking risky decisions, a common pitfall that the managers face is:

A) seeing too many possibilities.
B) holding pessimistic beliefs.
C) gathering too much information.
D) relying on verbal expressions of probability.
E) relying on the rules of thumb.

Answer 2

D

Question 3

A firm supplies aircraft engines to the government and to private firms. It must decide between two mutually exclusive contracts. If it contracts with a private firm, its profit will be $2 million, $1 million, or -$1 million with probabilities .25, .4, and .35, respectively. If it contracts with the government, its profit will be $4 million or -$2.5 million with respective probabilities .4 and .6. Which contract offers the greater expected profit or loss?

A) The private contract offers the greater expected profit.
B) The government contract offers the greater expected profit.
C) Both contracts offer the same expected profit.
D) The private contract results in a greater expected loss.
E) The government contract results in a greater expected loss.

Answer 3

A

Question 4

If a fair coin is tossed 1,000 times, the frequency of heads will be close to:

A) )6.
B) )5.
C) )3.
D) )2.
E) There is not enough information to provide an answer.

Question 5

An investment has the possibility of earning $10,000, $8,000 or $2,000 depending on the state of the economy that is prosperity, modern growth, and recession respectively. The probabilities of prosperity, moderate growth, and recession are .4, .3, and .3 respectively. The expected value of the investment is:

A) $10,000.
B) $21,000.
C) $7,000.
D) $3,000.
E) $8,000.

Question 6

A movie studio faces uncertainty about the cost of producing a film. Its cost can be $40 or $60 million with probabilities .6 and .4 respectively. The box office revenue from the film is also uncertain, either $60 million or $40 with probabilities .3 and .7 respectively. The film's expected profit is

A) $10 million
B) $12 million.
C) $4 million.
D) $16 million.
E) None of these answers is correct.

Question 7

The expected profit determined from a decision tree is the weighted average of all possible outcomes. The weights represent the:

A) probabilities of the outcomes.
B) utilities of the outcomes.
C) number of times the decision is likely to be repeated.
D) one divided by the total number of outcomes.
E) the total number of outcomes.

Question 8

Which of the following is true of subjective probability?

A) It is a measure of the historical frequency of an uncertain event.
B) It is a measure of the frequency of a certain event.
C) It represents the decision maker's best assessment, based on current information, of the likelihood of an uncertain event.
D) It represents an intuitive and ad hoc assessment.
E) It measures the degree of variation around the mean.

Question 9

A convenient way to represent decisions, chance events, and possible outcomes in choices under risk and uncertainty is known as a:

A) probability distribution.
B) decision table.
C) decision tree.
D) expected outcome tree.
E) risk table.

Question 10

An individual is uncertain whether to bet on a football game. He believes that the probability of his team winning is 40%. If his team wins, he will receive $180. If his team loses, he'll pay $120. If the decision is based on the expected value criterion, then the individual will:

A) not take the bet if he is risk loving.
B) be indifferent to the bet if he is risk-neutral.
C) take the bet only if he is risk averse.
D) not take the bet if he is risk averse.
E) Answers b and d are both correct.

Question 11

The probability of an outcome:

A) ranges between zero and one.
B) is an intuitive guess on the part of the decision maker.
C) measures the expected return from an outcome.
D) reflect the degree of the manager's confidence.
E) measures the degree of variation around the mean value.

Question 12

The accompanying figure shows the decision tree of an operations manager who is considering a new production technique. ER represents his expected return (in thousand $) from the new technique. If he does not adopt the technique his expected return would be zero. The probabilities of the technique being a success or a failure are .7 and .3 respectively. Compute the expected return (in thousand $) from the adoption of the new production technique.

A) $8,400
B) $1,000
C) -$2,000
D) $7,200
E) $8,000

Question 13

A risky outcome's expected value is:

A) the value of the most likely outcome.
B) the mid-point of the extreme (high and low) possible values.
C) the degree of dispersion of the possible outcomes.
D) the sum of the products of the probabilities of all outcomes and their values.
E) the equally-weighted average of all outcomes.

Question 14

Decision trees are numerically evaluated:

A) From left to right
B) By pruning low probability events from the tree.
C) By averaging at chance events.
D) By averaging at points of decision.
E) By selecting the best outcome at chance events

Question 15

Risk aversion describes a person's tendency to:

A) avoid risk at all cost.
B) be conservative in assessing a certainty equivalent.
C) select the safest option.
D) attach lower marginal utility to higher monetary outcomes.
E) always pay for 100% insurance against risks.

Question 16

Which of the following is true of a decision tree?

A) It's the basis for making logical decisions in the absence of uncertainty.
B) It represents decisions, chance events, and possible outcomes in choices under risk and uncertainty.
C) It's use to show the sequential moves and countermoves of strategic rivals.
D) It calculates the values associated with a decision in chronological order of occurrence.
E) None of the answers above is correct.

Question 17

When there is multiple possible outcomes from a decision, the result is:

A) a small margin of error in firm forecasts.
B) greater possible losses.
C) a significant degree of uncertainty.
D) lower overall risk.
E) greater expected returns.

Question 18

Which of the following is a feature of the expected-value standard?

A) It helps the decision taker to choose the course of action that involves the maximum risk and return.
B) It cannot be employed in situations involving multiple and related risks.
C) It is employed for short-term, one-time decisions involving high risks.
D) The expected value of a risky prospect represents the average monetary outcome if it were repeated indefinitely.
E) The expected-value standard is appropriate for playing short-run averages.

Question 19

A firm might be liable for $10 million if a lawsuit is brought against it. The firm judges that the probability the suit will be brought is .6. In addition, it believes that its chance of winning such a suit (in which case it owes $0) is .7. The firm's overall expected liability is:

A) $6 million.
B) $4.2 million.
C) $3 million.
D) $1.8 million.
E) $1.2 million.

Question 20

It is uncertain (odds are 50-50) whether Firm X will enter a new market in the next three months. Firm Y is thinking of entering the same market but won't be ready to do so for six months. Firm Y expects to earn $4 million if it is the sole market supplier but will lose $6 million if it must share the market with Firm X. If Firm X employs an optimal entry strategy, its overall expected profit (before Firm X has made its move is:

A) $0 (it should never enter).
B) $4 million (it should enter if Firm X does not).
C) $2 million (it should enter if Firm X does not).
D) $3 million.
E) $2 million (it should always enter).

Question 21

An individual is said to risk averse if his/her certainty equivalent for a risky prospect is:

A) always negative.
B) equal to its expected value.
C) equal to the average probability of the outcomes.
D) always zero.
E) less than its expected value.

Question 22

An investor estimates the expected return of option A to be $180,000 and its expected utility to be 400. The expected return of option B is $120,000, and its expected utility is 450. The investor should:

A) select option A because it has the higher expected return.
B) select option B because it has the higher expected utility.
C) select option A because 180,000/120,000 > 450/400.
D) be indifferent between option A and option B.
E) There is not enough information to answer this question.

Question 23

Based on the following utility schedule determine the decision maker's attitude toward risk.

Question 24

A manager reveals that she has a utility function U = 100M - 2M2, for 0 ≤ M ≤ 25, where 'U' stands for Utility, 'M' stands for Money. Is this person risk averse, risk neutral, or risk loving?

Question 25

A firm is thinking about introducing a new product. Marketing experts have determined that the product has a 10% chance of high success, a 60% chance of moderate success, and a 30% chance of failure. The gross profit from high success is $2.2 million and from moderate success $1.2 million. The estimated gross loss from failure is $500,000. Finally, the cost of introducing the product is $700,000. Should the firm introduce the product?

Question 26

Estimate the expected utility of two individuals, A and B, from the investment that has the following possible outcomes:

Question 27

How are certainty equivalent and attitude toward risk related? Illustrate with an example.

Question 28

A manager who chooses among options by applying the expected value criterion is:

A) risk neutral.
B) risk averse.
C) risk loving.
D) willing to insure or hedge his bets.
E) a risk minimizer.

Question 29

The following is the distribution of outcomes from two alternative advertising strategies:
Which strategy is the riskier strategy? Explain.

Question 30

An individual is risk neutral if her utility curve for wealth is:

A) linear.
B) concave.
C) convex.
D) decreasing.
E) horizontal.

Question 31

A manufacturer of air-conditioning systems expects to sell 10,000 units next year if the economy recovers from the present recession. If the economy remains at its present state, the firm expects to sell 7,000 units, and if the recession worsens, sales will fall to 3,000 units. A survey of 40 economists reveals that 30 of them are forecasting recovery, 5 of them are expecting no change, and the rest expect a worse recession. Estimate the expected sales of air-conditioning systems for next year.

Question 32

Define probability with an example.

Question 33

An individual has a utility of money function U = 20 +.5M and considers two options:
Option 1: Invest $100,000 in a building plot, which will be sold for $150,000 if interest rates decrease or for $80,000 the interest rates do not change.
Option 2: Invest the same $100,000 in bonds, which will be worth $135,000 if interest rates decrease, and $100,000 if the interest rates remain the same.
The consensus among economic forecasters is that interest rates have an 80% chance of decreasing and 20% chance of remaining constant.
Which investment option will this individual select?

Question 34

If a decision is made on the basis of expected utility, which of the two investments, investment R and investment C, should the decision-maker choose?

Question 35

Given the opportunity, a rational decision-maker should always select the alternative with the:

A) greatest expected return regardless of risk.
B) lowest expected return regardless of risk.
C) greatest expected utility.
D) lowest probability of occurrence.
E) greatest marginal utility.

Question 36

Consider a situation where an insurance contract has a negative expected value for the purchaser. Under this insurance policy, the premium paid exceeds the expected payout. Is it rational to buy this insurance? Give explanation with reason.

Question 37

Apply the expected-value criterion to choose between these investments.
Investment A has possible outcomes: $100,000 (50% chance), $40,000 (30% chance), and $50,000 (20% chance). Investment B has possible outcomes: $150,000, $60,000, $20,000, and $80,000 with each outcome equally likely.

Question 38

A manager who sets U($20,0000) = 20, U($40,000) = 40, U($60,000) = 70 has a utility function that:

A) exhibits increasing marginal utility.
B) is decreasing.
C) is linear.
D) exhibits decreasing marginal utility.
E) is concave.

Question 39

Define uncertainty with an example.

Question 40

Consider the following risky prospect: $\begin{array} { | c | c | c | } \hline \text { MONEY } & \text { UTLITY } & \text { PROBABILTTY } \\\hline \$ 20,000 & 10 & 0.2 \\\hline \$ 30,000 & 18 & 0.2 \\\hline \$ 40,000 & 24 & 0.6 \\\hline\end{array}$ The expected utility is equal to:

A) $30,000.
B) 18.
C) 20.
D) 24.
E) $34,000.

Question 41

Firm X is currently selling a consumer good and faces two related decisions, one with respect to pricing and the other with respect to marketing. With respect to pricing, it can maintain its "standard" price or it can adopt a lower "discount" price. With respect to marketing, it can keep with its current advertising campaign or it can expand its advertising. The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will continue healthy growth or whether it will experience a recession. The table below shows the firm's possible profit results (in $ millions) depending on its price and advertising actions. Finally, the firm judges that there is an 80% chance of growth and a 20% chance of a recession.
(a) Firm X must make its decision now (before knowing the future course of the economy). Which of the four alternatives maximizes its expected profit?

Question 42

A financial analyst considers three funds. The funds' estimated returns depend on future economic conditions - summarized by outcomes A, B, C, or D. The table lists the probabilities of these outcomes and each fund's expected return for each outcome.
(a) Which fund has the greatest expected monetary return?

Question 43

Mary runs her own small business, and has a utility function for assets of:
U(A) = 22A - .07A²‚ for all 0≤ A ≤ 100, where A denotes total assets in thousands of dollars.
(a) Describe Mary's attitude toward risk.

Question 44

A manager's utility of money schedule is (monetary amounts are in $,000s):
Two investment opportunities have the following net present values (again in $000s):
(a) Select the optimal investment based on the expected-value criterion.

Question 45

Suppose that Rick is fortunate enough to receive a gift from a family member of $5,000, which he may use as he does see fit. Rick is then offered a chance to receive an additional $2,000 with certainty, or a 50-50 chance of either $5,000 or $0.
(a) Which would Rick accept?

Question 46

You are the chief appraiser for a large art dealer in a major American city. You are offered a chance to examine, and buy, a work of art. You have reason to believe that it is a piece from a famous artist of the 15th century that has been lost to the art world for hundreds of years. Such a painting would have an estimated market value of $1 million. However, you face two risks. First, the painting may be a forgery, a chance that you estimate to be .4. Second, even if the painting is authentic it may be stolen. Once you buy the painting, you bear all risk. If it is a fake, its value is $0. If it proves to be stolen (a .2 risk in your estimation), you must return the painting to its rightful owner and you cannot recover the purchase price.
(a) You have the chance to buy the painting for $500,000. As a risk-neutral decision maker, should you make the purchase?

Question 47

A chemical company is in the process of studying two long-term plans. The first plan involves expansion of their industrial division. The second plan emphasizes expansion in the business of consumer pharmaceuticals. Market research reveals the following (preliminary) results (returns are in $ millions):
The planning committee has the (risk averse) utility function U = 10M - 0.05M2. Discuss the long-term planning decision based on the preliminary predictions and the given utility function:

Question 48

(a) You are offered a choice between two lotteries, K and L:
Lottery K: You win $1,000 with complete certainty.
Lottery L: You win: $5,000 with probability .10
$1,000 with probability .75
$0 with probability .15
Compute the expected value of both lotteries, and indicate which you would choose. Explain your choice, using the concept of certainty equivalent.

Question 49

Consumer surveys indicate that 40% of newspaper readers read automobile ads and 5% of those who read the ads actually purchase automobiles. On the other hand, 50% of magazine readers read automobile ads but only 3% of those who read the ads actually buy a car. Among those who do not read either newspaper or magazine auto ads, 1% buys cars anyway. Sixty percent of the population reads newspapers, while 20 percent primarily read magazines. Compute the overall percentage of the population that purchases automobiles in a given year. (To aid your analysis, you might wish to draw a decision tree listing appropriate probabilities for the three aforementioned reading segments.)