Posted: January 21st, 2021

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**Microeconomics****, ****8e**** (Pindyck/Rubinfeld)**

**Chapter 5 Uncertainty and Consumer Behavior**

**5.1 Describing Risk**

**Scenario 5.1:**

Aline and Sarah decide to go into business together as economic consultants. Aline believes they have a 50-50 chance of earning $200,000 a year, and that if they don’t, they’ll earn $0. Sarah believes they have a 75% chance of earning $100,000 and a 25% chance of earning $10,000.

1) Refer to Scenario 5.1. The expected value of the undertaking,

- A) according to Sarah, is $75,000.
- B) according to Sarah, is $100,000.
- C) according to Sarah, is $110,000.
- D) according to Aline, is $200,000.
- E) according to Aline, is $100,000.

Answer: E

Diff: 1

Section: 5.1

2) Refer to Scenario 5.1. The probabilities discussed in the information above are

- A) objective because they are single numbers rather than ranges.
- B) objective because they have been explicitly articulated by the individuals involved.
- C) objective because the event hasn’t happened yet.
- D) subjective because the event hasn’t happened yet.
- E) subjective because they are estimates made by individuals based upon personal judgment or experience.

Answer: E

Diff: 1

Section: 5.1

**Scenario 5.2:**

Randy and Samantha are shopping for new cars (one each). Randy expects to pay $15,000 with 1/5 probability and $20,000 with 4/5 probability. Samantha expects to pay $12,000 with 1/4 probability and $20,000 with 3/4 probability.

3) Refer to Scenario 5.2. Which of the following is true?

- A) Randy has a higher expected expense than Samantha for the car.
- B) Randy has a lower expected expense than Samantha for the car.
- C) Randy and Samantha have the same expected expense for the car, and it is somewhat less than $20,000.
- D) Randy and Samantha have the same expected expense for the car: $20,000.
- E) It is not possible to calculate the expected expense for the car until the true probabilities are known.

Answer: A

Diff: 1

Section: 5.1

4) Refer to Scenario 5.2. Randy’s expected expense for his car is

- A) $20,000.
- B) $19,000.
- C) $18,000.
- D) $17,500.
- E) $15,000.

Answer: B

Diff: 1

Section: 5.1

5) Refer to Scenario 5.2. Samantha’s expected expense for her car is

- A) $20,000.
- B) $19,000.
- C) $18,000.
- D) $17,500.
- E) $15,000.

Answer: C

Diff: 1

Section: 5.1

Consider the following information about job opportunities for new college graduates in Megalopolis:

** Table 5.1**

**MajorProbability of Receiving**

**an Offer in One Year**

**Average Salary Offer**Accounting.95$25,000Economics.90$30,000English.70$24,000Poli Sci.60$18,000Mathematics1.00$21,000

6) Refer to Table 5.1. Expected income for the first year is

- A) highest in accounting.
- B) highest in mathematics.
- C) higher in English than in mathematics.
- D) higher in political science than in economics.
- E) highest in economics.

Answer: E

Diff: 1

Section: 5.1

7) Refer to Table 5.1. Ranked highest to lowest in expected income, the majors are

- A) economics, accounting, English, mathematics, political science.
- B) mathematics, English, political science, accounting, economics.
- C) economics, accounting, mathematics, English, political science.
- D) English, economics, mathematics, accounting, political science.
- E) accounting, English, mathematics, political science, economics.

Answer: C

Diff: 1

Section: 5.1

**Scenario 5.3:**

Wanting to invest in the computer games industry, you select Whizbo, Yowzo and Zowiebo as the three best firms. Over the past 10 years, the three firms have had good years and bad years. The following table shows their performance:

**CompanyGood Year RevenueBad Year RevenueNumber of Good Years**Whizbo$8 million$6 million8Yowzo$10 million$4 million4Zowiebo$30 million$1 million1

8) Refer to Scenario 5.3. Where is the highest expected revenue, based on the 10 years’ past performance?

- A) Whizbo
- B) Yowzo
- C) Zowiebo
- D) Whizbo and Yowzo
- E) Yowzo and Zowiebo

Answer: A

Diff: 1

Section: 5.1

9) Refer to Scenario 5.3. Based on the 10 years’ past performance, what is the probability of a good year for Zowiebo?

- A) 30/31
- B) 1/31
- C) 0.9
- D) 0.1

Answer: D

Diff: 1

Section: 5.1

10) Refer to Scenario 5.3. Based on the 10 years’ past performance, rank the companies’ expected revenue, highest to lowest:

- A) Whizbo, Yowzo, Zowiebo
- B) Whizbo, Zowiebo, Yowzo
- C) Zowiebo, Yowzo, Whizbo
- D) Zowiebo, Whizbo, Yowzo
- E) Zowiebo, with Whizbo and Yowzo tied for second

Answer: A

Diff: 1

Section: 5.1

11) Refer to Scenario 5.3. The expected revenue from all three companies combined is

- A) $11 million
- B) $17.9 million.
- C) $25.5 million.
- D) $29.5 million.
- E) $48 million.

Answer: B

Diff: 1

Section: 5.1

The information in the table below describes choices for a new doctor. The outcomes represent different macroeconomic environments, which the individual cannot predict.

** Table 5.3**

**Outcome 1Outcome 2**Job ChoiceProb.IncomeProb.IncomeWork for HMO0.95$100,0000.05$60,000Own practice0.2$250,0000.8$30,000Research0.1$500,0000.9$50,000

12) Refer to Table 5.3. The expected returns are highest for the physician who

- A) works for an HMO.
- B) opens her own practice.
- C) does research.
- D) either opens her own practice or does research.
- E) either works for an HMO or does research.

Answer: A

Diff: 1

Section: 5.1

13) Refer to Table 5.3. Rank the doctor’s job options in expected income order, highest first.

- A) Work for HMO, open own practice, do research.
- B) Work for HMO, do research, open own practice.
- C) Do research, open own practice, work for HMO.
- D) Do research, work for HMO, open own practice.
- E) Open own practice, work for HMO, do research.

Answer: B

Diff: 1

Section: 5.1

14) In Table 5.3, the standard deviation is

- A) highest for the HMO choice, and it is $76,000.
- B) lowest for the HMO choice.
- C) higher for owning one’s own practice than for going into research.
- D) higher for the HMO choice than for going into research.

Answer: B

Diff: 2

Section: 5.1

15) Refer to Table 5.3. In order to weigh which of the job choices is riskiest, an individual should look at

- A) the deviation, which is the difference between the probabilities of the two outcomes.
- B) the deviation, which is the difference between the dollar amounts of the two outcomes.
- C) the average deviation, which is found by averaging the dollar amounts of the two outcomes.
- D) the standard deviation, which is the square root of the average squared deviation.
- E) the standard deviation, which is the squared average square root of the deviation.

Answer: D

Diff: 2

Section: 5.1

16) Refer to Table 5.3. Rank the doctor’s job choices in order, least risky first.

- A) Work for HMO, open own practice, do research
- B) Work for HMO, do research, open own practice
- C) Do research, open own practice, work for HMO
- D) Do research, work for HMO, open own practice
- E) Open own practice, work for HMO, do research

Answer: A

Diff: 2

Section: 5.1

17) Upon graduation, you are offered three jobs.

**CompanySalaryBonusProbability of Receiving Bonus**Samsa Exterminators100,00020,000.90Gradgrind Tech100,00030,000.70Goblin Fruits115,000——–——-

Rank the three job offers in terms of expected income, from the highest to the lowest.

- A) Samsa Exterminators, Gradgrind Tech, Goblin Fruits
- B) Samsa Exterminators, Goblin Fruits, Gradgrind Tech
- C) Gradgrind Tech, Samsa Exterminators, Goblin Fruits
- D) Gradgrind Tech, Goblin Fruits, Samsa Exterminators
- E) Goblin Fruits, Samsa Exterminators, Gradgrind Tech

Answer: C

Diff: 1

Section: 5.1

18) As president and CEO of MegaWorld industries, you must decide on some very risky alternative investments:

**ProjectProfit if SuccessfulProbability of SuccessLoss if FailureProbability of Failure**A$10 million.5-$6 million.5B$50 million.2-$4 million.8C$90 million.1-$10 million.9D$20 million.8-$50 million.2E$15 million.4$0.6

The highest expected return belongs to investment

- A) A.
- B) B.
- C) C.
- D) D.

Answer: B

Diff: 1

Section: 5.1

19) What is the advantage of the standard deviation over the average deviation?

- A) Because the standard deviation requires squaring of deviations before further computation, positive and negative deviations do not cancel out.
- B) Because the standard deviation does not require squaring of deviations, it is easy to tell whether deviations are positive or negative.
- C) The standard deviation removes the units from the calculation, and delivers a pure number.
- D) The standard deviation expresses the average deviation in percentage terms, so that different choices can be more easily compared.
- E) The standard deviation transforms subjective probabilities into objective ones so that calculations can be performed.

Answer: A

Diff: 2

Section: 5.1

** Table 5.4**

**JobOutcome 1DeviationOutcome 2Deviation**A$40W$60XB$20Y$50Z

20) Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then in absolute value

- A) W = X = $10.
- B) W = X = $20.
- C) W = Y = $100.
- D) W = Y = $200.
- E) W = Y = $300.

Answer: A

Diff: 1

Section: 5.1

21) Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then the standard deviation of payoffs at Job A is

- A) $1.
- B) $10.
- C) $40.
- D) $50.
- E) $60.

Answer: B

Diff: 1

Section: 5.1

22) Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then in absolute value

- A) Y = Z = $6.
- B) Y = Z = $24.
- C) Y = Z = $35.
- D) Y = $24; Z = $6.
- E) Y = $6; Z = $24.

Answer: D

Diff: 1

Section: 5.1

23) Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then the standard deviation of payoffs at Job B is nearest which value?

- A) $10
- B) $12
- C) $20
- D) $35
- E) $44

Answer: B

Diff: 2

Section: 5.1

24) Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, and if at Job B the $20 outcome occurs with probability .1, and the $50 outcome occurs with probability .9, then

- A) Job A is safer because the difference in the probabilities is lower.
- B) Job A is riskier only because the expected value is lower.
- C) Job A is riskier because the standard deviation is higher.
- D) Job B is riskier because the difference in the probabilities is higher.
- E) There is no definite way given this information to tell how risky the two jobs are.

Answer: C

Diff: 2

Section: 5.1

25) The expected value is a measure of

- A) risk.
- B) variability.
- C) uncertainty.
- D) central tendency.

Answer: D

Diff: 1

Section: 5.1

26) Assume that one of two possible outcomes will follow a decision. One outcome yields a $75 payoff and has a probability of 0.3; the other outcome has a $125 payoff and has a probability of 0.7. In this case the expected value is

- A) $85.
- B) $60.
- C) $110.
- D) $35.

Answer: C

Diff: 1

Section: 5.1

27) The weighted average of all possible outcomes of a project, with the probabilities of the outcomes used as weights, is known as the

- A) variance.
- B) standard deviation.
- C) expected value.
- D) coefficient of variation.

Answer: C

Diff: 1

Section: 5.1

28) Which of the following is NOT a generally accepted measure of the riskiness of an investment?

- A) Standard deviation
- B) Expected value
- C) Variance
- D) none of the above

Answer: B

Diff: 1

Section: 5.1

29) The expected value of a project is always the

- A) median value of the project.
- B) modal value of the project.
- C) standard deviation of the project.
- D) weighted average of the outcomes, with probabilities of the outcomes used as weights.

Answer: D

Diff: 1

Section: 5.1

30) An investment opportunity has two possible outcomes, and the value of the investment opportunity is $250. One outcome yields a $100 payoff and has a probability of 0.25. What is the probability of the other outcome?

- A) 0
- B) 0.25
- C) 0.5
- D) 0.75
- E) 1.0

Answer: D

Diff: 1

Section: 5.1

31) The variance of an investment opportunity:

- A) cannot be negative.
- B) has the same unit of measure as the variable from which it is derived.
- C) is a measure of central tendency.
- D) is unrelated to the standard deviation.

Answer: A

Diff: 2

Section: 5.1

32) An investment opportunity is a sure thing; it will pay off $100 regardless of which of the three possible outcomes comes to pass. The variance of this investment opportunity:

- A) is 0.
- B) is 1.
- C) is 2.
- D) is -1.
- E) cannot be determined without knowing the probabilities of each of the outcomes.

Answer: A

Diff: 2

Section: 5.1

33) An investment opportunity has two possible outcomes. The expected value of the investment opportunity is $250. One outcome yields a $100 payoff and has a probability of 0.25. What is the payoff of the other outcome?

- A) -$400
- B) $0
- C) $150
- D) $300
- E) none of the above

Answer: D

Diff: 2

Section: 5.1

**Scenario 5.4:**

Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and pay-offs are given below:

**OutcomeProbabilityPay-offs**A.3$100B?50C.2?

The expected value of the investment is $25. Although all the information is correct, information is missing.

34) Refer to Scenario 5.4. What is the probability of outcome B?

- A) 0
- B) -0.5
- C) 0.5
- D) 0.4
- E) 0.2

Answer: C

Diff: 2

Section: 5.1

35) Refer to Scenario 5.4. What is the pay-off of outcome C?

- A) -150
- B) 0
- C) 25
- D) 100
- E) 150

Answer: A

Diff: 2

Section: 5.1

36) Refer to Scenario 5.4. What is the deviation of outcome A?

- A) 30
- B) 50
- C) 75
- D) 100

Answer: C

Diff: 2

Section: 5.1

37) Refer to Scenario 5.4. What is the variance of the investment?

- A) -75
- B) 275
- C) 3,150
- D) 4,637.50
- E) 8,125

Answer: E

Diff: 2

Section: 5.1

38) Refer to Scenario 5.4. What is the standard deviation of the investment?

- A) 0
- B) 16.58
- C) 56.12
- D) 90.14
- E) none of the above

Answer: D

Diff: 2

Section: 5.1

39) Blanca has her choice of either a certain income of $20,000 or a gamble with a 0.5 probability of $10,000 and a 0.5 probability of $30,000. The expected value of the gamble:

- A) is less than $20,000.
- B) is $20,000.
- C) is greater than $20,000.
- D) cannot be determined with the information provided.

Answer: B

Diff: 1

Section: 5.1

40) Use the following statements to answer this question:

- Subjective probabilities are based on individual perceptions about the relative likelihood of an event.
- To be useful in microeconomic analysis, all interested parties should agree on the values of the relevant subjective probabilities for a particular problem.
- A) I and II are true.
- B) I is true and II is false.
- C) II is true and I is false.
- D) I and II are false.

Answer: B

Diff: 1

Section: 5.1

41) People often use probability statements to describe events that can only happen once. For example, a political consultant may offer their opinion about the probability that a particular candidate may win the next election. Probability statements like these are based on ________ probabilities.

- A) frequency-based
- B) objective
- C) subjective
- D) universally known

Answer: C

Diff: 1

Section: 5.1

42) To optimally deter crime, law enforcement authorities should:

- A) set higher fines for crimes that have a lower probability of being caught.
- B) set the fine equal to the expected benefit, even if it is difficult to catch the offenders.
- C) ignore the probabilities of catching offenders and attempt to prevent crime at all costs.
- D) set very high fines regardless of the probability that an offender is caught.

Answer: A

Diff: 1

Section: 5.1

43) Tom Wilson is the operations manager for BiCorp, a real estate investment firm. Tom must decide if BiCorp is to invest in a strip mall in a northeast metropolitan area. If the shopping center is highly successful, after tax profits will be $100,000 per year. Moderate success would yield an annual profit of $50,000, while the project will lose $10,000 per year if it is unsuccessful. Past experience suggests that there is a 40% chance that the project will be highly successful, a 40% chance of moderate success, and a 20% probability that the project will be unsuccessful.

- Calculate the expected value and standard deviation of profit.
- The project requires an $800,000 investment. If BiCorp has an 8% opportunity cost on invested funds of similar riskiness, should the project be undertaken?

Answer:

**a.**

Expected Value

=

———————————–

100,000 .4 40,000

50,000 .4 20,000

-10,000 .2 -2,000

_____________

= 58,000

Standard deviation

σ =

[ – ] P

————————————————————————

100,000 42,000 1,764,000,000 705,600,000

50,000 -8,000 64,000,000 25,600,000

-10,000 -68,000 4,624,000,000 924,800,000

= 1,656,000,000

*σ* = 40,693.98

Bio-Corp’s opportunity cost is 8% of 800,000 or

0.08 × 800,000 = 64,000.

The expected value of the project is less than the opportunity cost.

Bi-Corp should not undertake the project.

Diff: 2

Section: 5.1

44) John Smith is considering the purchase of a used car that has a bank book value of $16,000. He believes that there is a 20% chance that the car’s transmission is damaged. If the transmission is damaged, the car would be worth only $12,000 to Smith. What is the expected value of the car to Smith?

Answer: Expected Value = E($) = Pr(X1) + (1 – Pr)(X2),

where Pr is the probability of no transmission damage and Xi is the book value of the car without and with transmission damage, respectively.

E($) = .80(16,000) + .20(12,000)

= 12,800 + 2,400

= $15,200

Diff: 2

Section: 5.1

45) C and S Metal Company produces stainless steel pots and pans. C and S can pursue either of two distribution plans for the coming year. The firm can either produce pots and pans for sale under a discount store label or manufacture a higher quality line for specialty stores and expensive mail order catalogs. High initial setup costs along with C and S’s limited capacity make it impossible for the firm to produce both lines. Profits under each plan depend upon the state of the economy. One of three conditions will prevail:

growth (probability = 0.3)

normal (probability = 0.5)

recession (probability = 0.2)

The outcome under each plan for each state of the economy is given in the table below. Figures in the table are profits measured in dollars. The probabilities for each economic condition represent crude estimates.

Economic Condition Discount Line Specialty Line

Growth 250,000 400,000

Normal 220,000 230,000

Recession 140,000 20,000

- Calculate the expected value for each alternative.
- Which alternative is more risky? (Calculate the standard deviation of profits for each alternative.)
- Taking into account the importance of risk, which alternative should an investor choose?

Answer:

**a.**

Expected Value Discount Line

0.3(250,000) + 0.5(220,000) + 0.2(140,000)

EV = 213,000 (*π* = 213,000)

Expected Value Specialty Line

0.3(400,000) + 0.5(230,000) + 0.2(20.000)

EV = 239,000 (*π* = 239,000)

σ2 for discount line.

[ – ] Pi

—————————————————

250,000 37,000 410,700,000

220,000 7,000 24,500,000

140,000 -73,000 1,065,800,000

———————-

σ2 = 1,501,000,000

*σ* = 38,743

Expected Value Specialty Line:

[ – ] Pi

——————————————————

400,000 161,000 7,776,300,000

230,000 -9,000 40,500,000

20,000 -219,000 9,592,200,000

———————–

*σ*2 = 16,809,000,000

*σ* = 129,650

The discount store opportunity is far less risky.

The specialty store offers a higher expected return but not in proportion to the increased risk (one could compute the coefficient of variation or observe this fact).

Diff: 3

Section: 5.1

46) Calculate the expected value of the following game. If you win the game, your wealth will increase by 36 times your wager. If you lose, you lose your wager amount. The probability of winning is 1/38 Calculate the variance of the game.

Answer: The expected value (*EV*) of the game is calculated as

*EV* = (36*w) *+ (-*w) *= -. The variance of the game is calculated as

*Var* = + () = *w*2 + 1.03*w*2 = 35.09*w*2.

Diff: 3

Section: 5.1

47) Calculate the expected value of the following game. If you win the game, your wealth will increase by 100,000,000 times your wager. If you lose, you lose your wager amount.

The probability of winning is .

Answer: The expected value of the game is calculated as

*EV* = (100,000,000*w*) + (-*w*) = *w* ≈ 49*w*.

Diff: 2

Section: 5.1

**5.2 Preferences Toward Risk**

1) Assume that two investment opportunities have identical expected values of $100,000. Investment A has a variance of 25,000, while investment B’s variance is 10,000. We would expect most investors (who dislike risk) to prefer investment opportunity

- A) A because it has less risk.
- B) A because it provides higher potential earnings.
- C) B because it has less risk.
- D) B because of its higher potential earnings.

Answer: C

Diff: 1

Section: 5.2

**Scenario 5.5:**

Engineers at Jalopy Automotive have discovered a safety flaw in their new model car. It would cost $500 per car to fix the flaw, and 10,000 cars have been sold. The company works out the following possible scenarios for what might happen if the car is not fixed, and assigns probabilities to those events:

Scenario Probability Cost

- No one discovers flaw .15 $0
- Government fines firm .40 $10 million

(no lawsuits)

- Resulting lawsuits are lost .30 $12 million

(no government fine)

- Resulting lawsuits are won .15 $2 million

(no government fine)

2) Refer to Scenario 5.5. The expected cost to the firm if it does not fix the car is

- A) $0.
- B) $24 million.
- C) $7.9 million.
- D) $2 million.
- E) $3.6 million.

Answer: C

Diff: 1

Section: 5.2

3) Refer to Scenario 5.5. Which of the following statements is true?

- A) The expected cost of not fixing the car is less than the cost of fixing it.
- B) The expected cost of not fixing the car is greater than the cost of fixing it.
- C) It is not possible to tell whether the expected cost of fixing the car is less than the cost of fixing it, because the probabilities are subjective.
- D) It is not possible to tell whether the expected cost of fixing the car is less than the cost of fixing it, because the probabilities are not equal.

Answer: B

Diff: 2

Section: 5.2

4) Refer to Scenario 5.5. Jalopy Automotive’s executives,

- A) if risk-neutral, would fix the flaw because it enables them to have a sure outcome.
- B) if risk-neutral, would fix the flaw because the cost of fixing the flaw is less than the expected cost of not fixing it.
- C) if risk-loving, would fix the flaw because it enables them to have a sure outcome.
- D) if risk-averse, would not fix the flaw because the cost of fixing the flaw is more than the expected cost of not fixing it.
- E) would fix the flaw regardless of their risk preference, because of the large probability of high-cost outcomes.

Answer: B

Diff: 2

Section: 5.2

5) Other things equal, expected income can be used as a direct measure of well-being

- A) always.
- B) no matter what a person’s preference to risk.
- C) if and only if individuals are not risk-loving.
- D) if and only if individuals are risk averse.
- E) if and only if individuals are risk neutral.

Answer: E

Diff: 1

Section: 5.2

6) A person with a diminishing marginal utility of income

- A) will be risk averse.
- B) will be risk neutral.
- C) will be risk loving.
- D) cannot decide without more information

Answer: A

Diff: 1

Section: 5.2

7) An individual with a constant marginal utility of income will be

- A) risk averse.
- B) risk neutral.
- C) risk loving.
- D) insufficient information for a decision

Answer: B

Diff: 1

Section: 5.2

**Figure 5.1**

8) In Figure 5.1, the marginal utility of income is

- A) increasing as income increases.
- B) constant for all levels of income.
- C) diminishes as income increases.
- D) None of the above is necessarily correct.

Answer: A

Diff: 1

Section: 5.2

9) An individual whose attitude toward risk is illustrated in Figure 5.1 is

- A) risk averse.
- B) risk loving.
- C) risk neutral.
- D) None of the above is necessarily correct.

Answer: B

Diff: 1

Section: 5.2

10) The concept of a risk premium applies to a person that is

- A) risk averse.
- B) risk neutral.
- C) risk loving.
- D) all of the above

Answer: A

Diff: 1

Section: 5.2

11) John Brown’s utility of income function is U = log(I+1), where I represents income. From this information you can say that

- A) John Brown is risk neutral.
- B) John Brown is risk loving.
- C) John Brown is risk averse.
- D) We need more information before we can determine John Brown’s preference for risk.

Answer: C

Diff: 3

Section: 5.2

12) Amos Long’s marginal utility of income function is given as: MU(I) = I1.5, where I represents income. From this you would say that he is

- A) risk averse.
- B) risk loving.
- C) risk neutral.
- D) none of the above

Answer: B

Diff: 3

Section: 5.2

13) Blanca would prefer a certain income of $20,000 to a gamble with a 0.5 probability of $10,000 and a 0.5 probability of $30,000. Based on this information:

- A) we can infer that Blanca neutral.
- B) we can infer that Blanca is risk averse.
- C) we can infer that Blanca is risk loving.
- D) we cannot infer Blanca’s risk preferences.

Answer: B

Diff: 1

Section: 5.2

14) The difference between the utility of expected income and expected utility from income is

- A) zero because income generates utility.
- B) positive because if utility from income is uncertain, it is worth less.
- C) negative because if income is uncertain, it is worth less.
- D) that expected utility from income is calculated by summing the utilities of possible incomes, weighted by their probability of occurring, and the utility of expected income is calculated by summing the possible incomes, weighted by their probability of occurring, and finding the utility of that figure.
- E) that the utility of expected income is calculated by summing the utilities of possible incomes, weighted by their probability of occurring, and the expected utility of income is calculated by summing the possible incomes, weighted by their probability of occurring, and finding the utility of that figure.

Answer: D

Diff: 3

Section: 5.2

**Scenario 5.6:**

Consider the information in the table below, describing choices for a new doctor. The outcomes represent different macroeconomic environments, which the individual cannot predict.

**Outcome 1Outcome 2**Job ChoiceProb.IncomeProb.IncomeWork for HMO0.95$100,0000.05$60,000Own practice0.2$250,0000.8$30,000Research0.1$500,0000.9$50,000

15) Refer to Scenario 5.6. The expected utility of income from research is

- A) u($275,000).
- B) u($95,000).
- C) [u($500,000) + u($50,000)]/2.
- D) .1 u($500,000) + .9 u($50,000).
- E) dependent on which outcome actually occurs.

Answer: D

Diff: 1

Section: 5.2

16) Refer to Scenario 5.6. The utility of expected income from research is

- A) U($275,000).
- B) U($95,000).
- C) [U($500,000) + U($50,000)]/2.
- D) .1U($500,000) + .9U($50,000).
- E) dependent on which outcome actually occurs.

Answer: B

Diff: 2

Section: 5.2

17) Refer to Scenario 5.6. If the doctor is risk-averse, she would accept

- A) $50,000 for sure rather than take the risk of being a researcher.
- B) $60,000 for sure (the minimum HMO outcome) rather than take the risk of being a researcher.
- C) $95,000 for sure rather than face option 1 and option 2 in research.
- D) $275,000 for sure (the average of option 1 and option 2 in research), but not less, rather than face the risk of those two options.
- E) the research position because it has the highest possible income.

Answer: C

Diff: 2

Section: 5.2

18) In the figure below, what is true about the two jobs?

- A) Job 1 has a lower standard deviation than Job 2.
- B) All outcomes in both jobs have the same probability of occurrence.
- C) A risk-averse person would prefer Job 2.
- D) A risk-neutral person would prefer Job 1.
- E) Job 1 has a higher expected income than Job 2.

Answer: A

Diff: 2

Section: 5.2

19) In figure below, what is true about the two jobs?

- A) Job 1 has a larger standard deviation than Job 2.
- B) All outcomes in both jobs have the same probability of occurrence.
- C) A risk-averse person would prefer Job 2.
- D) A risk-neutral person would prefer Job 1.
- E) Job 1 has the same expected income as Job 2.

Answer: E

Diff: 2

Section: 5.2

20) Upon graduation, you are offered three jobs.

**CompanySalaryBonusProbability of Receiving Bonus**Samsa Exterminators100,00020,000.90Gradgrind Tech100,00030,000.70Goblin Fruits115,000——–——-

Which of the following is true?

- A) If you’re risk-neutral, you go work for Goblin Fruits.
- B) If you’re risk-loving, you go work for Goblin Fruits.
- C) If you’re risk-neutral, you go work for Samsa Exterminators.
- D) If you’re risk-neutral, you go work for Gradgrind Tech.

Answer: D

Diff: 2

Section: 5.2

21) A risk-averse individual prefers

- A) the utility of expected income of a risky gamble to the expected utility of income of the same risky gamble.
- B) the expected utility of income of a risky gamble to the utility of expected income of the same risky gamble.
- C) outcomes with 50-50 odds to those with more divergent probabilities, no matter what the dollar outcomes.
- D) outcomes with higher probabilities assigned to more favorable outcomes, no matter what the outcomes are.
- E) outcomes with highly divergent probabilities so that one of the outcomes is almost certain.

Answer: A

Diff: 2

Section: 5.2

22) A risk-averse individual has

- A) an increasing marginal utility of income.
- B) an increasing marginal utility of risk.
- C) a diminishing marginal utility of income.
- D) a diminishing marginal utility of risk.
- E) a constant marginal utility of income, but a diminishing marginal utility of risk.

Answer: C

Diff: 1

Section: 5.2

23) Any risk-averse individual would always

- A) take a 10% chance at $100 rather than a sure $10.
- B) take a 50% chance at $4 and a 50% chance at $1 rather than a sure $1.
- C) take a sure $10 rather than a 10% chance at $100.
- D) take a sure $1 rather than a 50% chance at $4 and a 50% chance at losing $1.
- E) do C or D above.

Answer: C

Diff: 3

Section: 5.2

24) What would best explain why a generally risk-averse person would bet $100 during a night of blackjack in Las Vegas?

- A) Risk aversion relates to income choices only, not expenditure choices.
- B) Risk averse people may gamble under some circumstances.
- C) The economics of gambling and the economics of income risk are two different things.
- D) Risk-averse people attach high subjective probabilities to favorable outcomes, even when objective probabilities are known.

Answer: B

Diff: 2

Section: 5.2

25) Dante has two possible routes to travel on a business trip. One is more direct but more exhausting, taking one day but with a probability of business success of 1/4. The second takes three days, but has a probability of success of 2/3. If the value of Dante’s time is $1000/day, the value of the business success is $12,000, and Dante is risk neutral,

- A) it doesn’t matter which path he takes, because he doesn’t consider risk.
- B) he should take the 1-day trip, because he doesn’t consider risk.
- C) he should take the 1-day trip, because $11,000 is greater than $9,000.
- D) he should take the 3-day trip, because it will increase his expected net revenue by $3,000.
- E) he should take the 3-day trip, because it will increase his expected net revenue by $5,000.

Answer: D

Diff: 3

Section: 5.2

**Scenario 5.7:**

As president and CEO of MegaWorld industries, Natasha must decide on some very risky alternative investments. Consider the following:

**ProjectProfit if SuccessfulProbability of SuccessLoss if FailureProbability of Failure**A$10 million.5-$6 million.5B$50 million.2-$4 million.8C$90 million.1-$10 million.9D$20 million.8-$50 million.2E$15 million.4$0.6

26) Refer to Scenario 5.7. Since Natasha is a risk-neutral executive, she would choose

- A) A.
- B) B.
- C) C.
- D) D.
- E) E.

Answer: B

Diff: 1

Section: 5.2

27) Refer to Scenario 5.7. As a risk-neutral executive, Natasha

- A) is indifferent between projects D and E.
- B) prefers project E to project D, but do not necessarily consider E the best.
- C) prefers project E to all other projects.
- D) seeks the highest “profit if successful” of all the projects.
- E) seeks the project with the most even odds.

Answer: A

Diff: 1

Section: 5.2

Consider the following information about job opportunities for new college graduates in Megalopolis:

** Table 5.1**

**MajorProbability of Receiving**

**an Offer in One Year**

**Average Salary Offer**Accounting.95$25,000Economics.90$30,000English.70$24,000Poli Sci.60$18,000Mathematics1.00$21,000

28) Refer to Table 5.1. A risk-neutral individual making a decision solely on the basis of the above information would choose to major in

- A) accounting.
- B) economics.
- C) English.
- D) political science.
- E) mathematics.

Answer: B

Diff: 1

Section: 5.2

29) Refer to Table 5.1. A risk-averse student making a decision solely on the basis of the above information

- A) would definitely become a math major.
- B) would definitely not become an English major.
- C) would definitely become a political science major.
- D) might be either a mathematics major or English major, depending upon the utility of the average offer.
- E) would definitely be indifferent between the accounting major and the English major if the probability of finding a job in accounting were any value higher than 0.95.

Answer: D

Diff: 3

Section: 5.2

**Figure 5.2**

30) The individual pictured in Figure 5.2

- A) must be risk-averse.
- B) must be risk-neutral.
- C) must be risk-loving.
- D) could be risk-averse, risk-neutral, or risk-loving.
- E) could be risk-averse or risk-loving, but not risk-neutral.

Answer: A

Diff: 1

Section: 5.2

31) The individual pictured in Figure 5.2

- A) prefers a 50% chance of $100 and a 50% chance of $50 to a sure $75.
- B) would receive a utility of 300 from a 50% chance of $100 and a 50% chance of $50.
- C) would receive a utility of 300 from a sure $75.
- D) would receive a utility of 250 from a sure $75.
- E) is one for whom income is a measure of well-being.

Answer: D

Diff: 2

Section: 5.2

32) When facing a 50% chance of receiving $50 and a 50% chance of receiving $100, the individual pictured in Figure 5.2

- A) would pay a risk premium of 10 utils to avoid facing the two outcomes.
- B) would want to be paid a risk premium of 10 utils to give up the opportunity of facing the two outcomes.
- C) would pay a risk premium of $7.50 to avoid facing the two outcomes.
- D) would want to be paid a risk premium of $7.50 to avoid facing the two outcomes.
- E) has a risk premium of 10 utils.

Answer: C

Diff: 3

Section: 5.2

**Figure 5.3**

33) The individual pictured in Figure 5.3

- A) must be risk-averse.
- B) must be risk-neutral.
- C) must be risk-loving.
- D) could be risk-averse, risk-neutral, or risk-loving.
- E) could be risk-averse or risk-loving, but not risk-neutral.

Answer: C

Diff: 1

Section: 5.2

34) The individual pictured in Figure 5.3

- A) prefers a sure $6000 to a 50% chance of $4000 and a 50% chance of $8000.
- B) has an expected utility of 12 from a 50% chance of $4000 and a 50% chance of $8000.
- C) would receive a utility of 12 from a sure $6000.
- D) would receive a utility of 18 from a sure $6000.

Answer: C

Diff: 2

Section: 5.2

35) The individual pictured in Figure 5.3

- A) would pay a risk premium of 2 utils to avoid facing the two outcomes.
- B) would want to be paid a risk premium of 2 utils to give up the opportunity of facing the two outcomes.
- C) would pay a risk premium of $1000 to avoid facing the two outcomes.
- D) would want to be paid a risk premium of $1000 to give up the opportunity of facing the two outcomes.
- E) has a risk premium of 2 utils.

Answer: D

Diff: 2

Section: 5.2

36) A new toll road was built in Southern California between San Juan Capistrano and Costa Mesa. On average, drivers save 10 minutes taking this road as opposed to the old road. The toll is $2; the fine for not paying the toll is $76. The probability of catching and fining someone who does not pay the toll is 90%. Individuals who take the road and pay the toll must therefore value 10 minutes at a minimum

- A) between $1.80 and $68.40.
- B) between $2 and $68.40.
- C) $1.80.
- D) between $1.80 and $76.
- E) more than $76.

Answer: B

Diff: 3

Section: 5.2

37) Consider the following statements when answering this question;

- Without fire insurance, the expected value of home ownership for a risk averse homeowner is $W. Insurance companies are willing to sell this homeowner a policy that guarantees the homeowner a wealth of $W.
- In a neighborhood where the price of houses are identical, the probability of a fire is identical, and the value of damage done by fires is identical, the risk premium for an insurance policy that repays all the cost of the fire damage does not vary across homeowners.
- A) I and I are true.
- B) I is true, and II is false.
- C) I is false, and II is true.
- D) I and II are false.

Answer: D

Diff: 3

Section: 5.2

38) A farmer lives on a flat plain next to a river. In addition to the farm, which is worth $F, the farmer owns financial assets worth $A. The river bursts its banks and floods the plain with probability P, destroying the farm. If the farmer is risk averse, then the willingness to pay for flood insurance unambiguously falls when

- A) F is higher, and A is lower.
- B) P is lower, and F is higher.
- C) F & A are higher.
- D) P is lower, and A is lower.
- E) A is higher, and F is lower.

Answer: E

Diff: 3

Section: 5.2

39) Bill’s utility function takes the form U(I) = exp(I) where I is Bill’s income. Based on this utility function, we can see that Bill is:

- A) risk averse
- B) risk neutral
- C) risk loving
- D) He can exhibit two or more of these risk behaviors under this utility function.

Answer: C

Diff: 3

Section: 5.2

40) Consider two upward sloping income-utility curves with income on the horizontal axis. The steeper curve represents risk preferences that are more:

- A) risk averse.
- B) risk loving.
- C) loss averting.
- D) We cannot answer this question without more information about the shapes of the curves.

Answer: D

Diff: 1

Section: 5.2

41) Suppose your utility function for income that takes the form U(I) = , and you are considering a self-employment opportunity that may pay $10,000 per year or $40,000 per year with equal probabilities. What certain income would provide the same satisfaction as the expected utility from the self-employed position?

- A) $15,000
- B) $22,500
- C) $25,000
- D) $27,500

Answer: B

Diff: 1

Section: 5.2

42) Farmer Brown grows wheat on his farm in Kansas, and the weather during the growing season makes this a risky venture. Over the many years that he has been in business, he has learned that rainfall patterns can be categorized as highly productive (HP) with a probability of .2, moderately productive (MP) with a probability of .6, and not productive at all (NP) with a probability of .2. With these various rainfall patterns, he has also learned that the inflation adjusted yields are $25,000 with NP weather, $10,000 with MP weather, and $50,000 with HP weather. Calculate the expected yield from growing wheat on Farmer Brown’s farm. What can be learned about Brown’s attitude toward risk from this problem? Explain.

Answer:

E(Yield) = (HP)[PHP] + (MP)[ PMP] + (NP)[ PNP]

= (50,000)[.2] + 10,000 [.6] + (-25,000)[.2]

= 10,000 + 6,000 – 5,000

= $11,000

We don’t have enough information to say anything about this person’s attitude toward risk. We only know what can be expected from growing wheat in this location.

Diff: 2

Section: 5.2

43) Virginia Tyson is a widow whose primary income is provided by earnings received from her husband’s $200,000 estate. The table below shows the relationship between income and total utility for Virginia.

Income Total Utility

5,000 12

10,000 22

15,000 30

20,000 36

25,000 40

30,000 42

- Construct the marginal utility table for Virginia. What is her attitude toward risk? Explain your answer including a description of the marginal utility for individuals whose risk preferences are different from Virginia’s.
- Virginia is currently earning 10% on her $200,000 in a riskless investment. Alternatively, she could invest in a project that has a 0.4 probability of yielding a $30,000 return on her investment and a 0.6 probability of paying $10,000. Should she alter her strategy and move her $200,000 to the more risky project?

Answer:

Income TU MU

5,000 12

10,000 22 10

15,000 30 8

20,000 36 6

25,000 40 4

30,000 42 2

Virginia is a risk averter as indicated by her declining marginal utility of income. A risk lover’s marginal utility rises, while someone who is indifferent to risk has a constant marginal utility.

She currently earns $20,000, receiving a total utility of 36. Her expected utility under the project would be:

Expected Utility = 0.4U(30,000) + 0.6U(10,000)

= 0.4(42) + 0.6(22)

Expected Utility = 30

Expected utility is less than current utility, so she should not change.

Diff: 2

Section: 5.2

44) The relationship between income and total utility for three investors (A, B, and C) is shown in the tables below.

** A B C**

Income TU Income TU Income TU

5,000 14 5,000 4 5,000 6

10,000 24 10,000 8 10,000 14

15,000 32 15,000 12 15,000 24

20,000 38 20,000 16 20,000 36

25,000 43 25,000 20 25,000 52

30,000 47 30,000 24 30,000 72

35,000 49 35,000 28 35,000 100

Each investor has been confronted with the following three investment opportunities. The first opportunity is an investment which pays $15,000 risk free. Opportunity two offers a 0.4 probability of a $25,000 payment and a 0.6 probability of paying $10,000. The final investment will either pay $35,000 with a probability of 0.25 or $5,000 with a probability of 0.75. Determine the alternative each of the above investors would choose. Provide an intuitive explanation for the differences in their choices.

Answer:

Investment 1 15,000 risk free

Investment 2 25,000 0.4

10,000 0.6

Investment 3 35,000 0.25

5,000 0.75

Expected utility for person A

Investment 1

- 15,000 risk free utility = 32

Investment 2

- 25,000 0.4 utility = 43

10,000 0.6 utility = 24

0.4(43) + 0.6(24) = 31.6

Investment 3

- 35,000 0.25 utility = 49

5,000 0.75 utility = 14

0.25(49) + 0.75(14) = 22.75

A would choose 15,000 risk free

Utility expected for person B

Investment 1

- 15,000 risk free utility = 12

Investment 2

- 25,000 0.4 utility = 20

10,000 0.6 utility = 8

0.4(20) + 0.6(8) = 12.8

Investment 3

- 35,000 0.25 utility = 28

5,000 0.75 utility = 4

0.25(28) + 0.75(4) = 10

B would choose investment 2.

Utility expected for person C

Investment 1

- 15,000 risk free utility = 24

Investment 2

- 25,000 0.4 utility = 52

10,000 0.6 utility = 14

0.4(52) + 0.6(14) = 29.2

Investment 3

- 35,000 0.25 utility = 100

5,000 0.75 utility = 6

0.25(100) + 0.75(6) = 29.5

Investor C would choose project 3.

Investment A is least risky, B is more risky, and C is most risky.

The risk averter in this case prefers no risk; A chooses project 1.

The risk neutral, B, pursues the mid-risk project 2.

The risk lover, C, prefers the gamble implied by project 3.

Diff: 2

Section: 5.2

45) Connie’s utility depends upon her income. Her utility function is U = I1/2. She has received a prize that depends on the roll of a pair of dice. If she rolls a 3, 4, 6 or 8, she will receive $400. Otherwise she will receive $100.

- What is the expected payoff from this prize? [Hint: The probability of rolling a 3 is 1/18, the probability of rolling a 4 is 3/36, the probability of rolling a 6 is 5/36, and the probability of rolling an 8 is 5/36.]
- What is the expected utility from this prize?
- Connie is offered an alternate prize of $169 (no dice roll is required). Will she accept the alternate prize or roll the dice?
- What is the minimum payment that Connie will accept to forego the roll of the dice?

Answer:

Expected return on stock:

The probability of receiving $400 is 5/12. The probability of receiving $100 is 7/12.

Expected payoff = ($400)(5/12) + ($100)(7/12)

= $166.67 + $58.33

= $225

The utility from $400 is (400)1/2 = 20 utils. The utility from $100 is (100)1/2 = 10 utils.

Expected utility = (20 utils)(5/12) + (10 utils)(7/12)

= 8.33 utils + 5.83 utils

= 14.16 utils

The utility from $169 is (169)1/2 = 13 utils. The utility from rolling the dice (14.16 utils) is greater than the utility from a certain $169, therefore, Connie will turn down the $169 alternative prize and roll the dice.

To convince Connie to accept a cash payment in lieu of rolling the dice the cash payment will have to provide more utility than rolling the dice. The expected utility from rolling the dice is 14.16 utils (see 1b). The cash payment that will yield 14.16 utils is calculated as follows:

14.16 = I1/2

14.162 = I

200.51 = I

Connie is indifferent between a cash payment or $200.51 and a roll of the dice. A payment of $200.52 is preferred to the roll of the dice.

Diff: 3

Section: 5.2

46) Describe Larry, Judy and Carol’s risk preferences. Their utility as a function of income is given as follows

Larry: *UL*(*I*) = 10.

Judy: *UJ* (*I*) = 3*I*2.

Carol: *UC* (*I*) = 20*I*.

Answer: Larry’s marginal utility of income is . As income increases, his marginal utility of income diminishes. This implies that Larry is risk-averse. Judy’s marginal utility of income is 6*I*. As income increases, her marginal utility of income increases. This implies that Judy is a risk-lover. Carol’s marginal utility of income is 20. As income increases, her marginal utility of income is constant. This implies that Carol is risk-neutral.

Diff: 2

Section: 5.2

47) Steve has received a stock tip from Monica. Monica has told him that XYZ Corp. will increase in value by 100%. Steve believes that Monica has a 25% chance of being correct. If Monica is incorrect, Steve expects the value of XYZ Corp. will fall by 50%. What is Steve’s expected utility from buying $1,000 worth of XYZ Corp. stock? Steve’s utility of income is *U*(*I*) = 50*I*. Should Steve purchase the stock?

Answer: Steve’s Expected utility from purchasing the stock is

*EV*[*U*(*I*)] = *U*($2,000) + *U*($500) = (100,000) + (25,000) = 43,750. Steve’s utility from receiving $1,000 if he doesn’t purchase the stock is 50,000. Steve should not purchase the stock, because his expected utility from holding the $1000 exceeds his expected utility from undertaking the transaction.

Diff: 2

Section: 5.2

48) George Steinbrenner, the owner of the New York Yankees, has a utility function of wins in a season given by *U*(*w*) = *w*2. Mr. Steinbrenner has been offered a trade. He believes if he completes the trade, his probability of winning 125 games is 15%. There is also an 85% chance the team won’t gel and the Yankees will win only 90 games. Without the trade, Mr. Steinbrenner believes the Yankees will win 94 games. Given Mr. Steinbrenner’s risk attitude, will he complete the trade?

Answer:

Mr. Steinbrenner’s expected utility from undergoing the trade is

*EV*[*U*(*w*)] = 0.15*U*(125) + 0.85*U*(90)

= 0.15(7,812.5) + 0.85(4,050)

= 4,614.375.

Mr. Steinbrenner’s utility from foregoing the trade is U(94) = = 4,418. Since the expected utility from the trade exceeds his utility with certainty, we would expect Mr. Steinbrenner to make the trade.

Diff: 2

Section: 5.2

49) Irene’s utility of income function is *U*(*I*) = 20*I* + 300. Irene is offered the following game of chance. The odds of winning are 1/100 and the pay-off is 75 times the wager. If she loses, she loses her wager amount. Calculate Irene’s expected utility of the game.

Answer: Irene’s Expected Utility of the game is:

*EV*[*U*(*I*) ] = (20 (*I *+ 75*w*) + 300) + (20 (*I* – *w*) + 300)

= 20*I –* 4.8*w* + 300.

Irene’s expected utility loss of playing the game is 4.8 times her wager amount.

Diff: 2

Section: 5.2

50) Sam’s utility of wealth function is *U*(*w*) = 15. Sam owns and operates a farm. He is concerned that a flood may wipe out his crops. If there is no flood, Sam’s wealth is $360,000. The probability of a flood is 1/15. If a flood does occur, Sam’s wealth will fall to $160,000. Calculate the risk premium Sam is willing to pay for flood insurance.

Answer:

Sam’s expected utility is *EV*[*U*(*w*)] = [15] + [15].

= 400 + 8,400 = 8,800.

The level of wealth Sam needs with certainty to ensure this same level of utility is found by solving

*U*(*wC*) = 15 = 8,800 for *wC. *This will be *wC =* = $344,177.76. Sam’s risk premium is then the difference between his current wealth and *wC*. This implies Sam is willing to pay $15,822.24 for insurance against a flood.

Diff: 2

Section: 5.2

51) Richard is a stock market day trader. His utility of wealth function is *U*(*w*) = 4 . Richard has seen a recent upward trend in the price of Yahoo stock. He feels that there is a 30% chance the stock will rise from $175 per share to $225. Otherwise, he believes the stock will settle to about $150 per share. Richard’s current wealth is $1.75 million. Assume that if Richard purchases the stock, he will use his entire wealth. Given his risk preferences, will Richard buy Yahoo?

Answer: Richard will purchase the stock if his expected utility from owning the stock exceeds his current utility of wealth. His currently utility of wealth is:

*U*(*w* = $1,750,000) = 4(1.75)2 = 12.25.

Richard’s expected utility from owning the stock is:

*EV*[*U*(*w*)] = 0.3[4(2.25)2] + 0.7[4(1.5)2]

= 0.3(20.25) + 0.7(9)

= 12.375.

Since Richard’s expected utility of wealth from owning the stock exceeds his utility of wealth with certainty, Richard will buy the stock.

Diff: 2

Section: 5.2

52) Marsha owns a boat that is harbored on the east coast of the United States. Currently, there is a hurricane that is approaching her harbor. If the hurricane strikes her harbor, her wealth will be diminished by the value of her boat, as it will be destroyed. The value of her boat is $250,000. It would cost Marsha $15,000 to move the boat to a harbor out of the path of the hurricane. Marsha’s utility of wealth function is *U*(*w*) = . Marsha’s current wealth is $3 million including the value of the boat. Past evidence has influenced Marsha to believe that the hurricane will likely miss her harbor, and so she plans not to move her boat. Suppose the probability the hurricane will strike Marsha’s harbor is 0.7. Calculate Marsha’s expected utility given that she will not move her boat. Calculate Marsha’s expected utility if she moves her boat. Which of the two options gives Marsha the highest expected utility?

Answer: If she will not move her boat, Marsha’s expected utility is

*EV*[*U*(*w*)] = 0.7(2.75)2 + 0.3(3)2 = 7.99375. If Marsha moves her boat, here expected utility is

*U*(*w*) = (3 – .015)2 = 8.910225. Marsha derives higher expected utility if she moves her boat.

Diff: 2

Section: 5.2

**5.3 Reducing Risk**

1) The object of diversification is

- A) to reduce risk and fluctuations in income.
- B) to reduce risk, but not to reduce fluctuations in income.
- C) to reduce fluctuations in income, but not to reduce risk.
- D) neither to reduce risk, nor to reduce fluctuations in income.

Answer: A

Diff: 1

Section: 5.3

2) Which of these is NOT a generally accepted means of reducing risk?

- A) Diversification
- B) Insurance
- C) Obtaining more information
- D) none of the above

Answer: D

Diff: 1

Section: 5.3

3) The law of large numbers:

- A) can be used to explain why some people are risk averse and others are risk neutral or risk loving.
- B) can be used to explain why some people choose to self-insure against random, single and largely unpredictable events.
- C) states that large amounts of information are often preferred to small amounts of information.
- D) states that the average outcome of a large number of similar events can often be predicted.

Answer: D

Diff: 1

Section: 5.3

4) Smith just bought a house for $250,000. Earthquake insurance, which would pay $250,000 in the event of a major earthquake, is available for $25,000. Smith estimates that the probability of a major earthquake in the coming year is 10 percent, and that in the event of such a quake, the property would be worth nothing. The utility (U) that Smith gets from income (I) is given as follows:

U(I) = I0.5.

Should Smith buy the insurance?

- A) Yes.
- B) No.
- C) Smith is indifferent.
- D) We need more information on Smith’s attitude toward risk.

Answer: A

Diff: 2

Section: 5.3

5) Individuals who fully insure their house and belongings against fire

- A) have wasted their money if a fire does not occur.
- B) generally do so in order that their after-fire wealth can be equal to their before-fire wealth.
- C) generally do so in order that their after-fire wealth can be higher than their before-fire wealth.
- D) generally do so in order to guarantee that the worst outcome, a fire with no insurance, does not occur.
- E) can never come out as well financially after a fire as they were before it.

Answer: D

Diff: 1

Section: 5.3

6) How might department stores best protect themselves against the risk of recession?

- A) Buy insurance policies that pay off when a recession occurs.
- B) Stand ready to go out of business if a recession occurs.
- C) Sell goods that are complements to one another.
- D) Sell both substitute and complement goods.
- E) Sell both normal and inferior goods.

Answer: E

Diff: 2

Section: 5.3

7) In Eugene, Oregon, next year there is a 2% chance of an earthquake severe enough to destroy all buildings and personal property. Quincy, who has $3,000,000 in buildings and personal property, has the opportunity to purchase complete earthquake insurance. Which is true?

- A) Quincy should not purchase earthquake insurance unless he can get it for less than $60,000, because that’s all he could possibly lose in an earthquake.
- B) Quincy should not purchase earthquake insurance unless he can get it for less than $60,000, because that’s his expected loss in an earthquake.
- C) If Quincy buys earthquake insurance, and an earthquake does not occur, he will have received no utility from the transaction.
- D) What Quincy is willing to pay for the earthquake insurance depends upon his degree of risk aversion.
- E) Quincy should be willing and able to pay up to $3,000,000 for earthquake insurance.

Answer: D

Diff: 2

Section: 5.3

8) One reason individuals are willing to pay for information in uncertain situations is that information

- A) can reduce uncertainty.
- B) is a way to diversify.
- C) is a method of insurance.
- D) is a method of self-insurance.
- E) always reduces the difference between the probabilities of possible outcomes.

Answer: A

Diff: 1

Section: 5.3

**Scenario 5.8:**

Risk-neutral Icarus Airlines must commit now to leasing 1, 2, or 3 new airplanes. It knows with certainty that on the basis of business travel alone, it will need at least 1 airplane. The marketing division says that there is a 50% chance that tourism will be big enough for a second plane only. Otherwise, tourism will be big enough for a third plane. This, plus revenue information, yields the following table:

Planes Tourism Revenue Expected

Leased Light Heavy Profit

2 $90 million $30 million $60 million

3 $10 million $140 million $75 million

9) Refer to Scenario 5.8. Without additional information, Icarus Airlines would

- A) lease only the one airplane it is sure it can use.
- B) lease 2 airplanes in order to guarantee it avoids the worst outcome, $10 million.
- C) lease 3 airplanes because $140 million is greater than $90 million.
- D) lease 3 airplanes because $75 million is greater than $60 million.
- E) lease 3 airplanes because heavy tourism is more likely than light tourism.

Answer: D

Diff: 2

Section: 5.3

10) Refer to Scenario 5.8. Given that the two outcomes are equally likely, Icarus Airlines’ expected profit under complete information would be

- A) $40 million.
- B) $90 million.
- C) $115 million.
- D) $120 million.
- E) $125 million.

Answer: C

Diff: 2

Section: 5.3

11) Refer to Scenario 5.8. The value to Icarus Airlines of complete information is

- A) $40 million.
- B) $90 million.
- C) $115 million.
- D) $120 million.
- E) $125 million.

Answer: A

Diff: 2

Section: 5.3

**Scenario 5.9:**

Torrid Texts, a risk-neutral new firm that specializes in making college textbooks more interesting by inserting contemporary material wherever possible, is planning for next year’s production and must decide how many paper producers to contract with. It knows fairly well what the general demand for textbooks is, but is uncertain how faculty will react to this new material. If faculty react very negatively, the firm expects course orders to be down. The executives at Torrid believe that the likelihood of a positive faculty response is 75%. The table below contains profit information under the different possible outcomes.

Producers Faculty Reaction Expected

Contracted Negative Positive Profit

1 $3 million $30 million $23.25 million

2 $1 million $60 million $45.25 million

12) Refer to Scenario 5.9. Without additional information, Torrid Texts would

- A) contract with one paper producer in order to guarantee it avoids the worst outcome, $1 million.
- B) contract with two paper producers because $60 million is greater than $30 million.
- C) contract with two paper producers because $61 million is greater than $33 million.
- D) contract with two paper producers because $45.25 million is greater than $23.25 million.
- E) not be able to come to any decision on how many producers to contract with.

Answer: D

Diff: 2

Section: 5.3

13) Refer to Scenario 5.9. Given that the probability of a positive faculty response is 75%, Torrid Texts’ expected profit under complete information would be

- A) $23.25 million.
- B) $45 million.
- C) $45.25 million.
- D) $45.75 million.
- E) $60 million.

Answer: D

Diff: 2

Section: 5.3

14) Refer to Scenario 5.9. The value to Torrid Texts of complete information is

- A) $0.25 million.
- B) $0.5 million.
- C) $1 million.
- D) $14.75 million.
- E) $30 million.

Answer: B

Diff: 2

Section: 5.3

15) Actual insurance premiums charged by insurance companies may exceed the actuarially fair rates because:

- A) the insurance companies have monopoly rights issued by state regulators.
- B) the insurance companies are risk averse.
- C) there are administrative costs and other expenses that must be covered by the premia.
- D) insurance companies tend to over-state the risks they face.

Answer: C

Diff: 1

Section: 5.3

16) We may not be able to fully remove risk by diversification if:

- A) a completely risk-free asset does not exist.
- B) the asset returns in our portfolio are positively correlated.
- C) buying stock on margin is not allowed by financial regulators.
- D) none of the above

Answer: B

Diff: 1

Section: 5.3

17) Suppose you cannot buy information that completely removes the uncertainty from a business decision that you face, but you could buy information that reduces the degree of uncertainty. Based on the discussion in this chapter, the value of this partial information could be determined as the:

- A) expected outcome under complete certainty minus the expected outcome under the partial information case.
- B) expected outcome under the partially uncertain case minus the expected outcome under the completely uncertain case.
- C) utility of the partially certain case minus the utility of the completely certain case.
- D) We cannot determine the value of information under partial certainty.

Answer: B

Diff: 1

Section: 5.3

18) During the most recent recession, many people temporarily lost substantial value in their retirement investment portfolios because most of the assets (including stocks, bonds, and real estate) all declined in value at the same time. In hindsight, what was the problem with these portfolios?

- A) The portfolios were not adequately diversified because the assets were negatively correlated, so all of the assets had negative returns at the same time.
- B) The portfolios were not adequately diversified because the assets were more positively correlated than expected, so all of the assets had negative returns at the same time.
- C) The portfolios were adequately diversified, but the assets should have been more positively correlated to protect against recession risk.
- D) The investors should not have diversified their investments to protect against recession risk.

Answer: B

Diff: 1

Section: 5.3

19) United Plastics Company produces large plastic cups in a variety of colors. United can produce plain plastic cups that are sold in department stores in inexpensive ten cup bundles. Alternatively, United can sell Novelty Cups which are imprinted with slogans and designs. The printed cups cost more to produce, but they sell for a higher price. The appropriate strategy for United depends upon the state of the economy. Plain cups do better during a recession, while Novelty Cups earn higher profits during normal economic conditions. During a recession, United will earn a $100,000 profit selling plain cups and $40,000 with the Novelty line. Under normal economic conditions, United will earn $120,000 with the plain cups and a $200,000 profit with Novelty Cups. United currently does not use economic forecasts and simply assigns equal probabilities to a recession and normal conditions.

- Using the probabilities assumed by United, what is the expected value of each alternative? Which alternative should the firm pursue? (Your recommendation should include separate recommendations for alternative attitudes toward risk.)
- Calculate and interpret the value to the firm of complete information.

Answer:

**a.**

E.V. Plain Cups = 0.5(100,000) + 0.5(120,000)

= 110,000

E.V. Novelty Cups = 0.5(40,000) + 0.5(200,000)

= 120,000

If United were risk neutral, it would choose Novelty Cups. “A risk averter” would probably choose plain cups, ensuring at least a $100,000 profit. A risk lover would choose Novelty Cups, hoping to realize the $200,000 profit.

**b.**

With complete information, the firm would choose plain cups during recession and Novelty Cups during normal conditions. Expected value would be:

0.5(100,000) + 0.5(200,000) = 150,000

Value Complete Information:

Expected value under certainty 150,000

Expected value under uncertainty 120,000

Value Complete Information 30,000

Firm should pay up to $30,000 to obtain complete information.

Diff: 2

Section: 5.3

20) Mary is a fervent Iowa State University Cyclone Basketball fan. She derives utility as a function of the ISU team winning the Big XII championship and from income according to the function

*U*(*Ic*, *w*) = 35* Ic* + *w*, where = {

and w is her level of wealth. Mary believes the probability of a Cyclone championship is 1/4. Mary has been offered the following “insurance policy.” The insurance policy costs $16. If the Cyclones win the championship, she pays only the policy cost of $16. If the Cyclones lose, she will receive $21.50 (so that after taking into account the policy cost of $16, her net return is $5.50). Will Mary’s expected utility increase if she purchases the policy?

Answer: If Mary does not purchase the policy, her expected utility will be:

*E*[*U*(*Ic, w*) ] = (35 + *w*) + *w* = *w *+ 8.75. If Mary purchases the policy, her expected utility will be: *E*[*U*(*Ic, w*) ] = (35 + *w –* 16) + (*w* + 5.50) = *w *+ 8.875. Mary’s expected utility with the policy is higher.

Diff: 2

Section: 5.3

21) Jonathan and Roberto enjoy playing poker. Jonathan’s utility as a function of winning a poker hand is *UJ* = {.

Roberto’s utility as a function of winning a poker hand is *UR* = {.

Unfortunately for Jonathan, he has a habit of whistling only when he gets a full-house or better. Roberto, however, has not noticed this habit. Roberto currently has three-of-a-kind (which will lose to a full-house or better). Roberto believes that the probability Jonathan can beat his three-of-a-kind is 1/10. Roberto could choose to fold or play the hand. Calculate Roberto’s expected utility according to his beliefs. Jonathan is currently whistling. How much could Roberto increase his utility by recognizing Jonathan’s whistling habit?

Answer: According to Roberto’s beliefs, his expected utility from playing the hand is

*UR* = 1 + (100) = 90.1. Since Roberto’s expected utility from not folding exceeds his utility from folding, we will expect Roberto to play. However, if he plays, we know Roberto’s actual utility will be 1 because Jonathan is whistling. If Roberto would recognize Jonathan’s whistling habit in this instance, he would fold and raise his utility by 24 units.

Diff: 3

Section: 5.3

22) Sandra lives in the Pacific Northwest and enjoys walking to and from work during sunny days. Her utility is sharply diminished if she must walk while it is raining. Sandra’s utility function is

*U* = 1,000 *I*1 + 250* I*2 + 1* I*3 where *I*2 = 1 if she walks and there is no rain and *I*1 = 0 otherwise, *I*2 = 1 if she drives to work and *I*2 = 0 otherwise, and *I*3 = 1 if she walks and it rains and *I*3 = 0 otherwise. Sandra believes that the probability of rain today is 3/10. Given her beliefs, what is her expected utility from walking to work? What is her expected utility from driving to work according to her beliefs? If Sandra maximizes her expected utility according to her beliefs, will she drive or walk to work? Sandra missed the weather report this morning that stated the true probability of rain today is 4/5. Given the weather report is accurate, what is Sandra’s true expected utility from walking and driving to work? How much could Sandra increase her expected utility if she read and believed the weather report?

Answer: Sandra’s expected utility from walking according to her belief is

*EV*[*U*] = (1) + (1,000) = 700.3. Also, according to Sandra’s belief, her expected utility from driving is 250. If Sandra acts on her beliefs, we would expect her to walk to work today. If the weather report is accurate, her expected utility from walking to work is *EV*[*U*] = (1) + (1,000) = 200.8. Her expected utility from driving is still 250. However, given these probabilities, Sandra would rather drive. Sandra would increase her expected utility 450.3 units by reading the weather report.

Diff: 2

Section: 5.3

23) Reginald enjoys hunting whitetail deer. He has a dilemma of deciding each morning where to locate his hunting stand. Reginald would like to choose the location that gives him the deer with the highest Pope and Young score in the smallest amount of time. Reginald will also kill the first deer he sees that offers any Pope and Young score. His utility is a function of the Pope and Young score (*b*), time in minutes spent hunting (*t*) and wealth in dollars (*w*) and is given by

*U*(*b*, *t*, *w*) = – + *w*. If Reginald chooses stand A, he will kill a deer with Pope and Young score of 120 in 300 minutes. If Reginald chooses stand B, he will kill a deer with a Pope and Young score of 190 in 480 minutes. In dollars, how much would Reginald be willing to give up to learn of the outcomes from each stand?

Answer: If Reginald goes to stand A, his utility will be *w +* 1,390. If Reginald goes to stand B, his utility will be *w +* 3,530. Since $1 of wealth is equal to 1 unit of utility, we see that Reginald would be willing to pay $2,140 to learn about his outcomes at each stand and avoid going to stand A.

Diff: 2

Section: 5.3

**5.4 The Demand for Risky Assets**

1) The demand curve for a particular stock at any point in time is

- A) very inelastic but not infinitely so.
- B) almost infinitely inelastic.
- C) infinitely elastic.
- D) fairly elastic but not infinitely elastic.

Answer: C

Diff: 1

Section: 5.4

2) Which of the following assets is almost riskless?

- A) Common stocks
- B) Long-term corporate bonds
- C) U.S. Treasury bills
- D) Long-term government bonds
- E) Apartment buildings

Answer: C

Diff: 1

Section: 5.4

3) Which of the following statements is true?

- A) The expected return and standard deviation of return are greater for common stock than for U.S. Treasury bills.
- B) The expected return on common stocks is greater than the expected return on U.S Treasury bills, but the standard deviation of return for common stocks is less than the standard deviation of return for U.S. Treasury bills
- C) The expected return on common stocks is less than the expected return on U.S Treasury bills, but the standard deviation of return for common stocks is greater than the standard deviation of return for U.S. Treasury bills.
- D) The expected return and standard deviation of return are less for common stocks than for U.S. Treasury bills.

Answer: A

Diff: 2

Section: 5.4

**Scenario 5.10:**

Hillary can invest her family savings in two assets: riskless Treasury bills or a risky vacation home real estate project on an Arkansas river. The expected return on Treasury bills is 4 percent with a standard deviation of zero. The expected return on the real estate project is 30 percent with a standard deviation of 40 percent.

4) Refer to Scenario 5.10. If Hillary invests 30 percent of her savings in the real estate project and the remainder in Treasury bills, the expected return on her portfolio is:

- A) 4 percent.
- B) 11.8 percent.
- C) 17 percent.
- D) 22.2 percent.
- E) 30 percent.

Answer: B

Diff: 2

Section: 5.4

5) Refer to Scenario 5.10. If Hillary invests 30 percent of her savings in the real estate project and remainder in Treasury bills, the standard deviation of her portfolio is:

- A) 0 percent.
- B) 12 percent.
- C) 28 percent.
- D) 30 percent.
- E) 40 percent.

Answer: B

Diff: 2

Section: 5.4

6) Refer to Scenario 5.10. Hillary’s indifference curves showing her preferences toward risk and return can be shown in a diagram. Expected return is plotted on the vertical axis and standard deviation of return on the horizontal axis. Although her indifference curves are upward sloping and bowed downward, their slope is very gradual (they are almost horizontal). These indifference curves reveal that Hillary is:

- A) risk neutral.
- B) risk averse.
- C) risk loving.
- D) irrational.

Answer: B

Diff: 2

Section: 5.4

7) Refer to Scenario 5.10. Hillary’s indifference curves showing her preferences toward risk and return can be shown in a diagram. Expected return is plotted on the vertical axis and standard deviation of return on the horizontal axis. Although her indifference curves are upward sloping and bowed downward, their slope is very gradual (they are almost horizontal). With these indifference curves Hillary will invest:

- A) most of her savings in Treasury bills, and a small percentage in the real estate project.
- B) all of her savings in Treasury bills.
- C) half of her savings in Treasury bills and half in the real estate project.
- D) most of her savings in the real estate project, and a small percentage in Treasury bills.

Answer: D

Diff: 3

Section: 5.4

8) Assume that an investor invests in one risky and one risk free asset. Let σm be the standard deviation of the risky asset and b the proportion of the portfolio invested in the risky asset. The standard deviation of the portfolio is then equal to ________.

- A)
- B)
- C) (1 – b) σm
- D) b σm

Answer: D

Diff: 2

Section: 5.4

9) The slope of the budget line that expresses the tradeoff between risk and return for an asset can be represented by

- A) (Rf – Rm)/σm.
- B) (Rm – Rf)/σm.
- C) Rm – Rf.
- D) b.

Answer: B

Diff: 2

Section: 5.4

10) Last year, on advice from your sister, you bought stock in Burpsy Soda at $100/share. During the year, you collected a $2 dividend and then sold the stock for $120/share. You experienced a

- A) dividend yield of 9%.
- B) dividend yield of 20%.
- C) dividend yield of 11%.
- D) total return of 20%.
- E) total return of 22%.

Answer: E

Diff: 1

Section: 5.4

11) This year, on advice from your sister, you bought tobacco company stock at $50/share. During the year, you collected an $8 dividend, but due to the company’s losses in medical lawsuits its stock fell to $40/share. At this point, you sell, realizing a

- A) dividend yield of -16% and a capital loss of 20%.
- B) dividend yield of 16% and a capital loss of 20%.
- C) dividend loss 10%.
- D) capital loss of 10%.
- E) total loss of 20%.

Answer: B

Diff: 1

Section: 5.4

12) The correlation between an asset’s real rate of return and its risk (as measured by its standard deviation) is usually

- A) positive.
- B) strictly linear.
- C) flat.
- D) negative.
- E) chaotic.

Answer: A

Diff: 1

Section: 5.4

13) Because of the relationship between an asset’s real rate of return and its risk, one would expect to find all of the following, except one. Which one?

- A) Corporate stocks have higher rates of return than U.S. Treasury bonds.
- B) Corporate stocks have higher rates of return than U.S. Treasury bills.
- C) Corporate stocks have higher rates of return than corporate bonds.
- D) Stocks of smaller companies have higher expected rates of return than stocks of larger companies.
- E) Mutual funds including stocks of companies in politically volatile developing countries do not have as high a rate of return as mutual funds restricted to stocks of companies in developed economies.

Answer: E

Diff: 2

Section: 5.4

14) Nervous Norman holds 70% of his assets in cash, earning 0%, and 30% of his assets in an insured savings account, earning 2%. The expected return on his portfolio

- A) is 0%.
- B) is 0.6%
- C) is 1%.
- D) is 2%.
- E) cannot be determined without knowing what the dollar value of his assets is.

Answer: B

Diff: 1

Section: 5.4

15) Daring Dora holds 90% of her assets in high-technology stocks, earning 12%, and 10% in long-term government bonds, earning 6%. The expected return on her portfolio

- A) is 6%.
- B) is 9%.
- C) is 11.4%
- D) is 12%.
- E) cannot be determined without knowing what the dollar value of her assets is.

Answer: C

Diff: 1

Section: 5.4

16) The standard deviation of a two-asset portfolio (with a risky and a non-risky asset) is equal to

- A) the fraction invested in the risky asset times the standard deviation of the non-risky asset.
- B) the fraction invested in the non-risky asset times the standard deviation of the risky asset.
- C) the fraction invested in the risky asset times the standard deviation of that asset.
- D) the fraction invested in the non-risky asset times the standard deviation of that asset.

Answer: C

Diff: 2

Section: 5.4

17) The slope of the budget line, faced by an investor deciding what percentage of her portfolio to place in a risky asset, increases when the

- A) standard deviation of the portfolio gets smaller.
- B) standard deviation of the risky asset gets larger.
- C) rate of return on the risk-free asset gets larger.
- D) rate of return on the risky asset gets larger.
- E) rate of return on money gets larger.

Answer: D

Diff: 2

Section: 5.4

18) The budget line in portfolio analysis shows that

- A) the expected return on a portfolio increases as the standard deviation of that return increases.
- B) the expected return on a portfolio increases as the standard deviation of that return decreases.
- C) the expected return on a portfolio is constant.
- D) the standard deviation of a portfolio is constant.
- E) a riskless portfolio will earn a zero return.

Answer: A

Diff: 2

Section: 5.4

19) The indifference curve between expected return and the standard deviation of return for a risk-averse investor

- A) is downward-sloping.
- B) is upward-sloping.
- C) is horizontal.
- D) is vertical.
- E) can take any shape.

Answer: B

Diff: 1

Section: 5.4

20) The indifference curves of two investors are plotted against a single budget line. Indifference curve A is shown as tangent to the budget line at a point to the left of indifference curve B’s tangency to the same line.

- A) Investors A and B are equally risk averse.
- B) Investor A is more risk averse than investor B.
- C) Investor A is less risk averse than investor B.
- D) It is not possible to say anything about the risk aversion of the two investors, but they will hold the same portfolio.
- E) It is not possible to say anything about either the risk aversion or the portfolio of the two investors.

Answer: B

Diff: 2

Section: 5.4

21) The indifference curves of two investors are plotted against a single budget line. Indifference curve A is shown as tangent to the budget line at a point to the left of indifference curve B’s tangency to the same line.

- A) Investors A and B will hold the same portfolio.
- B) Investors A and B will have different portfolios of the same standard deviation.
- C) Investors A and B will have different portfolios of the same rate of return.
- D) Investors A and B will have different portfolios but have the same level of risk aversion.
- E) Investor A will expect to earn a lower rate of return than investor B.

Answer: E

Diff: 2

Section: 5.4

22) Jack is near retirement and worried that if the stock market falls he will not be able to wait to take his funds out, and will have to sell at the bottom of the market. Richard thinks the probability of a stock market downturn is the same, but he is only 40 and could therefore wait for another turnaround. They face the same budget line. Jack’s risk/return indifference curve

- A) will be concave; Richard’s will be convex.
- B) will be convex; Richard’s will be concave.
- C) will be tangent to the budget line at a point to the left of Richard’s.
- D) will be tangent to the budget line at a point to the right of Richard’s.
- E) must still be tangent to the budget line at the same point as Richard’s.

Answer: C

Diff: 2

Section: 5.4

23) Consider the following statements when answering this question;

- The variance of the returns of an investor’s portfolio can be reduced by selling assets from the portfolio, and investing the proceeds in other assets where returns are positively correlated with the portfolio’s remaining assets.
- The value of complete information is always positive.
- A) I and II are true.
- B) I is true, and II is false.
- C) I is false, and II is true.
- D) I and II are false.

Answer: D

Diff: 3

Section: 5.4

24) Consider the following statements when answering this question;

- The allocation of a risk averse investor’s portfolio between a risk free asset and a risky asset never changes if the rate of return on both assets increases by the same amount.
- Given the choice between investing in a risk free asset or a risky asset with higher expected returns, the utility maximizing portfolio of a risk neutral or risk loving investor would never include the risk free asset.
- A) I and II are true.
- B) I is true, and II is false.
- C) I is false, and II is true.
- D) I and II are false.

Answer: B

Diff: 3

Section: 5.4

25) Is it possible for an investor to allocate more than 100% of their assets to the stock market?

- A) No, this is not theoretically plausible.
- B) No, federal law prohibits this kind of investment.
- C) Yes, investors can borrow money to buy stocks on margin.
- D) none of the above

Answer: C

Diff: 1

Section: 5.4

26) Suppose an investor equally allocates their wealth between a risk-free asset and a risky asset. If the MRS of the current allocation is less than the slope of the budget line, then the investor should:

- A) shift more of their wealth to the risky asset.
- B) shift more of their wealth to the risk-free asset.
- C) keep the same asset allocation.
- D) We do not have enough information to answer this question.

Answer: A

Diff: 1

Section: 5.4

27) Use the following statements to answer this question:

- The real rate of return on an investment is the nominal return minus the rate of inflation.
- The real rate of return on an investment cannot be negative.
- A) I and II are true.
- B) I is true and II is false.
- C) II is true and I is false.
- D) I and II are false.

Answer: B

Diff: 1

Section: 5.4

28) The risk-return indifference curves for a risk-neutral investor are:

- A) vertical lines.
- B) straight lines with slope equal to one.
- C) horizontal lines.
- D) upward sloping lines that are bowed downward.

Answer: C

Diff: 1

Section: 5.4

29) Joan Summers has $100,000 to invest and is considering two alternatives. She can buy a risk free asset that will pay 10% or she can invest in a stock that has a 0.4 chance of paying 15%, a 0.3 chance of paying 18%, and a 0.3 chance of providing a 6% return. Joan plans to invest $70,000 in the stock and $30,000 in the risk free asset.

- Determine the expected percentage return on the stock and the standard deviation.
- Calculate the weighted average return on the portfolio, given the planned investment strategy outlined above.
- Determine the standard deviation for the portfolio.
- Write the equation that represents the budget line in the risk-return tradeoff. What is the slope of the budget line? Interpret this slope.

Answer:

**a.**

Expected return on stock:

0.4(15) + 0.3(18) + 0.3(6) = 13.2%

Expected Return = 13.2% =

Standard Deviation For Stock:

[ – ]

15 1.8 3.24 1.30

18 4.8 23.04 6.91

6 -7.2 51.84 15.55

σ2 = 23.76

σs = 4.87 where σs represents standard deviation of stock.

**b****.**

weighted average portfolio return

Rp = bRS + (1 – b)RF

where b = proportion in risky asset

RS = return on stock (13.2)

RF = risk free

*b* = = 0.7

Rp = 0.7(13.2) + (1 – 0.7)(10)

Rp = 12.24

**c****.**

standard deviation for portfolios, σP

σP = b σs

σP = 0.7(4.87)

σP = 3.41

**d****.**

Rp = RF + ∙ σP

Rp = 10 + ∙ 3.41

Slope is = = 0.66

The slope represents the price of risk, since it tells how much extra risk must be accepted for a higher return.

Diff: 3

Section: 5.4

30) Mel and Christy are co-workers with different risk attitudes. Both have investments in the stock market and hold U.S. Treasury securities (which provide the risk free rate of return). Mel’s marginal rate of substitution of return for risk ( / MU *RP*, *σP) is *= where *RP* is the individual’s portfolio rate of return and σ*P* is the individual’s portfolio risk. Christy’s

= . Each co-worker’s budget constraint is *RP* = *RF* + *σP*, where *Rj* is the risk-free rate of return, *Rm* is the stock market rate of return, and *σm* is the stock market risk. Solve for each co-worker’s optimal portfolio rate of return as a function of *Rj*, *Rm*, and *σm*.

Answer: We know that the slope of the indifference curve will be equal to the slope of the budget constraint at the optimal choice. This implies that for Mel:

= Þ *σP* = . We can then substitute this risk level into the budget constraint and solve for Mel’s optimal portfolio return. This is done as follows:

*RP* = *Rj* + ()* RP* Þ *RP* = .

We can perform the same techniques for Christy. That is,

= Þ *σP* = .

Again, we can substitute this risk level into Christy’s budget constraint and get:

*RP* = *Rj* + ()* RP* Þ *RP* = .

Diff: 2

Section: 5.4

31) Donna is considering the option of becoming a co-owner in a business. Her investment choices are to hold a risk free asset that has a return of *Rj* and co-ownership of the business, which has a rate of return of *Rb* and a level of risk of *σb*. Donna’s marginal rate of substitution of return for risk

( / ) is = where *RP* is Donna’s portfolio rate of return and σ*P* is her optimal portfolio risk. Donna’s budget constraint is given by

*RP* = *Rj* + *σP*. Solve for Donna’s optimal portfolio rate of return and risk as a function of *Rj*, *Rb* and *σb*. Suppose the table below lists the relevant rates of returns and risks. Use this table to determine Donna’s optimal rate or return and risk.

**Investment Rate of Return Risk**

Risk Free 0.06 0

Business 0.25 0.39

Answer:

To find Donna’s optimal portfolio return and portfolio risk, we need to first equate the slope of her indifference curve to the slope of her budget constraint.

This implies = Þ *σP* = *Rp*. We may then substitute this level of portfolio risk into her budget constraint to find her optimal rate of return

*RP* = *Rj* + *RP* Þ *RP* = . We can plug this optimal portfolio return into the expression for portfolio risk above and get:

*σP* = . Using the values from the table, we see that Donna’s optimal portfolio return is

*RP* = = 0.079. Donna’s optimal portfolio risk is *σP* = = 0.123.

Diff: 2

Section: 5.4

**5.5 Bubbles**

1) What form of irrational behavior can cause asset price bubbles?

- A) People do not based their investment decision on the fundamental value of the asset but only on the belief that the asset price will continue to increase.
- B) People accidentally buy assets that they did not want, and this drives up the asset price.
- C) Asset owners panic and begin to sell their assets as quickly as possible.
- D) People throw darts at a list of stocks and buy whatever the dart lands on without thinking about the reasons.

Answer: A

Diff: 1

Section: 5.5

2) Which of the following statements is NOT true?

- A) Speculative demand for an asset may contribute to the formation of a bubble.
- B) Some asset prices purchased during the formation of a bubble may be rational.
- C) Asset price bubbles are always harmful to the general economy.
- D) Speculative demand is based on the assumption that the asset price will continue to rise.

Answer: C

Diff: 1

Section: 5.5

3) When did housing prices start to fall during the most recent housing boom?

- A) 2005
- B) 2006
- C) 2007
- D) 2008

Answer: B

Diff: 1

Section: 5.5

4) Which price index measures the change in housing prices from repeated sales information?

- A) S&P / Case-Shiller index
- B) GDP deflator
- C) Chain-weighted consumer price index
- D) Dow-Jones index

Answer: A

Diff: 1

Section: 5.5

5) What is an informational cascade?

- A) An excess flow of market information that makes it difficult for an investor to form a rational decision.
- B) A continual decline in the quality of market information from public sources due to sequential budget cuts.
- C) A continual increase in the quality of market information from public sources due to broader use of the internet by market participants.
- D) A sequence of decisions based on the actions of others rather than fundamental information.

Answer: D

Diff: 1

Section: 5.5

6) Which of the following statements is NOT true?

- A) The sharp decline in housing prices that first appeared in the U.S. during 2006 also spread to other countries around the world.
- B) The housing price bubble that burst in 2006 was the first housing bubble in U.S. history.
- C) One reason for the formation of the housing price bubble was an unfounded belief that housing prices always increased over time.
- D) Speculative demand was an important contributor to the most recent housing price bubble.

Answer: B

Diff: 1

Section: 5.5

7) Which of the following events will help to burst an asset price bubble?

- A) Speculative demand for the asset quickly declines.
- B) Speculative demand for the asset quickly increases.
- C) New information leads buyers to doubt that prices will continue to increase in the future.
- D) A and C are correct

Answer: D

Diff: 1

Section: 5.5

8) Which major asset experienced a price bubble just before the housing price bubble of 2006-2009?

- A) Internet or tech-stocks
- B) Tulip bulbs
- C) Japanese real estate
- D) Railroad stocks

Answer: A

Diff: 3

Section: 5.5

9) By 2011, how much had U.S. housing prices declined from their peak in 2006?

- A) 2 percent
- B) 33 percent
- C) 40 percent
- D) 50 percent

Answer: A

Diff: 1

Section: 5.5

10) Based on what we know about asset price formation, what steps can a government use to restrict the formation of an asset price bubble?

- A) Lower interest rates in order to discourage savings and investment
- B) Loosen lending requirements for banks, which encourages investors to buy bank stock rather than the “bubbling” asset
- C) Increase the money supply
- D) Raise interest rates in order to increase the costs of financing asset purchases

Answer: D

Diff: 1

Section: 5.5

**5.6 Behavioral Economics**

1) Which of the following is NOT an example of consumer behavior consistent with the standard assumptions of microeconomic theory?

- A) A concern for fairness can influence purchasing patterns.
- B) When demand increases, all else being equal, consumers expect price to rise.
- C) After a snowstorm, the demand for snow shovels increases.
- D) Snow shovels and snow plows are substitute goods.
- E) none of the above

Answer: A

Diff: 1

Section: 5.6

2) Which of the following is NOT an example of consumer behavior consistent with the standard assumptions of microeconomic theory?

- A) People are less likely to leave tips at restaurants that they are unlikely to visit again.
- B) Waiters and waitresses have an incentive to provide good service in order to earn tips.
- C) Due to the convention of tipping, restaurants pay a lower wage to waiters and waitresses than they would in the absence of any tipping rule.
- D) Although tipping reduces the amount of income available for purchasing goods, people usually leave tips at restaurants.
- E) none of the above

Answer: D

Diff: 1

Section: 5.6

3) What is a reference point?

- A) the value of a good on the black market
- B) the point from which an individual makes a consumption decision
- C) a subjective valuation of a good
- D) the minimum price that an individual would sell a good that she currently owns
- E) none of the above

Answer: B

Diff: 1

Section: 5.6

4) The tendency for individuals to assign higher values to goods when they own the goods than when they do not possess the goods is known as the:

- A) substitution effect.
- B) endowment effect.
- C) income effect.
- D) anchoring effect.

Answer: B

Diff: 1

Section: 5.6

5) Fine-dining restaurants commonly provide statements in their menus such as, “A 20% gratuity will be added to all checks for parties of six or more patrons.” Given that this statement tends to raise the level of tips or gratuities left by other groups of diners, the statement is a good example of:

- A) the endowment effect.
- B) loss aversion.
- C) anchoring.
- D) none of the above

Answer: C

Diff: 2

Section: 5.6

6) Some high-end retail stores that distribute mail-order catalogs will prominently offer some very high priced goods for sale (for example, a luxury sports car with gold-plated interior trim) in addition to their regular line of merchandise. Behavioral economists argue that the stores do not really plan to sell these goods, but they use these items to provide the customers with a high reference point for the prices of the other goods in the catalog. This practice is an example of:

- A) the ultimatim game.
- B) loss aversion.
- C) anchoring.
- D) none of the above

Answer: C

Diff: 2

Section: 5.6

7) To demonstrate the anchoring phenomenon, Kahneman and Tversky would ask research subjects very difficult questions that should be answered with a number between zero and 100. Before asking for the respondent’s answer, they would also spin a large wheel that generated random number outcomes from zero to 100. If the respondents were subject to the anchoring effect, then we should expect that:

- A) their responses are uncorrelated with the numbers generated by the wheel.
- B) their responses are correlated with the numbers generated by the wheel.
- C) their responses are wrong most of the time.
- D) none of the above

Answer: B

Diff: 2

Section: 5.6

8) Some recent developments in financial research focus on ways to make portfolio allocations and other investment decisions in ways that largely ignore the possible gains but protect against large losses. These tools are designed to reflect ________ behavior among investors.

- A) risk neutral
- B) substitution
- C) loss aversion
- D) anchoring

Answer: C

Diff: 1

Section: 5.6

9) The law of small numbers describes:

- A) the tendency for people to overstate the probability associated with rare events.
- B) the ability to correctly estimate the expected outcome from a small number of events.
- C) the higher probability that small numbers (like 1, 2, and 3) occur in random samples relative to large number (like 8 or 9).
- D) the improved accuracy of averages to estimate relatively small numbers (on the order of 1 or 10) than relatively large numbers (on the order of 1,000 or 10,000).

Answer: A

Diff: 1

Section: 5.6

10) Behavioral economists argue that asset price bubbles and other examples of herd behavior may be due to biases resulting from the law of small numbers. In particular, the investors may observe unusually ________ returns for some asset and use this limited information to ________ the probability that returns will be high in the future.

- A) low, over-estimate
- B) low, under-estimate
- C) high, over-estimate
- D) high, under-estimate

Answer: C

Diff: 1

Section: 5.6

11) Standard game theory predicts a solution to the ultimatum game that is rarely observed when people actually play the game. The key reason that behavioral economists believe the predicted and observed outcomes differ is because people account for ________ of the outcome when making decisions.

- A) loss aversion
- B) fairness
- C) efficiency
- D) utility

Answer: B

Diff: 1

Section: 5.6

12) Which of the following actions may be explained by the law of small numbers?

- A) People buy lottery tickets.
- B) People buy air travel insurance.
- C) People purchase extended or long-term warranties or maintenance contracts for new automobiles and appliances.
- D) all of the above

Answer: D

Diff: 1

Section: 5.6

13) Suppose your instructor gave hats with your school’s logo to half of your economics classmates. She then asked these students to value the hats, and the average response was $9 per hat. Under the endowment effect, we should expect that the average value assigned by the economics students who did NOT receive the hats to be:

- A) higher.
- B) lower.
- C) the same.
- D) We cannot answer this question without knowing more about the risk preferences of the students.

Answer: B

Diff: 1

Section: 5.6

14) Which of the following is an example of anchoring in retail prices?

- A) Price tags on the merchandise list a “high” price that is charged at a competing retailer and the a much lower price that the store actually charges.
- B) An appliance store lists a commercial-quality coffee maker that has high capacity and is very expensive, and all of the other coffee makers are smaller and less expensive.
- C) Restaurant menus include a premium entree like a steak and lobster dinner that is very expensive, and all of the other entree choices are priced at lower values.
- D) all of the above

Answer: D

Diff: 1

Section: 5.6

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