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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

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