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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,
Answer: E
Diff: 1
Section: 5.1
2) Refer to Scenario 5.1. The probabilities discussed in the information above are
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?
Answer: A
Diff: 1
Section: 5.1
4) Refer to Scenario 5.2. Randy’s expected expense for his car is
Answer: B
Diff: 1
Section: 5.1
5) Refer to Scenario 5.2. Samantha’s expected expense for her car is
Answer: C
Diff: 1
Section: 5.1
Consider the following information about job opportunities for new college graduates in Megalopolis:
Table 5.1
Major | Probability of Receiving
an Offer in One Year |
Average Salary Offer |
Accounting | .95 | $25,000 |
Economics | .90 | $30,000 |
English | .70 | $24,000 |
Poli Sci | .60 | $18,000 |
Mathematics | 1.00 | $21,000 |
6) Refer to Table 5.1. Expected income for the first year is
Answer: E
Diff: 1
Section: 5.1
7) Refer to Table 5.1. Ranked highest to lowest in expected income, the majors are
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:
Company | Good Year Revenue | Bad Year Revenue | Number of Good Years |
Whizbo | $8 million | $6 million | 8 |
Yowzo | $10 million | $4 million | 4 |
Zowiebo | $30 million | $1 million | 1 |
8) Refer to Scenario 5.3. Where is the highest expected revenue, based on the 10 years’ past performance?
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?
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:
Answer: A
Diff: 1
Section: 5.1
11) Refer to Scenario 5.3. The expected revenue from all three companies combined is
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 1 | Outcome 2 | |||
Job Choice | Prob. | Income | Prob. | Income |
Work for HMO | 0.95 | $100,000 | 0.05 | $60,000 |
Own practice | 0.2 | $250,000 | 0.8 | $30,000 |
Research | 0.1 | $500,000 | 0.9 | $50,000 |
12) Refer to Table 5.3. The expected returns are highest for the physician who
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.
Answer: B
Diff: 1
Section: 5.1
14) In Table 5.3, the standard deviation is
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
Answer: D
Diff: 2
Section: 5.1
16) Refer to Table 5.3. Rank the doctor’s job choices in order, least risky first.
Answer: A
Diff: 2
Section: 5.1
17) Upon graduation, you are offered three jobs.
Company | Salary | Bonus | Probability of Receiving Bonus |
Samsa Exterminators | 100,000 | 20,000 | .90 |
Gradgrind Tech | 100,000 | 30,000 | .70 |
Goblin Fruits | 115,000 | ——– | ——- |
Rank the three job offers in terms of expected income, from the highest to the lowest.
Answer: C
Diff: 1
Section: 5.1
18) As president and CEO of MegaWorld industries, you must decide on some very risky alternative investments:
Project | Profit if Successful | Probability of Success | Loss if Failure | Probability of Failure |
A | $10 million | .5 | -$6 million | .5 |
B | $50 million | .2 | -$4 million | .8 |
C | $90 million | .1 | -$10 million | .9 |
D | $20 million | .8 | -$50 million | .2 |
E | $15 million | .4 | $0 | .6 |
The highest expected return belongs to investment
Answer: B
Diff: 1
Section: 5.1
19) What is the advantage of the standard deviation over the average deviation?
Answer: A
Diff: 2
Section: 5.1
Table 5.4
Job | Outcome 1 | Deviation | Outcome 2 | Deviation |
A | $40 | W | $60 | X |
B | $20 | Y | $50 | Z |
20) Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then in absolute value
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
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
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?
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
Answer: C
Diff: 2
Section: 5.1
25) The expected value is a measure of
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
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
Answer: C
Diff: 1
Section: 5.1
28) Which of the following is NOT a generally accepted measure of the riskiness of an investment?
Answer: B
Diff: 1
Section: 5.1
29) The expected value of a project is always the
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?
Answer: D
Diff: 1
Section: 5.1
31) The variance of an investment opportunity:
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:
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?
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:
Outcome | Probability | Pay-offs |
A | .3 | $100 |
B | ? | 50 |
C | .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?
Answer: C
Diff: 2
Section: 5.1
35) Refer to Scenario 5.4. What is the pay-off of outcome C?
Answer: A
Diff: 2
Section: 5.1
36) Refer to Scenario 5.4. What is the deviation of outcome A?
Answer: C
Diff: 2
Section: 5.1
37) Refer to Scenario 5.4. What is the variance of the investment?
Answer: E
Diff: 2
Section: 5.1
38) Refer to Scenario 5.4. What is the standard deviation of the investment?
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:
Answer: B
Diff: 1
Section: 5.1
40) Use the following statements to answer this question:
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.
Answer: C
Diff: 1
Section: 5.1
42) To optimally deter crime, law enforcement authorities should:
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.
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
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
———————–
σ2 = 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 = (36w) + (-w) = -. The variance of the game is calculated as
Var = + () = w2 + 1.03w2 = 35.09w2.
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 = (100,000,000w) + (-w) = w ≈ 49w.
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
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 lawsuits)
(no government fine)
(no government fine)
2) Refer to Scenario 5.5. The expected cost to the firm if it does not fix the car is
Answer: C
Diff: 1
Section: 5.2
3) Refer to Scenario 5.5. Which of the following statements is true?
Answer: B
Diff: 2
Section: 5.2
4) Refer to Scenario 5.5. Jalopy Automotive’s executives,
Answer: B
Diff: 2
Section: 5.2
5) Other things equal, expected income can be used as a direct measure of well-being
Answer: E
Diff: 1
Section: 5.2
6) A person with a diminishing marginal utility of income
Answer: A
Diff: 1
Section: 5.2
7) An individual with a constant marginal utility of income will be
Answer: B
Diff: 1
Section: 5.2
Figure 5.1
8) In Figure 5.1, the marginal utility of income is
Answer: A
Diff: 1
Section: 5.2
9) An individual whose attitude toward risk is illustrated in Figure 5.1 is
Answer: B
Diff: 1
Section: 5.2
10) The concept of a risk premium applies to a person that is
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
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
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:
Answer: B
Diff: 1
Section: 5.2
14) The difference between the utility of expected income and expected utility from income is
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 1 | Outcome 2 | |||
Job Choice | Prob. | Income | Prob. | Income |
Work for HMO | 0.95 | $100,000 | 0.05 | $60,000 |
Own practice | 0.2 | $250,000 | 0.8 | $30,000 |
Research | 0.1 | $500,000 | 0.9 | $50,000 |
15) Refer to Scenario 5.6. The expected utility of income from research is
Answer: D
Diff: 1
Section: 5.2
16) Refer to Scenario 5.6. The utility of expected income from research is
Answer: B
Diff: 2
Section: 5.2
17) Refer to Scenario 5.6. If the doctor is risk-averse, she would accept
Answer: C
Diff: 2
Section: 5.2
18) In the figure below, what is true about the two jobs?
Answer: A
Diff: 2
Section: 5.2
19) In figure below, what is true about the two jobs?
Answer: E
Diff: 2
Section: 5.2
20) Upon graduation, you are offered three jobs.
Company | Salary | Bonus | Probability of Receiving Bonus |
Samsa Exterminators | 100,000 | 20,000 | .90 |
Gradgrind Tech | 100,000 | 30,000 | .70 |
Goblin Fruits | 115,000 | ——– | ——- |
Which of the following is true?
Answer: D
Diff: 2
Section: 5.2
21) A risk-averse individual prefers
Answer: A
Diff: 2
Section: 5.2
22) A risk-averse individual has
Answer: C
Diff: 1
Section: 5.2
23) Any risk-averse individual would always
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?
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,
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:
Project | Profit if Successful | Probability of Success | Loss if Failure | Probability of Failure |
A | $10 million | .5 | -$6 million | .5 |
B | $50 million | .2 | -$4 million | .8 |
C | $90 million | .1 | -$10 million | .9 |
D | $20 million | .8 | -$50 million | .2 |
E | $15 million | .4 | $0 | .6 |
26) Refer to Scenario 5.7. Since Natasha is a risk-neutral executive, she would choose
Answer: B
Diff: 1
Section: 5.2
27) Refer to Scenario 5.7. As a risk-neutral executive, Natasha
Answer: A
Diff: 1
Section: 5.2
Consider the following information about job opportunities for new college graduates in Megalopolis:
Table 5.1
Major | Probability of Receiving
an Offer in One Year |
Average Salary Offer |
Accounting | .95 | $25,000 |
Economics | .90 | $30,000 |
English | .70 | $24,000 |
Poli Sci | .60 | $18,000 |
Mathematics | 1.00 | $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
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
Answer: D
Diff: 3
Section: 5.2
Figure 5.2
30) The individual pictured in Figure 5.2
Answer: A
Diff: 1
Section: 5.2
31) The individual pictured in Figure 5.2
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
Answer: C
Diff: 3
Section: 5.2
Figure 5.3
33) The individual pictured in Figure 5.3
Answer: C
Diff: 1
Section: 5.2
34) The individual pictured in Figure 5.3
Answer: C
Diff: 2
Section: 5.2
35) The individual pictured in Figure 5.3
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
Answer: B
Diff: 3
Section: 5.2
37) Consider the following statements when answering this question;
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
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:
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:
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?
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
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
Investment 2
10,000 0.6 utility = 24
0.4(43) + 0.6(24) = 31.6
Investment 3
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
Investment 2
10,000 0.6 utility = 8
0.4(20) + 0.6(8) = 12.8
Investment 3
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
Investment 2
10,000 0.6 utility = 14
0.4(52) + 0.6(14) = 29.2
Investment 3
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.
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) = 3I2.
Carol: UC (I) = 20I.
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 6I. 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) = 50I. 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) = w2. 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)] = 0.15U(125) + 0.85U(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) = 20I + 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 + 75w) + 300) + (20 (I – w) + 300)
= 20I – 4.8w + 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
Answer: A
Diff: 1
Section: 5.3
2) Which of these is NOT a generally accepted means of reducing risk?
Answer: D
Diff: 1
Section: 5.3
3) The law of large numbers:
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?
Answer: A
Diff: 2
Section: 5.3
5) Individuals who fully insure their house and belongings against fire
Answer: D
Diff: 1
Section: 5.3
6) How might department stores best protect themselves against the risk of recession?
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?
Answer: D
Diff: 2
Section: 5.3
8) One reason individuals are willing to pay for information in uncertain situations is that information
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
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
Answer: C
Diff: 2
Section: 5.3
11) Refer to Scenario 5.8. The value to Icarus Airlines of complete information is
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
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
Answer: D
Diff: 2
Section: 5.3
14) Refer to Scenario 5.9. The value to Torrid Texts of complete information is
Answer: B
Diff: 2
Section: 5.3
15) Actual insurance premiums charged by insurance companies may exceed the actuarially fair rates because:
Answer: C
Diff: 1
Section: 5.3
16) We may not be able to fully remove risk by diversification if:
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:
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?
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.
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 I1 + 250 I2 + 1 I3 where I2 = 1 if she walks and there is no rain and I1 = 0 otherwise, I2 = 1 if she drives to work and I2 = 0 otherwise, and I3 = 1 if she walks and it rains and I3 = 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
Answer: C
Diff: 1
Section: 5.4
2) Which of the following assets is almost riskless?
Answer: C
Diff: 1
Section: 5.4
3) Which of the following statements is true?
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:
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:
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:
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:
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 ________.
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
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
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
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
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?
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
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
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
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
Answer: D
Diff: 2
Section: 5.4
18) The budget line in portfolio analysis shows that
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
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.
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.
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
Answer: C
Diff: 2
Section: 5.4
23) Consider the following statements when answering this question;
Answer: D
Diff: 3
Section: 5.4
24) Consider the following statements when answering this question;
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?
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:
Answer: A
Diff: 1
Section: 5.4
27) Use the following statements to answer this question:
Answer: B
Diff: 1
Section: 5.4
28) The risk-return indifference curves for a risk-neutral investor are:
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.
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 σP 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 σP 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?
Answer: A
Diff: 1
Section: 5.5
2) Which of the following statements is NOT true?
Answer: C
Diff: 1
Section: 5.5
3) When did housing prices start to fall during the most recent housing boom?
Answer: B
Diff: 1
Section: 5.5
4) Which price index measures the change in housing prices from repeated sales information?
Answer: A
Diff: 1
Section: 5.5
5) What is an informational cascade?
Answer: D
Diff: 1
Section: 5.5
6) Which of the following statements is NOT true?
Answer: B
Diff: 1
Section: 5.5
7) Which of the following events will help to burst an asset price bubble?
Answer: D
Diff: 1
Section: 5.5
8) Which major asset experienced a price bubble just before the housing price bubble of 2006-2009?
Answer: A
Diff: 3
Section: 5.5
9) By 2011, how much had U.S. housing prices declined from their peak in 2006?
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?
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?
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?
Answer: D
Diff: 1
Section: 5.6
3) What is a reference point?
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:
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:
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:
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:
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.
Answer: C
Diff: 1
Section: 5.6
9) The law of small numbers describes:
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.
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.
Answer: B
Diff: 1
Section: 5.6
12) Which of the following actions may be explained by the law of small numbers?
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:
Answer: B
Diff: 1
Section: 5.6
14) Which of the following is an example of anchoring in retail prices?
Answer: D
Diff: 1
Section: 5.6
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