Question 1

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

Accepted Answer

If the expected value of the investment opportunity is $250 and one outcome yields a $100 payoff with probability 0.25, then the other outcome must yield a payoff of $350 with probability 0.75 to achieve an expected value of $250. Therefore, the payoff of the other outcome is $350. Option D is the correct answer.

Question 2

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

Accepted Answer

Expected value is a measure of the average outcome or return of an investment, but it does not directly reflect the riskiness of the investment. Standard deviation and variance, on the other hand, are commonly used measures of volatility and variability, which are indicators of riskiness.

Question 3

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

Accepted Answer

Let the probability of the other outcome be x. 
We know that the sum of probabilities must equal 1. 
0.25 + x = 1 
x = 0.75 
Therefore, the probability of the other outcome is 0.75.

Question 4

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

Accepted Answer

The answer of Scenario 5.4:
Suppose an individual is considering an...

Question 5

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.

Accepted Answer

The variance of an investment opportunity cannot be negative as it is a measure of the variability or spread of possible returns, which cannot take negative values.

Question 6

Table 5.4
 
-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.

Accepted Answer

The standard deviation of payoffs at Job A can be calculated using the formula SD = sqrt(Σ(Pi - Pavg)^2 * Pi), where Pi is the probability of outcome i and Pavg is the average payoff. If outcomes 1 and 2 are equally likely at Job A, then Pi = 0.5 for both outcomes. Furthermore, the average payoff is (20 + 0)/2 = 10. Therefore, SD = sqrt((20-10)^2 * 0.5 + (0-10)^2 * 0.5) = sqrt(100) = 10. Thus, the standard deviation of payoffs at Job A is $10, which corresponds to answer choice B.

Question 7

Table 5.4
 
-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

Accepted Answer

To calculate standard deviation, we first need to calculate the expected value or mean of payoffs at Job B:
Expected value = (0.2 * $20) + (0.8 * $50) = $44
Next, we calculate the variance of payoffs:
Variance = ((0.2 * ($20-$44)^2) + (0.8 * ($50-$44)^2)) = $480
Finally, we take the square root of the variance to get the standard deviation:
Standard deviation = sqrt($480) = $21.91
The answer closest to this value is B: $12.

Question 8

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.

Accepted Answer

Since the investment opportunity is a sure thing, meaning it will always pay off $100 regardless of the outcome, there is no variability in its returns. Therefore, the variance is 0.

Question 9

Table 5.4
 
-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.

Accepted Answer

Job A is considered riskier because the standard deviation, which measures the spread or variability of outcomes, is higher when outcomes are equally likely compared to Job B, where one outcome is much more likely than the other.

Question 10

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

Accepted Answer

The answer of Scenario 5.4:
Suppose an individual is considering an...

Question 11

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:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the deviation of outcome A?
A) 30
B) 50
C) 75
D) 100

Accepted Answer

To calculate the deviation of Outcome A, we need to subtract the expected value from the payoff of Outcome A and take its absolute value.

Deviation of Outcome A = |$20 - $25| = $5

The best choice depends on the individual's risk tolerance and investment goals. If they are risk-averse, they may choose Outcome B with a lower potential payoff but a higher probability of success. If they are more risk-tolerant, they may choose Outcome C with a higher potential payoff but a lower probability of success. It ultimately comes down to the individual's personal preferences and investment strategy.

Question 12

Table 5.4
 
-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.

Accepted Answer

Using the formula for Y and Z from Table 5.4, we get:
Y = (.2)($50) - (.8)($20) = $10
Z = (.8)($50) - (.2)($20) = $36
Taking absolute value of Y and Z, we get:
|Y| = $10
|Z| = $36
Therefore, the answer is D as Y = $24 and Z = $6 have absolute values that match with |Y| and |Z|.

Question 13

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.

Accepted Answer

The expected value of a project is defined as the weighted sum of the possible outcomes, with probabilities of each outcome used as weights. Therefore, choice D, which states that the expected value is the weighted average of outcomes, is the correct answer. Choices A and B are incorrect because the expected value is not necessarily the median or mode of the project outcomes. Choice C is also incorrect because the expected value is not the same as the standard deviation of the project.

Question 14

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.

Accepted Answer

The expected value of the gamble is calculated as (0.5 * $10,000) + (0.5 * $30,000) = $5,000 + $15,000 = $20,000, which is equal to the certain income of $20,000.

Question 15

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.

Accepted Answer

To calculate the expected value, we use the formula: 
Expected value = (probability of outcome 1 x value of outcome 1) + (probability of outcome 2 x value of outcome 2)

In this case, the expected value is:
(0.3 x 75) + (0.7 x 125) = 22.5 + 87.5 = $110

Therefore, the best choice is to choose the option with the higher expected value, which is $110.

Question 16

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:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the pay-off of outcome C?
A) -150
B) 0
C) 25
D) 100
E) 150

Accepted Answer

The answer of Scenario 5.4:
Suppose an individual is considering an...

Question 17

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.

Accepted Answer

The weighted average of all possible outcomes with their respective probabilities is the definition of the expected value. The variance and standard deviation are measures of the spread or variability of the outcomes, while the coefficient of variation is a relative measure of the variability. Therefore, C is the best choice as it directly aligns with the given definition.

Question 18

The expected value is a measure of
A) risk.
B) variability.
C) uncertainty.
D) central tendency.

Accepted Answer

The expected value is a measure of central tendency, meaning it represents the average value we expect out of a set of possible outcomes. It is not a measure of risk, variability, or uncertainty.

Question 19

Use the following statements to answer this question:
I. Subjective probabilities are based on individual perceptions about the relative likelihood of an event.
II. 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.

Accepted Answer

Statement I is true because subjective probabilities are based on individual perceptions. However, statement II is false because it is not necessary for all interested parties to agree on the values of subjective probabilities for a particular problem. In fact, different individuals may have different perceptions and assigning probabilities based on their subjective perceptions is a common practice in microeconomic analysis.

Question 20

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

Accepted Answer

The answer of Scenario 5.4:
Suppose an individual is considering an...

Quiz 5: Uncertainty and Consumer Behavior

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?

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

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?

The variance of an investment opportunity:

Table 5.4 -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

Table 5.4 -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?

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:

Table 5.4 -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

Table 5.4 -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

The expected value of a project is always the

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:

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

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

The expected value is a measure of