Question 1

Suppose you are offered the following two prospects, a: (0, 1, 0: 3000, 2000, 1000)or b: (1/2, 1/4, 1/4: 3000, 2000, 1000). You are risk averse if:
A)b is preferred to a.
B)you cannot rank the two prospects.
C)a is preferred to b.
D)you are indifferent between a and b.

Accepted Answer

A risk-averse individual prefers a certain outcome over a gamble with the same expected value. Prospect a offers a certain outcome of $2000, while prospect b is a gamble with the same expected value. Therefore, a risk-averse person would prefer a over b.

Question 2

Pat's utility function is u(y)= y^1/2and his income is $100. He is offered a gamble paying $300 with probability 1/2 and $0 with probability 1/2. What is the certainty equivalent of this gamble? A)100 B)150 C)50 D)75

Accepted Answer

The expected utility of the gamble is 0.5*(300^0.5) + 0.5*(0^0.5) = 0.5*17.32 + 0 = 8.66. The certainty equivalent is the amount of money that gives the same utility as the expected utility of the gamble: CE^0.5 = 8.66, so CE = 8.66^2 = 75.

Question 3

Suppose you are offered the following 2 prospects, a: (0, 1, 0: 3000, 2000, 1000)or b: (1/2, 1/4, 1/4: 3000, 2000, 1000). If your preference ordering is such that a is preferred to b, then:
A)you are a risk- neutral individual.
B)you are a risk- averse individual.
C)you are a risk- inclined individual.
D)your risk preferences cannot be determined without further information.

Accepted Answer

If a is preferred to b, it means that you prefer a certain outcome of (0,1,0) with lower payouts over a riskier outcome of (1/2, 1/4, 1/4) with the same payouts. This shows risk aversion, as you prefer a certain outcome over a riskier one with the same expected value.

Question 4

Stephanie's utility function is given by U = W^1/2where W is the value of her house. She is considering whether to buy tornado insurance for her house. Her house is currently valued at $105,625. She knows that her house will be destroyed by a tornado with probability .10 this spring. If it is hit, the rubble will be worth $15,625. What is the maximum amount that she is willing to pay for insurance if the insurance company pays $46875 and refunds her insurance premium in case of a tornado? A)2,345 B)1,055 C)8,835 D)10,995

Accepted Answer

Stephanie's utility without insurance is a weighted average of the utility if her house is destroyed and if it isn't, based on the probability of a tornado. Without insurance, her expected utility is 0.9U($105,625) + 0.1U($15,625). With insurance, and paying a premium X, her utility becomes 0.9U($105,625 - X) + 0.1U($105,625 + $46,875 - X) because the insurance pays out $46,875 and refunds the premium X if the tornado hits. The maximum she would pay for insurance is the value of X that makes her indifferent between having insurance and not having it. Calculating the exact amount requires solving for X in the utility equations, but the correct choice is based on understanding the insurance's impact on her expected utility.

Question 5

Which of the following phenomena constitutes examples of risk- spreading?
A)an insurance market
B)"sharing the bounty"
C)a risk- pooling arrangement
D)syndicate ownership

Accepted Answer

The answer of Which of the following phenomena constitutes examples...

Question 6

Risk- aversion:
A)means that an individual would accept a bet that reduces risk while holding the expected wealth constant.
B)indicates convex preferences.
C)implies that buying insurance is always a good strategy.
D)is tantamount to avoiding all risks.

Accepted Answer

Risk-aversion means that an individual prefers to avoid risk and would accept a bet that reduces risk while keeping expected wealth constant.

Question 7

A risk- inclined individual is characterized by a utility function that exhibits:
A)falling marginal utility of wealth.
B)falling total utility of wealth.
C)constant marginal utility of wealth.
D)rising marginal utility of wealth.

Accepted Answer

A risk-inclined individual is willing to take more risk in exchange for the potential of higher returns. This implies that they would have a preference for a higher marginal utility of wealth, which is represented by a rising utility function. Therefore, choice D is the correct answer.

Question 8

In choices involving risk, an individual chooses:
A)the choice with the highest probability of winning.
B)the option with the largest monetary value.
C)the choice with the lowest probability of loss.
D)the choice that yields the largest expected utility.

Accepted Answer

The best choice when facing a decision under risk is the one that yields the largest expected utility, which takes into account both the probability of winning or losing and the individual's preferences or values. Simply choosing based on the probability of winning (A), the monetary value (B), or the probability of loss (C) does not necessarily lead to the best outcome for the individual.

Question 9

State- dependent preferences depend on:
A)state income tax laws.
B)subjective probabilities.
C)observed probabilities.
D)perfect information.

Accepted Answer

State-dependent preferences refer to an individual's preference for a decision depending on the state of the world at the time the decision is made. This state can be subjective probabilities (option B) that are based on an individual's personal beliefs and expectations about the future. State income tax laws (option A) and observed probabilities (option C) are not relevant factors in state-dependent preferences. Perfect information (option D) is also not necessarily relevant as state-dependent preferences are based on an individual's perception of the future rather than perfect knowledge of it.

Question 10

When dealing with individual behaviour in risky situations which of the following assumptions concerns the way in which individuals choose between prospects having the same two outcomes but different probabilities?
A)the transitivity assumption
B)the ordering assumption
C)the continuity assumption
D)the substitution assumption

Accepted Answer

The ordering assumption concerns the way in which individuals rank or order different prospects based on their expected outcomes and probabilities. It assumes that individuals have a consistent and stable preference order when choosing between prospects with the same two outcomes but different probabilities. This assumption is important in decision-making and risk assessment, as it helps understand how individuals evaluate and compare different options in uncertain situations. The other assumptions (transitivity, continuity, and substitution) refer to different aspects of individual behaviour in risky situations, such as consistency, smoothness, and trade-offs between risk and reward.

Question 11

Consider two identical fishermen with utility functions U(x)= x/2, where x is the number of fish caught. Assume that the probability of either fisherman catching a fish is .05 and that it is impossible for either of them to catch more than one fish. If the two fishermen decided to divide whatever catch was taken, the expected utility of each fisherman would be:
A)0.1.
B)less than 0.025.
C)greater than 0.025 and less than 0.1.
D)more than 0.1.

Accepted Answer

Since the probability of either fisherman catching a fish is 0.05, the expected number of fish caught between the two of them is 0.05. 
If they decide to divide the catch equally, each fisherman will have an expected catch of 0.025 (half of 0.05). 
Using their utility function U(x)= x/2, the expected utility of each fisherman with a catch of 0.025 is 0.0125. 
Therefore, the expected utility of each fisherman if they divide the catch equally is greater than 0.025 (which is the utility they would get if they caught 1 fish alone) and less than 0.1 (which would be the utility they would get if they caught all 10 fish alone). Hence, the answer is C.

Question 12

An individual is said to be risk- averse if: A)w₁is preferred with certainty to a gamble expected to payoff w₁. B)the utility function exhibits increasing marginal utility of wealth. C)the utility function exhibits constant marginal utility of wealth. D)prefer all certain prospects over a particularly risky prospect.

Accepted Answer

Risk-averse individuals prefer a certain outcome over a gamble with the same expected payoff, indicating a preference for certainty.

Question 13

In the state space, along the 45 degree line where wealth in the two states is the same, the slope of an indifference curve is
A)1 - q.
B)q(1 - q).
C)q.
D)q/(1 - q).

Accepted Answer

The answer of In the state space, along the 45...

Question 14

Given a risk- averse individual and a competitive insurance market in which firms are risk- neutral and incur no operating costs, it can be concluded that an individual's reservation price for
Full- insurance coverage:
A)is greater than that of an insurance company.
B)is less than that of an insurance company.
C)precludes a viable market for insurance.
D)is equal to that of an insurance company.

Accepted Answer

In a competitive insurance market, a risk-averse individual values full insurance coverage more than a risk-neutral insurance company because the individual is willing to pay a premium to avoid the uncertainty of loss, whereas the insurance company, being risk-neutral and incurring no operating costs, values the coverage based on the expected loss. Therefore, the individual's reservation price is higher.

Question 15

The expected utility hypothesis requires all of the assumptions used to study utility under certainty and all of the following except:
A)continuity.
B)ordering.
C)substitution.
D)income.

Accepted Answer

The expected utility hypothesis does not require an assumption about income, as it is primarily concerned with decision-making under uncertainty.

Question 16

Stephanie's utility function is given by U = W^1/2where W is the value of her house. Her house is currently valued at $105,625. She knows that her house will be destroyed by a tornado with probability .10 this spring. If it is hit, the rubble will be worth $15,625. What is her expected utility? A)375 B)355 C)255 D)305

Accepted Answer

Expected utility is calculated as the weighted average of utility in each state, considering the probabilities. Here, it's 0.9 * (105625^0.5) + 0.1 * (15625^0.5) = 305.

Question 17

Risk- averse individuals:
A)never buy stocks.
B)buy stocks as a way of spreading the risk.
C)do not spread risks, they avoid taking chances.
D)always buy insurance.

Accepted Answer

Risk-averse individuals are individuals who prefer lower risk investments even if it means lower returns. However, they may still choose to buy stocks as a way of diversifying their portfolio and spreading the risk. By diversifying, they can reduce the impact of any one investment's poor performance on their overall portfolio. This can be achieved through investing in different companies, different industries, and even in different countries.

Question 18

An individual is more likely to reject a risk- pooling arrangement if:
A)he or she experiences rising marginal utility of wealth.
B)he or she is risk loving.
C)he or she is risk averse.
D)he or she experiences decreasing marginal utility of wealth.

Accepted Answer

An individual with rising marginal utility of wealth is more likely to reject a risk-pooling arrangement because they value each additional unit of wealth more than the previous unit. This means that they are less willing to share their wealth with others in a risk-pooling arrangement, as they would rather keep their wealth for themselves.

Question 19

Maya's bracelet is worth $100. There is a 25% chance that it will be stolen from the locker room at the gym. Maya's utility function for money is U(W)= W². Maya is able to buy an insurance policy to cover her bracelet against theft. How much would she be willing to pay for the insurance? A)13.4 B)32.8 C)16.6 D)24.4

Accepted Answer

The expected utility of Maya's bracelet without insurance is 0.75*100^2 + 0.25*0 = 7500. The expected utility of Maya's bracelet with insurance is 100^2 = 10000. Therefore, Maya is willing to pay up to 10000 - 7500 = 2500 for the insurance.

Question 20

Which one of the sets below is a prospect?
A)(0.5,0,5,0.1: 100,150,100)
B)(0.4,0.4,0.1: 100,150,100)
C)(0.5,0.4,0.2: 100,150,100)
D)(0.4,0.4,0.2: 100,150,100)

Accepted Answer

The answer of Which one of the sets below is...

Quiz 17: Choice Making Under Uncertainty

Suppose you are offered the following two prospects, a: (0, 1, 0: 3000, 2000, 1000) or b: (1/2, 1/4, 1/4: 3000, 2000, 1000) . You are risk averse if:

Pat's utility function is u(y) = y^1/2and his income is $100. He is offered a gamble paying $300 with probability 1/2 and $0 with probability 1/2. What is the certainty equivalent of this gamble?

Suppose you are offered the following 2 prospects, a: (0, 1, 0: 3000, 2000, 1000) or b: (1/2, 1/4, 1/4: 3000, 2000, 1000) . If your preference ordering is such that a is preferred to b, then:

Which of the following phenomena constitutes examples of risk- spreading?

Risk- aversion:

A risk- inclined individual is characterized by a utility function that exhibits:

In choices involving risk, an individual chooses:

State- dependent preferences depend on:

When dealing with individual behaviour in risky situations which of the following assumptions concerns the way in which individuals choose between prospects having the same two outcomes but different probabilities?

An individual is said to be risk- averse if:

In the state space, along the 45 degree line where wealth in the two states is the same, the slope of an indifference curve is

Given a risk- averse individual and a competitive insurance market in which firms are risk- neutral and incur no operating costs, it can be concluded that an individual's reservation price for Full- insurance coverage:

The expected utility hypothesis requires all of the assumptions used to study utility under certainty and all of the following except:

Stephanie's utility function is given by U = W^1/2where W is the value of her house. Her house is currently valued at $105,625. She knows that her house will be destroyed by a tornado with probability .10 this spring. If it is hit, the rubble will be worth $15,625. What is her expected utility?

Risk- averse individuals:

An individual is more likely to reject a risk- pooling arrangement if:

Maya's bracelet is worth $100. There is a 25% chance that it will be stolen from the locker room at the gym. Maya's utility function for money is U(W) = W². Maya is able to buy an insurance policy to cover her bracelet against theft. How much would she be willing to pay for the insurance?

Which one of the sets below is a prospect?