Deck 17: Choice Making Under Uncertainty

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.

Answer 1

a is preferred to b.

Question 2

Pat's utility function is u(y)= y^1/2 and 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

Answer 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.

Answer 3

you are a risk- averse individual.

Question 4

Stephanie's utility function is given by U = W^1/2 where 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

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

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.

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.

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.

Question 9

State- dependent preferences depend on:

A)state income tax laws.
B)subjective probabilities.
C)observed probabilities.
D)perfect information.

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

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.

Question 12

An individual is said to be risk- averse if:

A)w₁ is 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.

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).

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.

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.

Question 16

Stephanie's utility function is given by U = W^1/2 where 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

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.

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.

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

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)

Question 21

The continuity assumption holds that consumers substitute:

A)the present value for a stated risky prospect accurately.
B)their preferences under certainty for those under risk accurately.
C)the expected value for a stated risky prospect accurately.
D)compound probabilities for simple probabilities accurately.

Question 22

The continuity assumption states that:

A)given any prospect, there is a riskless outcome that can be replaced by another without changing the expected utility from the prospect.
B)if two prospects involve the same outcomes, a probability, e^*, exists that makes an individual indifferent between the prospects.
C)there is a probability that allows a risky prospect to be substituted for a riskless prospect in an individual's preference ordering.
D)given any prospect, an equivalent prospect can be created by substituting a prospect that is equivalent to a particular outcome.

Question 23

When individuals are risk- averse:

A)they stay away from slot machines.
B)they avoid entering economic exchanges.
C)they never deal with risk- lovers.
D)they find ways to eliminate risk.

Question 24

A certainty equivalent income:

A)means that there is some amount of income that one will accept with certainty rather than face a gamble.
B)is an application of the continuity of preferences assumption.
C)is calculated using the marginal utility of wealth.
D)means that at high enough income levels there is always an amount of risk that makes one reject a gamble.

Question 25

Which of the following represents the utility function of someone that is risk neutral?

A)U(w)= w + 17
B)U(w)= w² + w + 17
C)U(w)= w^1/2 + w - 17
D)U(w)= w^1/8 - 17

Question 26

Most economic decisions are made under conditions of:

A)probability.
B)risk.
C)certainty.
D)uncertainty.

Question 27

Melanie must choose between two jobs. With job A, there is a 10% chance of earning $60,000 per year and a 90% chance of earning $50,000. With job B, there is a 50% chance of earning $46,000 and a 50% chance of earning $56,000. If Melanie is risk lover (U(W)= W²), which job will she choose?

A)her preferences violate the axioms of expected- utility theory.
B)job B
C)she is indifferent between the two jobs
D)job A

Question 28

If Monica says she is indifferent between the prospect (2 candy bars, shot in the head; .999, .001)and the prospect (1 candy bar; 1 orange juice)then:

A)her behaviour is violating the axioms of expected utility theory.
B)her behaviour is consistent with the continuity assumption.
C)her behaviour is consistent with the substitution assumption.
D)one would question her sanity.

Question 29

If one's indifference curves in a state space graph are concave to the origin, the individual is:

A)risk lover.
B)undecided about their attitude to risk.
C)not making rational decisions.
D)risk averse.

Question 30

A card game:

A)is characterized by asymmetric information.
B)isn't much joy for risk- averse individuals.
C)cannot be analyzed using game theory.
D)has no risk if bets are not made.

Question 31

A person that is a risk lover will have indifference curves in a state space graph that are

A)linear
B)concave to the origin
C)convex to the origin
D)L - shaped

Question 32

Risk pooling is most likely to be found among people who:

A)avoid risk.
B)are indifferent to risk.
C)prefer risk.
D)live in primitive cultures.

Question 33

The market for insurance:

A)is a risk- pooling arrangement.
B)needs risk- lovers to buy policies in order to be viable.
C)exists only of insurance firms are risk- lovers.
D)does not need the law of large numbers to operate.

Question 34

The expected utility hypothesis requires information about all of the following except:

A)prospects.
B)probabilities.
C)preferences.
D)outcomes.

Question 35

Subjective probabilities

A)are used both in the case of the case of risky situations and incomplete information.
B)are not central to the use of the expected- utility approach.
C)are used in the case of incomplete information but not in the case of risky situations.
D)are used in the case of risky situation but not in the case of incomplete information.

Question 36

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. The expected value of Maya's bracelet is:

A)75.
B)175.
C)150.
D)100.

Question 37

A risk- inclined individual will:

A)never like a bet.
B)place a smaller utility on gaining $100 than on losing $100.
C)always buy a lottery ticket, whatever his or her chances of winning.
D)place a greater utility on gaining $100 than on losing $100.

Question 38

The maximum that a risk- averse individual is willing to pay for full- insurance coverage is:

A)the certainty equivalent.
B)the value of the expected loss from a risky project.
C)the difference between the expected and the certainty equivalent wealth.
D)the difference between the initial and the certainty equivalent wealth.

Question 39

Consider the following gamble: on the toss of a fair coin, you receive $10 million if a head appears and nothing if a tail appears. What is the expected payoff from the gamble?

A)$3 million
B)$5 million
C)$2 million
D)$1.5 million

Question 40

Consider the following gamble: on the toss of a fair coin, you receive $10 million if a head appears and nothing if a tail appears. What is Diane Eaton's reservation price for the gamble?

A)$5 million
B)$6 million
C)$100,000
D)cannot be determined from the information provided

Question 41

If an individual prefers a risky prospect to a sure prospect then:

A)the two prospects must have the same expected value.
B)the risky prospect has a higher expected utility.
C)the individual is irrational.
D)the individual is risk lover.

Question 42

Suppose you are given the following preference information: a: (0, 1, 0: 3000, 2000, 1000)is indifferent to b: (3/4, 0, 1/4: 3000, 2000, 1000). Given the prospects c: (1/3, 1/3, 1/3: 3000, 2000, 1000)and c: (1/2, 1/4, 1/4: 3000, 2000, 1000), which of the following statements is true?

A)d is preferred to c
B)c is indifferent to d
C)c is preferred to d
D)A preference ranking cannot be found with the given information.

Question 43

If one's indifference curves in a state space graph are convex to the origin, the individual is:

A)risk averse.
B)risk inclined.
C)undecided about their attitude to risk.
D)risk neutral.

Question 44

The law of large numbers states that insurance companies:

A)are risk neutral.
B)risk preferences are irrelevant.
C)are risk averse.
D)are risk seekers.

Question 45

Which of the following represents the utility function of a risk lover?

A)U(w)= w^1/8 - 17
B)U(w)= w² + w + 17
C)U(w)= w^1/2 + w - 17
D)U(w)= w + 17

Question 46

The reservation demand price for insurance is:

A)the exact amount a person is willing to pay for insurance.
B)equal to the expected value of the gamble.
C)the minimum amount a person is willing to pay for insurance.
D)the maximum amount a person is willing to pay for insurance.

Question 47

The validity of the expected utility hypothesis requires that:

A)individuals carry out compound probability calculations.
B)individuals are risk- averse.
C)the continuity assumption is met.
D)preference orderings over riskless prospects are independent of the state that occurs.

Question 48

A compound prospect:

A)is the predicted interest rate for present value calculations.
B)is the view from a millionaire's vacation compound.
C)has a risky prospect as one of its outcomes.
D)pays off over several periods at compound interest.

Question 49

Expected values are found by:

A)public opinion surveys.
B)introspection about the future.
C)discovering the opportunity cost of risk.
D)calculating weighted averages.

Question 50

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's expected utility is:

A)12,500.
B)7,500.
C)10,000.
D)15,000.

Question 51

Which of the following assumptions concerning individual behaviour in risky situations guarantees that individuals will be willing to make trade offs between risky and riskless prospects?

A)the continuity assumption
B)the substitution assumption
C)the ordering assumption
D)the transitivity assumption

Question 52

A compound prospect can be defined as one which:

A)consists of risky outcomes discounted by a factor reflecting risk.
B)has as one of its outcomes a riskless prospect.
C)has as one of its outcomes another risky prospect.
D)as one characterized by complexity.

Question 53

A person that is risk a verse will have indifference curves in a state space graph that are

A)linear
B)convex to the origin
C)concave to the origin
D)L - shaped

Question 54

Given risk- inclined individuals and risk- neutral insurance firms, it is true that the individual's reservation price for full insurance coverage:

A)is less than that of an insurance company.
B)is greater than that of an insurance company.
C)establishes a viable market for insurance.
D)is equal to that of an insurance company.

Question 55

The continuity assumption holds that consumers facing risky decisions:

A)can choose only if the values of outcomes are continuous.
B)can be indifferent between a risky and a certain prospect.
C)require only the assumptions required under certainty.
D)prefer them to certain prospects.

Question 56

Melanie must choose between two jobs. With job A, there is a 10% chance of earning $60,000 per year and a 90% chance of earning $50,000. With job B, there is a 50% chance of earning $46,000 and a 50% chance of earning $56,000. If Melanie is risk averse (U(W)= W^1/2), which job will she choose?

A)job B
B)her preferences violate the axioms of expected- utility theory.
C)job A
D)she is indifferent between the two jobs

Question 57

If an individual is risk averse, then:

A)any allocation of risk is optimal.
B)that person will always consume in a corner.
C)that person will want to buy insurance at any price.
D)that person may at times accept a bet.

Question 58

Suppose you are given the following preference information: a: (0, 1, 0: 3000, 2000, 1000)is indifferent to b: (3/4, 0, 1/4: 3000, 2000, 1000). If U(3000)= 1, U(1000)= 0, and U(2000)=5/8. What is the correct preference ranking?

A)a is indifferent to b
B)a is preferred to b
C)b is preferred to a
D)a preference ranking cannot be found with the given information

Question 59

A risk- averse individual will:

A)always enter a risky venture over a particularly risky prospect.
B)enter a risky venture as long as expected utility increases.
C)prefer all certain prospects over a particularly risky prospect.
D)never play a slot machine.

Question 60

Marvin's utility function is given by U(W)= 10 - 3/(1 + W)and his initial wealth is zero. What is his expected utility from playing a game where he wins $2 on a coin toss if a head appears and nothing if a tail appears?

A)4.5
B)7.0
C)3.5
D)8.0

Question 61

A person that is risk neutral will have indifference curves in a state space graph that are

A)linear
B)concave to the origin
C)L - shaped
D)convex to the origin

Question 62

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. What is one fisherman's expected utility from fishing alone?

A)0.05
B)0.025
C)0.5
D)1.0

Question 63

The effort of carrying an umbrella reduces my utility by 1/2 a unit. If it rains and I have no umbrella, my utility falls by 3 units, whilst it only falls by 1 unit if I do have an umbrella. I consider that the probability it will rain is 1/2.Therefore I carry an umbrella.

Question 64

Risk- pooling:

A)is rarely witnessed among close- knit communities.
B)and risk- sharing are essentially identical mechanisms.
C)is a form of insurance.
D)is not relevant for a fishing party.

Question 65

Suppose you are given the following preference information: a: (0, 1, 0: 3000, 2000, 1000)is indifferent to b: (3/4, 0, 1/4: 3000, 2000, 1000). If U(3000)= 1 and U(1000)= 0, what is U(2000)?

A)depends on the specific person involved
B)0.25
C)0.75
D)0.50

Question 66

Which of the following is probably not an example of spreading risk?

A)a syndicate that owns a fishing boat
B)a farmer and landowner sharing crop output
C)a joint venture company exploring for offshore oil
D)General Motors buying fire insurance from a small insurance company

Question 67

Suppose that initially an individual owns $4 and a lottery ticket. The lottery ticket will be worth $12 with probability 1/2 and worth $0 with probability 1/2. The individual's VM utility function is u(w)= w^1/2 where w is wealth. What is the lowest price at which the individual would be willing to sell the lottery ticket?

Question 68

Suppose a person must accept one of three bets:
A. 0.5 chance of winning $100 and 0.5 chance of losing $100.
B. 0.75 chance of winning $100 and 0.25 chance of losing $300.
C. 0.9 chance of winning $100 and 0.1 chance of losing $900. Show that all of these are fair bets.

Question 69

Consumers whose marginal utility of wealth diminishes are:

A)risk averse.
B)risk neutral.
C)undecided about their attitude to risk.
D)risk seekers.

Question 70

When a consumer makes a risky decision, her:

A)utility function is weakly concave.
B)reservation price is her opportunity cost of risk.
C)consumption bundles are poorly defined.
D)demand functions are unknown.

Question 71

Consumers buy insurance because:

A)it increases their expected utility.
B)it decreases their current cost of living.
C)advertising overestimates the risks they face.
D)sales people will not leave without a deal.

Question 72

A slot machine:

A)is not an unfair bet.
B)is a proof that people are generally risk- loving.
C)is a proof that people are irrational.
D)gives a better average return than a state lottery.

Question 73

If a person is risk averse:

A)the certainty equivalent of a gamble is equal to the expected value of the gamble.
B)the certainty equivalent of a gamble is lower than the expected value of the gamble.
C)the certainty equivalent of a gamble is higher than the expected value of the gamble.
D)cannot be compared to the expected value of the gamble.

Question 74

Will is playing on a game show. He must choose between two offers. The first offer is a payment of $2000, which he can take for simply being on the show, or he can enter a gamble. In the gamble, he chooses one of two curtains that conceal two items. He makes a draw for curtain one or two, from a hat; he receives the gift behind the curtain picked. He knows that behind one curtain is an automobile valued at $4000 and behind other curtain is a set of encyclopedias valued at $500. If his initial wealth is $1000 and his utility function can be described by U(w)= 1 - 1000/w, then what must be the probability of drawing the car for Will to be indifferent between the two choices?

Question 75

Discuss the implications of the degree of realism characterizing the assumptions of the expected- utility theorem on its ability to generate true prediction.

Question 76

Show that if a person's utility of income function is convex (that is, exhibits an increasing marginal utility of income), he or she will prefer fair gambles to income certainty and may even be willing to accept somewhat unfair gambles. Do you believe this sort of risk- taking is common? What might tend to limit its occurrence?

Question 77

Which of the following individuals is likely to purchase insurance?

A)a risk neutral person when the insurance is over priced
B)a risk lover when the insurance is underpriced
C)a risk neutral person when the insurance is fairly priced
D)a risk- averse person when the insurance is fairly priced

Question 78

Lotteries are a form of gambling with an expected payoff of less than one. yet we often see that winners of very large prices bought their tickets as a group. Why does this seem contradictory?

Question 79

Consider the following prospects, in which w₁ > w₂ > w₃; a: (1/3, 1/3, 1/3: w₁, w₂, w₃); b: (1/4, 1/2, 1/4: w₁, w₂, w₃); and c: (0, 1, 0: w₁, w₂, w₃). Shelly reports that a is preferred to b, and that c is preferred to a.

A)Shelly is risk inclined.
B)Shelly is risk averse.
C)Shelly is risk neutral.
D)Her preferences are inconsistent with expected utility theory.

Question 80

Melanie must choose between two jobs. With job A, there is a 10% chance of earning $60,000 per year and a 90% chance of earning $50,000. With job B, there is a 50% chance of earning $46,000 and a 50% chance of earning $56,000. If Melanie is risk neutral (U(W)= W), which job will she choose?

A)she is indifferent between the two jobs
B)job A
C)job B
D)her preferences violate the axioms of expected- utility theory.