Deck 11: Choices Involving Risk

Question 1

Suppose Lily's indifference curves are defined as U = √F_S + √F_H, where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Lily receives 64 units of food when it is sunny and 16 units of food when there is a hurricane.What is the risk premium if the probability of sunshine is Π = 0.5?

A) 4
B) 6
C) 12
D) 16

Answer 1

4

Question 2

Suppose Alice is deciding whether or not to go to a New York Giants game.Alice's enjoyment and thus decision,depends upon two uncertain events that are out of her control: whether the Giants win and whether it snows.She will be happiest if the Giants win and it does not snow.The newspaper reports a 35% chance for snow and the Giants record suggests a 40% chance of winning.The probability that the Giants win and that it does not snow is:

A) 75%.
B) 5%.
C) 26%.
D) 35%.

Answer 2

26%.

Question 3

Refer to Figures d and e.Water is crucial for survival,but it is particularly valuable during a drought when water is scarce.The probability of a drought is (1 - P),W_D represents the quantity of water in a drought,while W_R represents the quantity of water in a rainy season.Which set of indifference curves above best represent a relatively high probability of a drought?

A) Figure d
B) Figure e
C) Probabilities do not influence indifference curves.
D) Both Figures represent a relatively low probability of a drought.

Answer 3

Figure e

Question 4

Suppose Brandon's indifference curves are defined as U = (3/4)√F_S + (1/4)√F_H,where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Further suppose Brandon receives 64 units of food when it is sunny and 16 units when there is a hurricane.If the probability of sunshine is Π = 0.75,expected food consumption is:

A) 28.
B) 40.
C) 52.
D) 80.

Question 5

Refer to Figure a.If Π (the probability of state S)decreases,the x-intercept for the solid constant expected consumption line:

A) increases.
B) decreases.
C) does not change.
D) The answer cannot be determined without more information.

Question 6

Suppose Lily's indifference curves are defined as U = √F_S + √F_H,where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Lily receives 64 units of food when it is sunny and 16 units of food when there is a hurricane.What is the certainty equivalent of the expected food consumption bundle if the probability of sunshine is Π = 0.5?

A) 6
B) 12
C) 25
D) 36

Question 7

Refer to Figure a.Assuming the solid line in the graph is a constant expected consumption line where Π (the probability of state S)= 0.50,which constant expected consumption line reflects an increase in Π?

A) The dotted line
B) The dashed line
C) An increase in Π does not result in a change in the expected consumption line.
D) A change in Π results in a parallel shift in the expected consumption line, so neither the dotted nor the dashed line reflects this change.

Question 8

Suppose Brandon's indifference curves are defined as U = (3/4)√F_S + (1/4)√F_H,where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Further suppose Brandon receives 64 units of food when it is sunny and 16 units when there is a hurricane.What is the certainty equivalent of the expected food consumption bundle if the probability of sunshine is Π = 0.75?

A) 49 units of food
B) 52 units of food
C) 7 units of food
D) 25 units of food

Question 9

Suppose Brandon's indifference curves are defined as U = (3/4)√F_S + (1/4)√F_H,where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Further suppose Brandon receives 64 units of food when it is sunny and 16 units when there is a hurricane.What is the risk premium if the probability of sunshine is Π = 0.75?

A) 52 units of food
B) 24 units of food
C) 49 units of food
D) 3 units of food

Question 10

Risk:

A) is inherent in every action or decision.
B) exists whenever the consequences of a decision are uncertain.
C) exists when outcomes are certain.
D) is a good that can be purchased.

Question 11

What is the standard deviation of the payoff from an investment that yields $1,000,000 with a probability of 0.001 and $0 with a probability of 0.999?

A) $998,001,000
B) $999,000
C) $316.07
D) $31,606.96

Question 12

A person is risk averse if:

A) his indifference curve is tangent to the constant expected consumption line at a point on the guaranteed consumption line.
B) he views variability as a bad thing.
C) for a given level of expected consumption, he prefers the riskless bundle to a risky one.
D) All of these answer choices are correct.

Question 13

What is the expected payoff of an investment that yields $5,000 with a probability of 0.15 and $500 with a probability of 0.85?

A) $325
B) $5,500
C) $1,175
D) $2,750

Question 14

Suppose Alice is deciding whether or not to go to a New York Giants game.Alice's enjoyment and thus decision,depends upon two uncertain events that are out of her control: whether the Giants win and whether it snows.She will be happiest if the Giants win and it does not snow.The newspaper reports a 35% chance for snow and the Giants record suggests a 40% chance of winning.The probability that the Giants lose and it snows is:

A) 21%.
B) 26%.
C) 95%.
D) 25%.

Question 15

What is the standard deviation of the payoff from an investment that yields $5,000 with a probability of 0.15 and $500 with a probability of 0.85?

A) $0
B) $2,581,875
C) $42.50
D) $1,606.82

Question 16

Refer to Figures b and c.In the figures above,the probability of sunny weather,state S,is higher in:

A)Figure b.
B)Figure c.
C)bundle C versus A in both figures.
D)bundle A versus C in both figures.

Question 17

What is the expected payoff of an investment that yields $1,000,000 with a probability of 0.001 and $0 with a probability of 0.999?

A) $1,000,000
B) $1,000
C) $10,000
D) $500,000

Question 18

Refer to Figures d and e.Bundle A is preferred to bundle B in Figure e and not in Figure d because:

A) the MRS between water in a rainy season and during a drought is higher in e than in d.
B) as the probability of a drought increases, consumers are no longer indifferent between the two bundles.
C) as the probability of a drought decreases, water in a rainy season becomes less valuable.
D) consumers are indifferent between bundles A and B as the probability of a drought increases.

Question 19

Refer to Figure b.Suppose consumers choose to consume water in two different states,sunny weather,W_S and during a hurricane,W_H.As the consumer moves from point A to B along the indifference curve,the variability of consumption:

A) decreases.
B) increases.
C) remains constant.
D) increases for one good, but decreases for the other.

Question 20

Suppose Lily's indifference curves are defined as U = √F_S + √F_H,where F_S is consumption during sunny weather and F_H is consumption during a hurricane.Lily receives 64 units of food when it is sunny and 16 units of food when there is a hurricane.If the probability of sunshine is Π = 0.5,the expected consumption is:

A) 52
B) 28
C) 40
D) 5

Question 21

Refer to Figure g.Lily's benefit function (dashed)is more concave than Millie's (dotted)in Figure g.Millie:

A) is more risk averse than Lily.
B) is less risk averse than Lily.
C) has a larger risk premium than Lily.
D) has a lower certainty equivalent than Lily.

Question 22

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 400 and W_R = 100 and the probability of drought is 0.75.Brandon's risk premium is:

A) 250 units of water.
B) 325 units of water.
C) 17.5 units of water.
D) 18.75 units of water.

Question 23

An insurance benefit is:

A) the contract that reduces the financial loss associated with some risky event.
B) the amount of money a policy holder pays for the insurance policy.
C) the amount of money a policy holder receives if a specific loss occurs.
D) the probability of loss from a specific event.

Question 24

A person is risk loving if:

A) for a given level of expected consumption, he prefers a risky bundle to a risk less one.
B) his indifference curve is convex to the origin.
C) his indifference curve is concave to the origin.
D) his indifference curve is concave to the origin and for a given level of expected consumption, he prefers a risky bundle to a risk less one.

Question 25

Suppose we can represent Brandon's preferences for water with an expected utility function U(W_R,W_D)= (1/4)√W_R + (3/4)√W_D, where W_D represents a quantity of water during a drought and W_R represents a quantity of water in a rainy season.Brandon is:

A) risk averse.
B) risk neutral.
C) risk loving.
D) There is not enough information to answer this question.

Question 26

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 36 and W_R = 25 and the probability of drought is 0.75.Brandon's certainty equivalent is:

A) 45.75 units of water.
B) 33.06 units of water.
C) 30.5 units of water.
D) 61 units of water.

Question 27

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 36 and W_R = 25 and the probability of drought is 0.75.Brandon's risk premium is:

A) 66.31 units of water.
B) 0.19 units of water.
C) 33.16 units of water.
D) 3.20 units of water.

Question 28

Refer to Figure f.A benefit function is plotted in Figure f.The distance C represents the:

A) risk premium of the consumption bundle.
B) expected utility of the consumption bundle.
C) certainty equivalent of the consumption bundle.
D) expected consumption.

Question 29

Refer to Figure f.A benefit function is plotted in Figure f.The letter D represents the:

A) risk premium of the consumption bundle.
B) expected utility of the consumption bundle.
C) certainty equivalent of the consumption bundle.
D) expected consumption.

Question 30

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 400 and W_R = 100 and the probability of drought is 0.75.What is Brandon's expected utility?

A) 10
B) 17.5
C) 20
D) 30

Question 31

Refer to Figure f.A benefit function is plotted in Figure f.The letter B represents the:

A) risk premium of the consumption bundle.
B) expected utility of the consumption bundle.
C) certainty equivalent of the consumption bundle.
D) expected consumption.

Question 32

Refer to Figure f.A benefit function,W(F),is plotted in Figure f.The letter A represents:

A) the risk premium of the consumption bundle.
B) the expected utility of the consumption bundle.
C) the certainty equivalent of the consumption bundle.
D) the expected consumption.

Question 33

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 400 and W_R = 100 and the probability of drought is 0.75.Expected water consumption is:

A) 500.
B) 250.
C) 325.
D) 175.

Question 34

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 36 and W_R = 25 and the probability of drought is 0.75.Expected water consumption is:

A) 33.25 units of water.
B) 61 units of water.
C) 30.5 units of water.
D) 27 units of water.

Question 35

Suppose Brandon's benefit function for water is S(W)= W².Brandon is:

A) risk averse.
B) risk neutral.
C) risk loving.
D) There is not enough information to answer this question.

Question 36

A person is risk neutral if:

A) her indifference curve is concave to the origin.
B) her indifference curve is convex to the origin.
C) her indifference curve coincides with the expected consumption line.
D) her indifference curve coincides with guaranteed consumption line.

Question 37

An insurance policy is:

A) the contract that reduces the financial loss associated with some risky event.
B) the amount of money a policy holder pays for the insurance policy.
C) the amount of money a policy holder receives if a specific loss occurs.
D) the probability of loss from a specific event.

Question 38

Refer to Figure g.Lily's benefit function (dashed)is more concave than Millie's benefit function (dotted).Lily:

A) is more risk averse than Millie.
B) is less risk averse than Millie.
C) has a smaller risk premium than Millie.
D) has a larger certainty equivalent than Millie.

Question 39

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 36 and W_R = 25 and the probability of drought is 0.75.What is Brandon's expected utility?

A) 5.75
B) 33.25
C) 11
D) 30.5

Question 40

Assume Brandon's benefit function for water is S(W)= √W and he consumes water both in droughts,W_D,or in the rainy season,W_R.Assume his current consumption bundle is W_D = 400 and W_R = 100 and the probability of drought is 0.75.Brandon's certainty equivalent is:

A) 250 units of water.
B) 306.25 units of water.
C) 18.75 units of water.
D) 17.5 units of water.

Question 41

Two variables are negatively correlated if:

A) they move in the same direction.
B) they move in the opposite direction.
C) their movements tend to be unrelated.
D) one is simply a multiple of the other.

Question 42

If an insurance policy is actuarially fair,then:

A) M = Π(1 - B)
B) Π = B(1 - M)
C) B = M(1 - Π)
D) M = B(1 - Π)

Question 43

If two investments are perfectly positively correlated:

A) there is no benefit from diversification.
B) bets are perfectly hedged and risks are canceled out.
C) diversification reduces risk without changing the expected payoff.
D) diversification reduces both risk and the expected payoff.

Question 44

$500 and there are two companies he could invest X dollars in: Dog Gone Salon,which has a payoff of 2X with 50% probability and $0 with 50% probability and Pretty Kitty Grooming,which has a payoff of 4X with 25% probability and $0 with 75% probability.Dean's expected payoff from investing $250 in both Dog Gone Salon and Pretty Kitty Grooming is:

A) $62.50.
B) $500.
C) $750.
D) $250.

Question 45

An insurance premium is:

A) the contract that reduces the financial loss associated with some risky event.
B) the amount of money a policy holder pays for the insurance policy.
C) the amount of money a policy holder receives if a specific loss occurs.
D) the probability of loss from a specific event.

Question 46

Two variables are uncorrelated if:

A) they move in the same direction.
B) they move in the opposite direction.
C) their movements tend to be unrelated.
D) one is simply a multiple of the other.

Question 47

Explain why a risk averse individual will purchase full insure if a policy is actuarially fair,but only partially insure or not insure at all,if it is not.Use graphs to support your answer.

Question 48

If two investments are perfectly negatively correlated:

A) diversification is not effective at reducing risk.
B) bets are perfectly hedged and risks are canceled out.
C) diversification reduces risk without changing the expected payoff.
D) diversification reduces both risk and the expected payoff.

Question 49

Suppose Dean has $500 and there are two companies he could invest X dollars in: Dog Gone Salon,which has a payoff of 2X with 50% probability and $0 with 50% probability and Pretty Kitty Grooming,which has a payoff of 4X with 25% probability and $0 with 75% probability.Dean's expected payoff from investing in Pretty Kitty Grooming only is:

A) $500.
B) $2,000.
C) $1,000.
D) $1,500.

Question 50

Two variables are positively correlated if:

A) they move in the same direction.
B) they move in the opposite direction.
C) their movements tend to be unrelated.
D) one is simply a multiple of the other.

Question 51

Explain the relationship between the correlation of payoffs and the risk reducing effects of diversification and hedging.

Question 52

What would be the actuarially fair premium for an insurance policy that pays $1,000 in the event of a loss that has a 25% chance of occurring?

A) $250
B) $750
C) $1,250
D) $500

Question 53

Suppose a consumer's expected utility function given two possible states of nature A and B can be expressed in terms of consumption of food,F,in both states as U(F_A,F_B)= [0.6 × ln(F_A)] + [0.4 × ln(F_B)].For this utility function,MU_A is (0.6/F_A)and MU_B is (0.4/F_B).Without insurance,the consumer can consume 200 in state A but only 50 in state B. The consumer can purchase insurance at a premium of 50 cents per dollar of benefit. What is the value of the insurance she purchases?

A) $4.74
B) $4.85
C) $12.67
D) $114.87

Question 54

Suppose Dean has $500 and there are two companies he could invest X dollars in: Dog Gone Salon,which has a payoff of 2X with 50% probability and $0 with 50% probability and Pretty Kitty Grooming,which has a payoff of 4X with 25% probability and $0 with 75% probability.Dean's expected payoff from investing in Dog Gone Salon only is:

A) $1,000.
B) $500.
C) $0.
D) $1,500.

Question 55

Suppose Dean has $500 and there are two companies he could invest X dollars in: Dog Gone Salon,which has a payoff of 2X with 50% probability and $0 with 50% probability and Pretty Kitty Grooming,which has a payoff of 4X with 25% probability and $0 with 75% probability.Which of the following is true?

A) It doesn't matter how distributes his $500 between the two investments, the expected payoff and the standard deviation will always be the same.
B) Even though the expected payoff is the same for both investments, investing in Dog Gone Salon involves less risk.
C) Even though the expected payoff is the same for both investments, investing in Pretty Kitty Grooming involves less risk.
D) Investing in Pretty Kitty Grooming offers a higher expected payoff.

Question 56

Suppose a consumer's expected utility function given two possible states of nature A and B can be expressed in terms of dollars worth of food consumption,F,in both states as U(F_A,F_B)= [0.6 × ln(F_A)] + [0.4 × ln(F_B)].For this utility function,MU_A is (0.6/F_A)and MU_B is (0.4/F_B).Without insurance,the consumer can consume 200 in state A but only 50 in state B. The consumer can purchase insurance at a premium of 50 cents per dollar of benefit. How much insurance will she purchase?

A) $50
B) $150
C) $250
D) $416.67

Question 57

If two investments are uncorrelated:

A) there is no benefit from diversification.
B) there is no benefit to hedging.
C) diversification reduces risk without changing the expected payoff.
D) diversification reduces both risk and the expected payoff.

Question 58

Suppose a consumer's expected utility function given two possible states of nature A and B can be expressed in terms of consumption of food,F,in both states as U(F_A,F_B)= [0.6 × ln(F_A)] + [0.4 × ln(F_B)].For this utility function,MU_A is (0.6/F_A)and MU_B is (0.4/F_B).Without insurance,the consumer can consume 200 in state A but only 50 in state B. The consumer can purchase insurance at a premium of 50 cents per dollar of benefit. Which of the following gives her budget line?

A) F_A = 250 - F_B
B) F_B = 250 - F_A
C) F_A = 200 - F_B
D) F_B = 50 - F_A