Question 1

Suppose that you face a gamble that has a payoff of $1000 with probability 0.2 and a payoff of $200 with probability 0.8.I approach you to sell you insurance with a premium of p and a benefit of

Accepted Answer

The expected value of the gamble is 0.2 * 1000 + 0.8 * 200 = 360. An actuarially fair premium is one that makes the expected value of the insurance policy equal to zero. This means that the expected value of the benefit must be equal to the premium.For option A, the expected value of the benefit is 0.2 * 10 + 0.8 * 10 = 10, which is equal to the premium. Therefore, option A is actuarially fair.For option B, the expected value of the benefit is 0.2 * 500 + 0.8 * 500 = 500, which is equal to the premium. Therefore, option B is actuarially fair.For option C, the expected value of the benefit is 0.2 * 900 + 0.8 * 900 = 900, which is equal to the premium. Therefore, option C is actuarially fair.Therefore, all of the options are actuarially fair.

Question 2

If the probability of the bad outcome is 0.5, the benefit level of actuarily fair insurance will be half the premium.

Accepted Answer

Actuarially fair insurance means the premium is equal to the expected loss, not half of it. If the probability of a bad outcome is 0.5, the premium for actuarially fair insurance would equal the expected loss, which is the probability of the bad outcome times the loss amount, not half the premium.

Question 3

Expected utility functions have to be concave if they are to represent risk averse tastes.

Accepted Answer

False

Question 4

Suppose an individual has state-independent tastes and invests in risky stocks rather than safe bonds.We can infer that he must be risk loving.

Accepted Answer

State-independent tastes mean that the individual's preferences do not change with different states of the world. Choosing risky stocks over safe bonds does not necessarily imply risk-loving behavior; it could be due to higher expected returns or other factors.

Question 5

Suppose that individuals with state-independent and risk-averse tastes insure each other through state-contingent trades.If there is no aggregate risk, the competitive equilibrium price will then result in actuarily fair insurance terms.

Accepted Answer

Actuarily fair insurance terms mean that the premium paid by an individual is equal to the expected value of the payout received in case of loss. When individuals with state-independent and risk-averse tastes insure each other through state-contingent trades, they are essentially engaging in risk sharing. If there is no aggregate risk, meaning that each individual's probability of loss is uncorrelated with the probability of loss of all other insured individuals, then the competitive equilibrium price will result in actuarily fair insurance terms. This is because in the absence of aggregate risk, the total payout by all insured individuals will equal the total premium paid, and each individual's premium will be equal to their expected payout, making it actuarily fair.

Question 6

Gamble A results in $10 with probability 0.4 and $30 with probability 0.6.Gamble B results in $20 with probability 1.If an individual prefers Gamble A to Gamble B, the independence axiom implies that he prefers Gamble C that gives $0 with probability 0.5, $10 with probability 0.2 and $30 with probability 0.3 to Gamble D that results in $20 with probability 0.5 and $0 with probability 0.5.

Accepted Answer

The independence axiom states that the preference between two gambles is independent of the outcomes of other gambles. In this case, the individual prefers Gamble A to Gamble B, which means that they prefer a gamble with a higher expected value. Gamble C has a higher expected value than Gamble D, so the individual should also prefer Gamble C to Gamble D.

Question 7

Which of the following is true about an individual's choice of insurance assuming state-independent tastes?

Accepted Answer

With state-independent tastes, risk-averse individuals will choose full insurance when it is actuarily fair, as in choice A. Risk-neutral individuals will not choose insurance if it is actuarily unfair, as in choice C, because they are indifferent to risk and would not pay more than the expected loss.

Question 8

The certainty equivalent is less than the expected value of a gamble when tastes are risk averse.

Accepted Answer

When a person is risk averse, they dislike uncertainty and are willing to pay a premium to avoid taking risks. The certainty equivalent is the amount of money that, if offered with certainty, a person would be willing to accept instead of taking a gamble with an uncertain outcome. Since risk-averse individuals are willing to pay a premium to avoid uncertainty, the certainty equivalent will always be less than the expected value of a gamble. Therefore, the statement is true for risk-averse individuals.

Question 9

Which of the following is true about a risk-averse individual facing a full menu of actuarily fair insurance contracts to choose from?

Accepted Answer

A risk-averse individual prefers to avoid uncertainty, leading them to fully insure when their tastes do not depend on the state of the world, which is consistent with choice (C). They are also more likely to "over-insure" if they value consumption more in the bad state, as insurance provides a safety net that is more valuable when the bad state is particularly undesirable, aligning with choice (B).

Question 10

The independence axiom implies that if I prefer a bottle of wine over a six pack of beer I will prefer half a bottle of wine with a bag of pretzels over half a sixpack of beer with a bag of pretzels.

Accepted Answer

The answer of The independence axiom implies that if I...

Question 11

Risk averse individuals will fully insure to avoid risk.

Accepted Answer

Risk-averse individuals may not fully insure if the cost of insurance is too high or if they have other means to mitigate risk.

Question 12

When tastes are risk averse, an individual will always choose less risk over more risk.

Accepted Answer

The answer of When tastes are risk averse, an individual...

Question 13

When tastes are risk loving, a person will always choose a gamble that is riskier over one that is less risky.

Accepted Answer

Risk-loving individuals have a preference for risk, but their choice to engage in riskier gambles over less risky ones also depends on the potential rewards. They weigh the expected benefits against the risks, so they might not always choose the riskier option if the less risky one offers comparable or better expected outcomes.

Question 14

The risk premium is negative when tastes are risk averse.

Accepted Answer

The risk premium is the amount of extra return an investor expects to receive for taking on additional risk. When tastes are risk averse, investors require a positive risk premium as compensation for taking on risk. Therefore, the risk premium cannot be negative when tastes are risk averse.

Question 15

Suppose that individuals with state-independent and risk-averse tastes insure each other through state-contingent trades.The competitive equilibrium price will then result in actuarily fair insurance terms.

Accepted Answer

In a market with risk-averse individuals, the competitive equilibrium price for insurance typically includes a risk premium above the actuarially fair price. This is because insurers need to charge more than the expected loss to cover administrative costs and to compensate for the risk they assume.

Question 16

Actuarily fair insurance reduces risk without changing the expected value of a gamble.

Accepted Answer

Actuarially fair insurance charges a premium that is equal to the expected value of the loss, hence reducing risk without altering the expected value of the gamble.

Question 17

The certainty equivalent of a gamble is negative when tastes are risk loving.

Accepted Answer

The certainty equivalent represents the amount of money that an individual is indifferent between receiving with certainty or taking a gamble with uncertain outcomes. When tastes are risk-loving, the individual prefers the gamble to the certain outcome, so the certainty equivalent would be positive, not negative.

Question 18

Suppose an investor with state-independent tastes is offered the choice between investment A and investment B.Investment A offers profit of $2,000 with probability 0.4, $4,000 with probability 0.2 and $6,000 with probability 0.4.Investment B offers profit of $2,000 with probability of 0.5 and $6,000 with probability 0.5.If the investor is risk averse, he will choose investment A.

Accepted Answer

A risk averse investor will choose the investment with the lower risk, which in this case is investment A. Although investment B offers a higher expected profit, it also has a higher variability or risk. Investment A offers lower expected profit but has less variability, making it the more suitable choice for a risk averse investor.

Question 19

Expected utility theory assumes that individuals have utility functions over a composite consumption good.

Accepted Answer

Expected utility theory assumes that individuals have utility functions over outcomes or prospects, not specifically over a composite consumption good. It focuses on how individuals make decisions based on the expected utility of different outcomes, considering probabilities and preferences.

Question 20

Two related ways to quantify a person's degree of risk aversion are the certainty equivalent and the risk aversion premium.

Accepted Answer

This statement is true. The certainty equivalent is the amount of guaranteed money that a risk-averse person would accept in place of taking a gamble, while the risk aversion premium is the amount of extra money that a person requires in order to take on a risky investment rather than a guaranteed one. Both concepts are commonly used to measure a person's degree of risk aversion.

Quiz 17: Choice and Markets in the Presence of Risk