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CHAPTER 5 CHOICE UNDER UNCERTAINTY REVIEW QUESTIONS 1. What does it mean to say that a person is risk averse? Why are some people likely to be risk averse, while others are risk lovers? A risk-averse person has a diminishing marginal utility of income and prefers a certain income to a gamble with the same expected income. A risk lover has an increasing marginal utility of income and prefers an uncertain income to a certain income. The economic explanation of whether an individual is risk averse or risk loving depends on the shape of the individual’s utility function for wealth. Also, a person’s risk aversion (or risk loving) depends on the nature of the risk involved and on the person’s income. 2. Why is the variance a better measure of variability than the range? Range is the difference between the highest possible outcome and the lowest possible outcome. Range does not indicate the probabilities of observing these high or low outcomes. Variance weighs the difference of each outcome from the mean outcome by its probability and, thus, is a more useful measure of variability than the range. 3. What does it mean for consumers to maximize expected utility? Can you think of a case where a person might not maximize expected utility? The expected utility is the sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur. To maximize expected utility means that the individual chooses the option that yields the highest average utility, where average utility is a probability-weighted sum of all utilities. This theory requires that the consumer knows the probability of every outcome. At times, consumers either do not know the relevant probabilities or have difficulty in evaluating low-probability, high-payoff events. In some cases, consumers cannot assign a utility level to these high-payoff events, such as when the payoff is the loss of the consumer’s life. 4. Why do people want to fully insure against uncertain situations when insurance is actuarially fair? If the cost of insurance is equal to the expected loss, (i.e., if the insurance is actuarially fair), risk-averse individuals will fully insure against monetary loss. The insurance premium assures the individual of having the same income regardless of whether or not a loss occurs. Because the insurance is actuarially fair, this certain income is equal to the expected income if the individual takes the risky option of not purchasing insurance. This guarantee of the same income, whatever the outcome, generates more utility for a risk-averse person than the average utility of a high income when there was no loss and the utility of a low income with a loss (i.e., because of risk aversion, E [ U ( x )] £ U ( E [ x ]). 5. Why is an insurance company likely to behave
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