Econ 4010 Lecture 9

# Econ 4010 Lecture 9 - 5 Uncertainty Risk...

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<Lecture 9> 5. Uncertainty Risk Premium Maximum amount of money that a risk-averse person will pay to avoid taking a risk Risk Premium (p.162) A. Certain Income (\$16,000) E(U) = 14 EV = \$16,000 Uncertain Income (0.5 * \$10,000 + 0.5 * 30,000) E(U) = 14 EV = \$20,000 Risk Premium = \$20,000 - \$16,000 = \$4,000 B. Certain Income (\$10,000) E(U) = 10 EV = \$10,000 Uncertain Income (0.5 * \$40,000 + 0.5 * \$0) E(U) = 10 EV = \$20,000 Risk Premium = \$20,000 - \$10,000 = \$10,000 The greater the variability of income, the more the person would be willing to pay to avoid the risky situation. Insurance We have seen that risk-averse people are willing to pay to avoid risk. Buying insurance assures a person of having the same income whether or not there is a loss. Because the insurance cost is equal to the expected loss, this certain income is equal to the expected income from the risky situation. For a risk-averse consumer, the guarantee of the same income regardless of the outcome generates more utility than would be the case if that person had a high income when there was no loss and a low income when a loss occurred. 1

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Suppose that a homeowner faces a 10% probability that his house will be burglarized and he will suffer a \$10,000 loss. He has \$50,000 worth of property. Insurance costs \$1,000. Insurance Burglary (Pr = .1) No Burglary (Pr = .9) EV Standard Dev. No \$40,000 \$50,000 \$49,000 3,000 Yes \$49,000 \$49,000 \$49,000 0 Expected wealth is the same in both cases. The variability, however, is quite different.
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• Spring '09
• Cheng

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