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
  • Risk premium, Natasha

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