Week_6_Lecture_Uncertainty[1]

Week_6_Lecture_Uncertainty[1] - Week 6 Uncertainty Choices...

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Week 6 Uncertainty
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Choices over uncertain objects Choices over actions that will lead to multiple possible outcomes Action 1: go on a road trip; Action 2: stay at home. Possible states of Nature: “car accident” (a) “no car accident” (na). • Accident occurs with probability π a , does not with probability π na ; π a + π na = 1.
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State-Contingent Budget Constraints C na C a 20 17 A state-contingent consumption with $17 consumption value in the accident state and $20 consumption value in the no-accident state.
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State-Contingent Budget Constraints Each $1 of accident insurance costs γ . Consumer has $m of wealth. • C na is consumption value in the no- accident state. C a is consumption value in the accident state.
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State-Contingent Budget Constraints Without insurance, • C a = m - L • C na = m.
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State-Contingent Budget Constraints C na C a m The endowment bundle. m L -
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State-Contingent Budget Constraints Buy $K of accident insurance. Price per dollar of insurance 0 < γ <1. • C na = m - γ K. • C a = m - L - γ K + K = m - L + (1- γ )K. • So K = (C a - m + L)/(1- γ ) • And C na = m - γ (C a - m + L)/(1- γ ) I.e. C m L C na a = - - - - γ 1 1
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State-Contingent Budget Constraints C na C a m The endowment bundle. Where is the most preferred state-contingent consumption plan? C m L C na a = - - - - γ 1 1 slope = - - 1 m L m L - Sell insurance
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Preferences Under Uncertainty Think of each option as a lottery. Example: L1 says that one can win $90 with probability 1/2 and win $0 with probability 1/2. Preference is defined for lotteries. For example, a person may strictly prefer L1 to L2, and be indifferent between L3 and L4. Can we find a utility representation for preferences over lotteries?
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Expected Utility Representation One type of utility representation is most easy to work with. If the preference is rational, cts and satisfies
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Week_6_Lecture_Uncertainty[1] - Week 6 Uncertainty Choices...

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