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Week 3b Lecture_Uncertainty

# Week 3b Lecture_Uncertainty - Week 3 Uncertainty Choices...

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Week 3 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.
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 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.
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 -
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 γ γ 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 γ γ γ 1 1 slope = - - γ γ 1 m L - γ γ m L - Sell insurance
Preferences Under Uncertainty Think of each option as a lottery. Win \$90 with probability 1/2 and win \$0 with probability 1/2. If the preference is rational, cts and satisfies independence axiom then it can be represented by expected utility . E.g. u(\$90) = 12, u(\$0) = 2. Expected utility is . 7 2 2 1 12 2 1 u(\$0) 2 1 u(\$90) 2 1 EU = × + × = × + × =

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Mixing Lotteries If A happens with probability 1/5 and B happens with probability 4/5, what’s the resulting lottery?
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Week 3b Lecture_Uncertainty - Week 3 Uncertainty Choices...

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