# 6F9B3196 - Chapter Twelve Uncertainty Uncertainty is...

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Chapter Twelve Uncertainty

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Uncertainty is Pervasive What is uncertain in economic systems? tomorrow’s prices future wealth future availability of commodities present and future actions of other people.
Uncertainty is Pervasive What are rational responses to uncertainty? buying insurance (health, life, auto) a portfolio of contingent consumption goods.

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States of Nature 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. Accident causes a loss of \$L.
Contingencies A contract implemented only when a particular state of Nature occurs is state- contingent. E.g. the insurer pays only if there is an accident.

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Contingencies A state-contingent consumption plan is implemented only when a particular state of Nature occurs. E.g. take a vacation only if there is no accident.
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. • C na = m - γ K. • C a = m - L - γ K + K = m - L + (1- γ )K.

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State-Contingent Budget Constraints Buy \$K of accident insurance. • 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
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 -

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Preferences Under Uncertainty Think of a lottery. Win \$90 with probability 1/2 and win \$0 with probability 1/2. U(\$90), U(\$0). Expected utility is EU=1/2*U(\$90)+1/2*U(0)
Preferences Under Uncertainty Think of a lottery. Win \$90 with probability 1/2 and win \$0 with probability 1/2. Expected money value of the lottery is EM \$90 \$0 = × + × = 1 2 1 2 45 \$ .

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Preferences Under Uncertainty EU and EM = \$45. U(\$45) > EU \$45 for sure is preferred to the lottery risk-aversion. U(\$45) < EU the lottery is preferred to \$45 for sure risk-loving. U(\$45) = EU the lottery is preferred equally to \$45 for sure risk-neutrality.
Preferences Under Uncertainty Wealth \$0 \$90 12 U(\$45) U(\$45) > EU risk-aversion. 2 EU \$45 MU declines as wealth rises.

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Preferences Under Uncertainty Wealth \$0 \$90 12 U(\$45) < EU risk-loving.
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