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# lecture_10_tab - ECOS2001 Lecture 10 1 Uncertainty States...

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Unformatted text preview: ECOS2001 Lecture 10 1 Uncertainty States of Nature Possible states of Nature: car accident (a) no car accident (na). Accident occurs with probability a, does not with probability na ; a + 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. ECOS2001 Lecture 10 2 State-Contingent Budget Constraints Each \$1 of accident insurance costs . Consumer has \$m of wealth. Cna is consumption value in the no-accident state. Ca is consumption value in the accident state Without insurance, Ca = m L Cna = m. ECOS2001 Lecture 10 3 With insurance: Buy \$K of accident insurance. Cna = m - K. Ca = m - L - K + K = m - L + (1- )K So K = (Ca - m + L)/(1- ) And Cna = m - (Ca - m + L)/(1- ) Hence na a m L C C 1 1 - =--- ECOS2001 Lecture 10 4 State-Contingent Budget Constraints C na C a m The endowment bundle. Where is the most preferred state-contingent consumption plan? na a m L C C 1 1 - =--- slope 1 = -- m L - m L- ECOS2001 Lecture 10 5 Preferences Under Uncertainty Think of a lottery. Win \$90 with probability 1/2 and win \$0 with probability 1/2. U(\$90) = 12, U(\$0) = 2. Expected utility is 1 1 EU U(\$90) U(\$0) 2 2 1 1 12 2 7. 2 2 = + = + = ECOS2001 Lecture 10 6 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 1 1 EM \$90 \$0 \$45. 2 2 = + = ECOS2001 Lecture 10 7 Preferences under uncertainty EU = 7 and EM = \$45. U(\$45) > 7 \$45 for sure is preferred to the lottery risk-aversion . U(\$45) < 7 the lottery is preferred to \$45 for sure risk-loving . U(\$45) = 7 the lottery is preferred equally to \$45 for sure risk-neutralit y . ECOS2001 Lecture 10 8 Preferences Under Uncertainty Wealth \$0 \$90 2 12 \$45 EU=7 U(\$45) > EU risk-aversion ECOS2001 Lecture 10 9 Preferences Under Uncertainty Wealth \$0 \$90 12 U(\$45) < EU risk-loving. 2 EU=7 \$45 U(\$45) ECOS2001 Lecture 10 10 Preferences Under Uncertainty Wealth \$0 \$90 12 U(\$45) = EU risk-neutrality. 2 U(\$45)= EU=7 \$45 ECOS2001 Lecture 10 11 Preferences under uncertainty State-contingent consumption plans that give equal expected utility are equally preferred. What is the MRS of an indifference curve?...
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## This note was uploaded on 04/20/2010 for the course ECOS 2001 taught by Professor None during the One '09 term at University of Sydney.

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lecture_10_tab - ECOS2001 Lecture 10 1 Uncertainty States...

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