lecture_10 - Uncertainty States of Nature Possible states...

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ECOS2001 Lecture 10 1 Uncertainty 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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ECOS2001 Lecture 10 2 State-Contingent Budget Constraints Each $1 of accident insurance costs γ . 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.
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ECOS2001 Lecture 10 3 With insurance: Buy $K of accident insurance. Cna = m - γ K. Ca = m - L - γ K + K = m - L + (1- γ )K So K = (Ca - m + L)/(1- γ ) And Cna = m - γ (Ca - m + L)/(1- γ ) Hence na a mL CC 11 γγ =− −−
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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 mL CC 11 γγ =− −− slope 1 γ
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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 11 EU U($90) U($0) 22 12 2 7. =
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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 11 EM $90 $0 $45. 22 =
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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 .
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ECOS2001 Lecture 10 8 Preferences Under Uncertainty Wealth $0 $90 2 12 $45 EU=7 U($45) > EU risk-aversion
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ECOS2001 Lecture 10 9 Preferences Under Uncertainty Wealth $0 $90 12 U($45) < EU risk-loving. 2 EU=7 $45 U($45)
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ECOS2001 Lecture 10 10 Preferences Under Uncertainty Wealth $0 $90 12 U($45) = EU risk-neutrality. 2 U($45)= EU=7 $45
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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? 21 1 12 2 dc MU(c ) . dc MU(c ) π =−
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ECOS2001 Lecture 10 12 State-Contingent Budget Constraints C na C a m Most preferred affordable plan MRS = slope of budget constraint; i.e.
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This note was uploaded on 02/16/2010 for the course ECOS Economics taught by Professor None during the One '09 term at University of Sydney.

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lecture_10 - Uncertainty States of Nature Possible states...

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