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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 statecontingent. E.g. the insurer pays only if there is an accident. ECOS2001 Lecture 10 2 StateContingent Budget Constraints Each $1 of accident insurance costs . Consumer has $m of wealth. Cna is consumption value in the noaccident 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 StateContingent Budget Constraints C na C a m The endowment bundle. Where is the most preferred statecontingent 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 riskaversion . U($45) < 7 the lottery is preferred to $45 for sure riskloving . U($45) = 7 the lottery is preferred equally to $45 for sure riskneutralit y . ECOS2001 Lecture 10 8 Preferences Under Uncertainty Wealth $0 $90 2 12 $45 EU=7 U($45) > EU riskaversion ECOS2001 Lecture 10 9 Preferences Under Uncertainty Wealth $0 $90 12 U($45) < EU riskloving. 2 EU=7 $45 U($45) ECOS2001 Lecture 10 10 Preferences Under Uncertainty Wealth $0 $90 12 U($45) = EU riskneutrality. 2 U($45)= EU=7 $45 ECOS2001 Lecture 10 11 Preferences under uncertainty Statecontingent 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.
 One '09
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