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Math Help - Von Neumann Morgenstern Utility - Expected Value Choice Under Uncertainty

  1. #1
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    Von Neumann Morgenstern Utility - Expected Value Choice Under Uncertainty

    If Mr.D doesnt break the speed limit he earns a guaranteed income of 30000. If he breaks speed limits he is able to double his income to 60,000 per
    year. If caught speeding he will be banned from driving and will only be able to earn
    10,000 per year in unskilled work. The probability of getting caught for speeding is
    0.5.

    The decision to speed (or not) is based on rational criteria, with all ethical and similar
    issues being irrelevant in this regard, i.e. Mr D seeks to maximise expected utility. He
    has a Von Neumann-Morgenstern utility function.

    Where  U = {Y}^{\propto  } and \propto  = 0.2

    To analyse whether Mr.D should speed or not, I need to calculate the expected utility values for Mr.D in both scenarios of when he speeds and when he doesn't.



    Certain expected utility from not speeding =  {30000}^{ 0.2} = 7.86

    Expected wealth from uncertain situation =  (0.5*10000)+(0.5*60000) = 35000

    Utility of expected wealth =  {35000}^{0.2 } = 8.13

    Expected Utility =  0.5*({10000}^{0.2 })+0.5*({60000}^{0.2 })= 7.66


    Therefore the utility of expected wealth > expected utility.

    As Mr.D seeks to maximise expected utilitu, the higest utility figure is 8.13, which is greater than 7.86, which was the utility of certain income. Would Mr.D still choose to speed in this instance, is it possible to compare the utilities of two different income levels. 35000 to the power of any value will always provide a higher value than 30000 to the same power, so would Mr.D always choose to speed ?

    In this case Mr.D recieves more utility from a certain 35000 than from an uncertain one. However where i am struggling to interpret this is that, the certain expected utility (7.86) is less than utility of expected wealth (8.13) so would Mr D choose to speed in this instance?
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  2. #2
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    Therefore the utility of expected wealth > expected utility.
    can you carefully explain why you think this is significant? in the absence of an insurance market The consumer does not have the option of getting his expected wealth with certainty.
    Last edited by SpringFan25; May 12th 2011 at 11:38 AM.
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