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Math Help - What have they done here?

  1. #1
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    What have they done here?

    Hello,

    I've run in to a problem that I hope is just me being stuck on something very simple.
    It's regarding the first order condition of expected utility.

    I have this:
    EU(V,I) = π(V)u(Y P(V,I)V L+I) + [1π(V)]u(Y P(V,I)V)

    And it becomes this:

    π(V)[1π(V)]u'(Y P(V,I)V L+I) = π(V)[1π(V)]u'(Y P(V,I)V)

    However, I can not for the life of me figure out what they've done here to end up with this. Any help?

    Thanks in advance!
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  2. #2
    MHF Contributor
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    Re: What have they done here?

    Hey Staffank.

    I vaguely recall results like Jensens inequality being used with utility theory for application in Insurance. Have you been given any other properties that the utility function and the random variable must satisfy?
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  3. #3
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    Re: What have they done here?

    Hi,

    Thank you for your answer.
    I probably should have added additional information to begin with.

    What I also have is this:

    P(V,I) = π1I if V = V1 > 0
    P(V,I) = π0I if V = V0 = 0

    (All the 1's and 0's in above are supposed to be subscript, so it's pi "one" and V "one", pi "zero" and V "zero". I hope you understand what I mean)

    I'm also supposed to take the FOC with respect to I.
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