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Math Help - Percentage Change Operator

  1. #1
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    Percentage Change Operator

    My finance prof is confusing me again... this time about the percentage change operator. I understand %chg = x2/x1-1, or [(x2-x1)/x1]. But can someone clarify the relationship between %chg and logs?

    Here's the context:
    In considering relative purchasing power parity, we have the following equation:

    S(USD/EUR) x (Peur/Pus) = k for all periods

    where:
    Peur = Price level in EU
    Pus = Price level in US
    S(USD/EUR) = Spot USD price of the EUR

    Now we apply the percentage chage operator (taking logs) to get:

    %chgS(USD/EUR) + %chgPus - %chgPeur = 0

    My sense is that this is a linear approximation....
    Any help would be appreciated.
    Many thx
    b
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  2. #2
    MHF Contributor
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    Good call! Here is an effective resource. It confirms your "sense".

    Logarithm transformation

    This is a wonderfully exploitable property of logarithms:

    log(a*b) = log(a) + log(b)

    It is called, sometimes, linearization. Turning intractable multiplication into addition is of great value. Turning nonlinear into linear nearly is magic.
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