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Math Help - A simple problem involving Calculus or not

  1. #1
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    A simple problem involving Calculus or not

    Hii recently ran into this problem and i can't seems to solve it. Can someone enlighten me to the method use to solve it?

    P = A1P1 + + A5P5


    Where

    A1 + + A5 = 1

    Let Ai represent the weight of good i (i will be a number between 1 and 5)

    P be the price level

    And Pi the price of good i

    Example
    Let the good and weights be given as follow in the table below

    Good ---------- Weight (Ai)

    Cake -----------0.4
    Oil ------------- 0.2
    Transport ----- 0.1
    Vacations ----- 0.1
    Hospital ------- 0.2

    Suppose the prices of the various goods change in the following way

    Cake +20% (dp1 = 0.2)
    Oil +20% (dp2 = 0.2)
    Transport +10% (dp3 = 0.1)
    Vacations +40% (dp4 = 0.4)
    Hospital +10% (dp5 = 0.1)

    Given the weights in the table, how much will the Price Level (P) rise? Express your answer in %.


    By the way i was wondering if i couldn't get the answer because my interpretation of the meaning of dp1 to dp5
    after the price increase was wrong .

    I inferred that dp1 after price increase, had an increment of 0.2 to it original value, and so on and so for, for the rest of the dp.
    Meaning the new value of dp1 = Original Value of dp1 + 0.2

    Did i made a wrong inference? Help on this part much appreciated
    Last edited by hoildaze; July 29th 2009 at 11:21 AM.
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  2. #2
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    1.2(.4) + 1.2(.2) + 1.1(.1) + 1.4(.1) + 1.1(.2) = 1.19

    19% increase overall
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  3. #3
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    Hi thanks for the reply

    skeeter your ans is this

    1.2(.4) + 1.2(.2) + 1.1(.1) + 1.4(.1) + 1.1(.2) = 1.19

    19% increase overall


    Actually the correct ans is 11%. Can i ask how did you get the value the new
    dp1 to dp5 price?
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  4. #4
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    Quote Originally Posted by hoildaze View Post
    Hi thanks for the reply

    skeeter your ans is this

    1.2(.4) + 1.2(.2) + 1.1(.1) + 1.4(.1) + 1.1(.2) = 1.19

    19% increase overall


    Actually the correct ans is 11%. Can i ask how did you get the value the new
    dp1 to dp5 price?
    used the change values you provided ... I guess I misunderstood your notation, sorry.
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  5. #5
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    By the way i also saw a mistake in the equation i gave.

    The original equation was

    P = A1P1 + + A5P5

    It should actually be

    P = A1p1 + + A5p5

    The highlighted p Should be in Small letter
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