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Math Help - Elasticity

  1. #1
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    Elasticity

    The price elasticity is given by

     \epsilon = -\frac{p}{q}\cdot\frac{dq}{dp}

    and the demand equation is given by
     q = 700-35p
    and p is given as 4 for  0\leq p \leq 20

    So i plus in 4. Which gives q as 560.

    Then i take derivative of q which is 35? and derivative of p which is one?

    Then throw them in the elasticity equation and get -0.25.

    Does that make sense?
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  2. #2
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    The derivative of q is -35, and you don't need the derivative of p; p = 4.
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  3. #3
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    so i have


     \frac{4}{560}\cdot\frac{-35}{0}


    That cant be right.

    if  p= \frac{700-q}{35}

    then derivative of p is one?
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  4. #4
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    Hi el123

    Quote Originally Posted by el123 View Post
    so i have


     \frac{4}{560}\cdot\frac{-35}{0}


    That cant be right.

    if  p= \frac{700-q}{35}

    then derivative of p is one?
    According to BobP's statement

    it is
     \epsilon = -\frac{p}{q}\cdot\frac{dq}{dp}

    and the demand equation is given by
     q = 700-35p
    \epsilon = - \frac{p}{q}*\frac{dq}{dp}

    and

     q = 700-35p

    => \frac{dq}{dp} = y' = -35

    so \epsilon = - \frac{p}{q}*\frac{dq}{dp} = - \frac{p}{q}*(-35)

    Yours
    Rapha
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  5. #5
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    If q = 700 -35p,, then the derivative of q wrt p is

    \frac{dq}{dp} = -35.

    Also, if q = 700 - 35p, then p = \frac{700 - q}{35}

    and the derivative of p wrt q would be

    \frac{dp}{dq} = -\frac{1}{35},

    but that particular derivative is not needed.
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  6. #6
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    indeed you are right.I see my mistake.

    Thanks guys ...or girls.

    One more thing , what does the ...for  0 \leq p\leq 20 mean?
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  7. #7
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    It means that p is to be greater than or equal to zero, and less than or equal to 20.

    i.e. p has to lie within the range zero to 20 inclusive.
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