Results 1 to 2 of 2

Math Help - Help rearranging this equation

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    57
    Thanks
    1

    Help rearranging this equation

    Can someone help me understand how to rearrange this equation to get the following answer(s)

    (x^p_y^p)^((1/p)-1) * x^(p-1) - Lambda*price1 = 0

    (x^p_y^p)^((1/p)-1) * y^(p-1) - Lambda*price2 = 0

    p*x + p*x = y = 0

    which are my Lagrange multipliers for the cobb douglas function (x^p+y^p)^(1/p) where p is alpha/beta

    the answer is

    x=y(price1/price2)^(1/(p-1)

    lambda = price1x + price2y

    My basic math is not up the scratch so could somebody help me understand how to solve for x in the equations given

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244

    Re: Help rearranging this equation

    I don't think I understand your entire question, but you have:

    (x^py^p)^{\frac{1}{p}-1}x^{p-1} - \lambda{price_1} = 0

    (x^py^p)^{\frac{1}{p}-1}y^{p-1} - \lambda{price_2} = 0

    Add \lambda{price_1} to both sides of the first equation and \lambda{price_2} to both sides of the second, resulting in:

    (x^py^p)^{\frac{1}{p}-1}x^{p-1} = \lambda{price_1}

    (x^py^p)^{\frac{1}{p}-1}y^{p-1} = \lambda{price_2}

    And then divide the first by the second, cancelling \lambda and (x^py^p)^{\frac{1}{p}-1}, giving:

    \left(\frac{x}{y}\right)^{p-1}=\frac{price_1}{price_2}

    and then solve for x.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. rearranging an equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 14th 2013, 09:42 AM
  2. help with rearranging equation please
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 27th 2009, 11:11 PM
  3. just rearranging an equation, is it possible?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 21st 2009, 07:12 AM
  4. Rearranging an equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 28th 2008, 08:53 PM
  5. Rearranging an equation
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: November 12th 2007, 08:52 AM

Search Tags


/mathhelpforum @mathhelpforum