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Need help to maxmize function

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data

    I need help to maximize the below function:

    2. Relevant equations

    Maximize u(x, y) = x^α * y^β subject to Ax + By = m

    Any help is greatly appreciated!

    / Gekkoo
     
    Last edited: Sep 1, 2010
  2. jcsd
  3. Sep 1, 2010 #2

    Mute

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  4. Sep 1, 2010 #3

    HallsofIvy

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    I'm a big fan of "Lagrange Multipliers" but if you don't know that method, you could just write y= (m- Ax)/B so that [itex]x^\alpha*y^\beta= x^\alpha*(m-Ax)^\beta/B^\beta[/itex]. Now, do you know how to find maxima and minima for that?
     
  5. Sep 2, 2010 #4
    Thanks for your answers.

    1 Solve constraint for y:

    y=(m-Ax)/B

    2 Plug into objective function:

    u=x^α*[(m-Ax)/B]^β

    3 Diff w.r.t. x & equate to zero to get critical point:

    FOC: x^α*ln(x)*????=0

    4 Solve FOC for x:

    x=????

    5 Plug that into constraint to get value for y:

    y = (m-A[????])/B

    6 Than I have a candidate solution & need to check SOC of objective function w.r.t x!

    But I fail to successfully derive FOC. Can anyone please help me out?
     
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