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Cobb-Douglas functions in economics

  1. Mar 24, 2008 #1
    [SOLVED] Cobb-Douglas functions in economics

    Hi. I'm an economics major. This problem isn't actually required, but I'm trying to learn more about Cobb-Douglas functions.

    1. The problem statement, all variables and given/known data
    Here [pdf] is a description of them. On that first page they go from [tex]U_{0} = X^{B}*Y^{1-B}[/tex]. Then they solve for Y and get [tex]Y = U^{1/1-B}_{0}*X^{-B/1-B}[/tex]. The question is simple: how did they do that algebraically?


    2. Relevant equations



    3. The attempt at a solution


    I tried to sort things around to get their solution. I got [tex]Y^{1-B} = U_{0}/X^{B}[/tex] Assuming that is right, I then took the natural log of both sides and divided both sides by [tex]1-B[/tex]. But here is where I'm stuck. Obviously the -B exponent on X in the solution makes it a fraction, but I'm just too rusty/untalented at this stuff to figure out how dividing by (1-B) can find a way into the exponents of the variables.

    Incidentally, how do I group things with fractions in Latex?

    Nevermind, I'm retarded. Of course if I take the root (1-B) of both sides I get that answer...duh...still curious about the Latex stuff though...
     
    Last edited: Mar 24, 2008
  2. jcsd
  3. Mar 25, 2008 #2

    Päällikkö

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