1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    http://rds.yahoo.com/_ylt=A0oGkj3DT...http://www.uvm.edu/~wgibson/cobb-douglas.pdf" [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 by a moderator: Apr 23, 2017
  2. jcsd
  3. Mar 25, 2008 #2


    User Avatar
    Homework Helper

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook