Cobb-Douglas functions in economics

[kurvmax]

[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.

Homework Statement

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 U_{0} = X^{B}*Y^{1-B}. Then they solve for Y and get Y = U^{1/1-B}_{0}*X^{-B/1-B}. The question is simple: how did they do that algebraically?

Homework Equations

The Attempt at a Solution

I tried to sort things around to get their solution. I got Y^{1-B} = U_{0}/X^{B} Assuming that is right, I then took the natural log of both sides and divided both sides by 1-B. 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...

 

[Päällikkö]

For the LaTeX part, http://en.wikipedia.org/wiki/Help:Displaying_a_formula is a decent syntax-listing. \frac{a}{b} produces \frac{a}{b}.