# Cobb-Douglas functions in economics

1. Mar 24, 2008

### 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.

1. The problem statement, all variables and given/known data
Here [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?

2. Relevant equations

3. 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...

Last edited: Mar 24, 2008
2. Mar 25, 2008