$\displaystyle [( \beta / \alpha) (px / py)]^\beta = [(\alpha / \beta (py / px)]^\alpha$
I have the solution but my simplifying isn't the best;
$\displaystyle \beta Px$ = $\displaystyle \alpha Py$
thanks
$\displaystyle [( \beta / \alpha) (px / py)]^\beta = [(\alpha / \beta (py / px)]^\alpha$
I have the solution but my simplifying isn't the best;
$\displaystyle \beta Px$ = $\displaystyle \alpha Py$
thanks
$\displaystyle \left(\frac{b}{a}\right)^b \left(\frac{px}{py}\right)^b = \left(\frac{a}{b}\right)^a \left(\frac{py}{px}\right)^a$
$\displaystyle \left(\frac{b}{a}\right)^b \left(\frac{a}{b}\right)^{-a} = \left(\frac{px}{py}\right)^{-b} \left(\frac{py}{px}\right)^a$
$\displaystyle \left(\frac{b}{a}\right)^b \left(\frac{b}{a}\right)^{a} = \left(\frac{py}{px}\right)^{b} \left( \frac{py}{px} \right)^a$
$\displaystyle \left(\frac{b}{a}\right)^{a+b} = \left(\frac{py}{px}\right)^{a+b}$
$\displaystyle \frac{b}{a} = \frac{py}{px}$
$\displaystyle bpx = apy$
Thanks, that was much clearer,
I have another question as well now
I have my Lagrangian functions
1) $\displaystyle y^{1/2} + \lambda px $
2) $\displaystyle (1/2) x^{-1/2} + \lambda px $
Are they correct? from the Cobb Douglas function $\displaystyle xy^{1/2}$
If they are, I've solved for Lambda
1)$\displaystyle \lambda = y^{1/2} / px$
2) $\displaystyle \lambda = (1/2) x^{-1/2} / py$
Are these correct? as I now have to put them equal to each other and solve for x and y but my answers look a little confusing
thanks