Can someone tell em if these two equations are the same
x = A[(s/δ)]^α/(1-α)
And
x = A[(δ/sA)^(1/(α-1))]^α
Thnaks
Edit: I can not seem to get TEX functions to work, sorry
Can someone tell em if these two equations are the same
x = A[(s/δ)]^α/(1-α)
And
x = A[(δ/sA)^(1/(α-1))]^α
Thnaks
Edit: I can not seem to get TEX functions to work, sorry
Without TEX, it's hard to figure out what your functions are. I'm guessing:
$\displaystyle x = A(\frac{s}{\delta})^\frac{\alpha}{1-\alpha}$
and
$\displaystyle x = A\left[(\frac{\delta}{sA})^{\frac{1}{\alpha-1}}\right]^\alpha$
To figure out if they're the same function, you use algebraic methods to put each in some standard form. The first one is:
$\displaystyle x = A(\frac{s}{\delta})^\frac{\alpha}{1-\alpha}= As^\frac{\alpha}{1-\alpha}\delta^\frac{-\alpha}{1-\alpha}$
The second one is:
$\displaystyle x = A\left[(\frac{\delta}{sA})^{\frac{1}{\alpha-1}}\right]^\alpha= A(\frac{\delta}{sA})^{\frac{\alpha}{\alpha-1}}= A\delta^{\frac{\alpha}{\alpha-1}}s^{\frac{-\alpha}{\alpha-1}}A^{\frac{-\alpha}{\alpha-1}}=A^{\frac{-1}{\alpha-1}}s^{\frac{-\alpha}{\alpha-1}}\delta^{\frac{\alpha}{\alpha-1}}$
So the answer is no, assuming I interpreted the functions correctly. If not, that's the general idea, so hopefully you can do it with the correct functions.
- Hollywood