# Elasticity of Substitution (CES)

This appears to be a nice forum. I just registered since I have a question...

I have a CES aggregator-function $$f(c,q) = (r c^{a} + b q^{a})^{1/a}.$$ It is postulated that it can be rewritten as $$f(c,q) = c \left[ r + b \left( \frac{q}{c} \right)^{a} \right]^{\frac{1}{a}}.$$

I don’t see how, and neither does Maple. Can anyone help? I’m confused and I don’t know what I have missed. I bet that there is insufficient information.

Thanks for the edit; I will write the problem in the correct language now.

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This is valid if $c > 0$. –  Robert Israel Jan 16 '13 at 0:33
It was enough! thank you! –  Hans Pede Jan 16 '13 at 0:39

Hint: $c = (c^a) ^{\frac {1}{a}}$ if $c > 0$.

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