# Optimizing Cobb-Douglas like functions

Economics isn't my home field, but I'm looking for references for a paper I'm working on and I'm hoping one of you can help. Are there many good references for optimizing a Cobb-Douglas like utility function for current consumption $x$, and future consumption $f(w-x)$: $$U(x)= x^\alpha f(1-x)^{1-\alpha},$$ where $x\in[0,w]$ and $f$ is assumed non-decreasing? I've worked out what restrictions $x(w)$ must have so that there exists some $f$ which gives $x(w)$ as the rational response, but I was curious if there is a stock reference I should cite. Thanks!

• possible duplicate... economics.stackexchange.com/questions/4997/… even if it isn't it is at least relevant. Optimising a Cobb-Douglas is pretty tricky. Using a linear transformation outlined in my answer to the earlier question is an effective technique. – Jamzy Aug 14 '15 at 2:43
• +1 for to the suggestion of a linear transformation. – cc7768 Aug 14 '15 at 15:48