<p>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! </p>

CC BY-SA 3.0
2015-08-14T02:43:55.197Z
possible duplicate... http://economics.stackexchange.com/questions/4997/marshallian-demand-for-cobb-douglas 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
CC BY-SA 3.0
2015-08-14T15:48:36.037Z
+1 for to the suggestion of a linear transformation.
cc7768
<utility><optimization><cobb-douglas><saving>
Optimizing Cobb-Douglas like functions
JoelNish
# Optimizing Cobb-Douglas like functions

(Asked by: username_0 on 2015-08-14)

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!

**Tags:** utility, optimization, cobb-douglas, saving

> **Comments:**
> **username_1**: possible duplicate... http://economics.stackexchange.com/questions/4997/marshallian-demand-for-cobb-douglas 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.  
> **username_2**: +1 for to the suggestion of a linear transformation.  

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## 0 answers

