I think I have an error in my calculation, because I should get at the end but I do not. Can someone please check to see where I've gone wrong?
Suppose you have:
Rewrite as
Expand the brackets:
To find golden rule consumption, take the partial:
Set that beastie equal to zero so we can find the local max:
Divide through by to get
Multiply both sides by
Raise both sides to the power of
Multiply both sides by
And finish by raising both sides by
We can rewrite as
But that hardly makes it look closer to , which I think is the right answer. What have I done wrong?