Hello everybody,

I am trying to find an utility function full filling the following properties. 1) u(x) is twice continously differentiable 2) u'(x) > 0 and u''(x) <0 3) with u'(1) = 1 and u(0) =0 4) and if x goes to + Infinity then u'(x) and u''(x) are going to positive Infinity

I tried several different types out. but I did not manage to find one type that full fills all conditions.

The most promising function i found was : Log[x] which does not full fill Log[0] is not 0. Making the function Log[1+x] will generate 0 if x=0 but u'(1) is not 1.

Maybe somemone got an idea about a function having this properties or can help me how to handle this issue. I am kind of stuck. I would appreciate all help that i get.

BW Dax Claude