= Inada utility with vanishing curvature
{c}
{title2=$U(x)=\log x+x^{-1}-\tfrac16x^{-2}$}
This smooth utility has $U'(x)=x^{-1}-x^{-2}+x^{-3}/3>0$ and $U''(x)=-(x-1)^2/x^4$. Its <derivative> is strictly decreasing, diverges at zero and tends to zero at infinity, so the utility is <strictly concave> and satisfies the <Inada conditions>. Yet its curvature vanishes at one. The <inverse marginal utility> cannot have a finite <derivative> at $y=1/3$, since differentiating $U'(I(y))=y$ there would give zero equal to one. Its dual is differentiable but not twice differentiable at that price.
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