 Elastic-demand utility with an interior reference

An interior reference point defines the utility of a continuous strictly decreasing demand function without requiring integrability of its inverse at zero. The inverse demand is decreasing, so the utility is strictly concave. For example $B(\lambda )=(1+\lambda {)}^{-1/2}$ has inverse $f^{-2}-1$, whose integral from zero diverges. The interior-reference utility still has the required derivative and is finite at every interior demand.