Before revision:  The conditions necessary for the existence of such "hyperbolic" long rates turn out to be those of so-called social discounting, which allow for long-term cash flows to be treated as broadly "just as important" as those of the short or medium term.
After revision:  The conditions necessary for the existence of such "hyperbolic" and "generalised hyperbolic" long rates are those of so-called social discounting, which allow for long-term cash flows to be treated as broadly "just as important" as those of the short or medium term.