Sustainability is compatible with decreasing social welfare

This note studies the determination of optimal path - i.e. maximizing the intertemporal social welfare - under a sustainability constraint defined as a non-decreasing intertemporal social welfare accross time. We show that this definition suffers from an important drawback : the path obtained is not Pareto optimal. It is a drawback because nothing in our intuition of sustainable allocation justifies to give up a Pareto improvement. This implies also the possibility of false-negative result in the empirical studies aiming to determine if a country is on a sustainable path.