In the economic literature, sustainability is often defined as the requirement of keeping something constant, or at least non-decreasing, along time (for example, consumption or utility). In this paper, we wonder under which conditions invariant quantities can be found along the optimal paths...

We study a model with an exhaustible resource and a substitute which is not a backstop technology. We focuse our attention on the optimal policy of consumption which is described by a Ramsey's rule as in the seminal paper of Dasgupta and Heal [1974] but with a discount rate which is not always...