Sustainability, optimality, and viability in the Ramsey model

The Ramsey model of economic growth is revisited from the point of view of viability. A viable state is a state from which there exists at least one tra jectory that remains in the set of constraints of minimal consumption and positive wealth. Viability is presented with a constraint of minimal consumption, then with an additional criterion of economic sustainability. The comparison of viability kernels with or without sustainability shows how much consumption should be reduced and when. The viable-optimal solution in the sense of inter-temporal consumption is obtained on the viability boundary of an auxiliary system. Technological progress works against population growth to favor the possibility for a given state of being viable or viable-sustainable.