Invariance in growth theory and sustainable development

This paper analyzes the general concept of sustainability from a different point of view than that generally found in the literature. If sustainability is defined as the requirement to keep something constant or at least non-decreasing throughout time, the choice of the thing to be preserved is controversial. Neo-classical models mainly assume that sustainability requires that consumption or a utility level has to be preserved. In this paper, we object to this a priori conception of sustainability and define all the quantities that can be preserved in neo-classical optimal growth models. We thus wonder if invariant quantities can be found along the optimal paths defined by a classical representation of an economy with an exhaustible resource. We use the Noether theorem to determine the conservation laws of dynamic systems. We examine under which conditions there is such invariance and how it could be interpreted as a sustainability indicator. We emphasize the limits of the economic growth theory for coping with the sustainability issue.