Avoiding Extinction : Equal Treatment of the Present and the Future

Equal treatment for the present and the future was required in two axioms for sustainable development introduced by the author. This article shows that the two axioms are equivalent to awareness of physical limits in the long run future. We prove that two optimization problems are equivalent: maximizing discounted utility with a long run survival constraint, and maximizing utilities that treat equally the present and the future. The equal treatment axioms are therefore the essence of sustainable development. The "weight" λ given to the long run future is identified with the marginal utility of the environmental asset along a path that narrowly avoids extinction. An existence theorem is provided for optimizing according to the welfare criterion that treats equally the present and the future. We show that no prior welfare criteria satisfy the axioms for sustainable development introduced in