What is Sustainable Development

Abstract

The paper proposes two axioms that capture the idea of sustainable devel­ opment and derives the welfare that they imply. The axioms require that neither the present nor the future should play a dictatorial roJe in society's choices over time. Theorem 1 shows there exist sustainable preferences, which satisfy these axioms. They exhibit sensitivity to the present and to the long-run future, and specify trade­ offs between them. lt exarnines other welfare criteria which are generally utilized: discounted utility, !im inf, long run averages, overtaking and catching-up criteria, Ramsey's criterion, Rawlsian rules, and the of satisfaction of basic needs, and finds that none satisfies the axioms for sustainability. Theorem 2 gives a characterization of all continuous sustainable preferences. Theorem 3 studies a Standard dynarnical system representing the growth of a renew­ able resource. Sustainable preferences are shown to be a natural extension of the equal treatment criterion for finitely many generations, in thesensethat the opti­ mal solutions for such preferences approach the turn pike of an equal-weight finite horizon optirnization problern as the horizon increases. Theorem 3 also shows that sustainable preferences match the experimental evidence in these cases, in the sense that they imply a rate of discount that decreases and approaches zero as time goes to infinity. Theorem 4 exhibits the differences between the optimal paths according to sustainable preferences and discounted utilitarianism in an extension of the classi­ cal Hotelling problern of the optimal depletion of an exhaustible resource. Theorem 5 shows that sustainable optima can be quite different from discounted optima, no matter how small is the discount factor. Subsequent examples show the implications 1 This paper was prepared for an invited presentation at a seminar on Reconsideration of Yalues at the Stanford Institute for Theoretical Economics, organized by K. J. Arrow in July 1993. lt was also an in­ vited presentation at the Intergovemamental Panel on Climate Change (IPCC) Seminar in Montreux, Switzerland, March 1994, at a Seminar on Inconmensurability of Values at Chateaux du Baffy, Nor­ mandy, April 1994, and at the Graduale School of Business of Stanford University in May 1994. 2 UNESCO Chair in Mathematics and Economics and Director, Program on Information and Resources,