Sustainable markets with short sales

Abstract

Market objectives can conflict with long-term goals. Behind the conflict is the impatience axiom introduced by T. Koopmans to describe choices over time. The conflict is resolved here by introducing a new concept, sustainable markets. These differ from Arrow-Debreu markets in that traders have sustainable preferences and no bounds on short sales. Sustainable preferences are sensitive to the basic needs of the present without sacrificing the needs of future generations and embody the essence of sustainable development (Chichilnisky 1996a, b). Theorems 1 and 2 show that limited arbitrage is a necessary and sufficient condition describing diversity and ensuring the existence of a sustainable market equilibrium where the invisible hand delivers sustainable as well as efficient solutions (Chichilnisky 1991, 1995; Chichilnisky and Heal 1998). In sustainable markets prices have a new role: they reflect both the value of instantaneous consumption and the value of the long-run future. The latter are suitably ambiguous, they are connected to the independence of the axiom of choice at the foundations of mathematics (Godel 1940).