Sustainable recursive social welfare functions

Geir B. Asheim 0 1 2 3 Tapan Mitra 0 1 2 3 Bertil Tungodden 0 1 2 3 0 T. Mitra Department of Economics, Cornell University , 448 Uris Hall, Ithaca, NY 14853, USA 1 We are grateful for helpful discussions with Wolfgang Buchholz, and many constructive comments by anonymous referees, Larry Blume, Walter Bossert, Graciela Chichilnisky, John Hartwick, Aanund Hylland, Larry Karp, Luc Lauwers, Mohamed Mabrouk, Marco Mariotti, Tomoichi Shinotsuka, Yves Sprumont, Kotaro Suzumura, Peter Wakker and seminar participants at Cornell University, Queen's University, Universitt Heidelberg, Universitt Osnabrck, Universit catholique de Louvain and Universit de Montral. Asheim thanks Cornell University and University of California at Santa Barbara for hospitality. This paper is part of the research activities at the center of Equality , Social Organization, and Performance (ESOP) at the Department of Economics at the University of Oslo. ESOP is supported by the Research Council of Norway 2 B. Tungodden Chr. Michelsen Institute , P.O. Box 6033, 5892 Bergen, Norway 3 B. Tungodden Department of Economics, Norwegian School of Economics and Business Administration , Helleveien 30, 5045 Bergen, Norway What ethical criterion for intergenerational justice should be adopted, e.g., when faced with the task of managing the global environment? Koopmans' axiomatization of discounted utilitarianism is based on seemingly compelling conditions, yet this criterion leads to hard-to-justify outcomes. The present analysis considers a class of sustainable recursive social welfare functions within Koopmans' general framework. This class is axiomatized by means of a weak equity condition (Hammond Equity for the Future) and general existence is established. Any member of the class - satisfies the key axioms of Chichilniskys sustainable preferences. The analysis singles out one of Koopmans original separability conditions (his Postulate 3 a), here called Independent Present, as particularly questionable from an ethical perspective. Intergenerational justice Sustainability Discounted utilitarianism 1 Introduction How should we treat future generations? From a normative point of view, what are the present generations obligations towards the future? What ethical criterion for intergenerational justice should be adopted if one seeks to respect the interests of future generations? Answering such questions is essential when faced with the task of managing the global environment, e.g., in the context of climate change.1 These questions can be approached and answered in at least two ways: 1. Through an axiomatic analysis one can investigate on what ethical conditions various criteria for intergenerational justice are based and then proceed to evaluate the normative appeal of these conditions. 2. By considering different technological environments, one can explore the consequences of various criteria for intergenerational justice, and compare the properties of the intergenerational well-being streams that are generated. It is consistent with Rawls (1971) reflective equilibrium to do both: criteria for intergenerational justice should be judged both by the ethical conditions on which they build and by their consequences in specific technological environments. In particular, we may question the appropriateness of a criterion for intergenerational justice if it produces unacceptable outcomes in relevant technological environments. This view has been supported by many scholars, including Koopmans (1967), Dasgupta and Heal (1979, p. 311), and Atkinson (2001, p. 206). When evaluating long-term policies, economists usually suggest to maximize the sum of discounted utilities. On the one hand, such discounted utilitarianism has been given a solid axiomatic foundation by Koopmans (1960).2 On the other hand, this criterion has ethically questionable implications when applied to economic models with resource constraints. This is demonstrated by Dasgupta and Heal (1974) in the so-called DasguptaHealSolow (DHS) model of capital accumulation and resource depletion (Dasgupta and Heal 1974, 1979; Solow 1974), where discounted utilitarianism for any 1 A separate set of important questions relates to how to implement policies that are designed to respect the interests of future generations and to assess their effectiveness; see, e.g., in the context of climate change, Burniaux and Martins (2010), Dutta and Radner (2010), Karp and Zhang (2010) and Ostrom (2010). In this context it is also of interest to investigate the validity of the Coase theorem, as done by Chipman and Tian (2010). Moreover, as pointed out by Lecocq and Hourcade (2010), optimal policies may require estimates of future intragenerational distribution. Finally, as illustrated by Rezai et al. (2010), in some cases, such policies may benefit all generations, and thus do not represent a question of intergenerational justice. 2 For an alternative set of axioms leading to discounted utilitarianism, see Lauwers (1997). positive discount rate undermines the well-being of generations in far future, even if sustainable streams with non-decreasing well-being are feasible. In this paper we revisit Koopmans framework, with numerical representability, sensitivity, and stationarity as its key features. In Sect. 2 we consider conditions that are sufficient to numerically represent the social welfare relation by means of a recursive social welfare function satisfying sensitivity, stationarity, and a condition requiring that the evaluation of two streams with the same present well-being not depend on what that level of well-being is, thereby echoing the analysis of Koopmans (1960, Sects. 37). In this framework we introduce an equity condition we call Hammond Equity for the Future, capturing the following ethical intuition: A sacrifice by the present generation leading to a uniform gain for all future generations cannot lead to a less desirable stream of well-being if the present remains better-off than the future even after the sacrifice.3 In Sect. 3 we point out that Hammond Equity for the Future is weak, as it is implied by all the standard consequentialist equity conditions suggested in the literature. We show that adding this condition leads to a class of sustainable recursive social welfare functions, where the well-being of the present generation is taken into account if and only if the future is better-off. Furthermore, we establish general existence by means of an algorithmic construction. Finally, we show that any member of this class of sustainable recursive social welfare functions satisfies the key axioms of Chichilnisky (1996) sustainable preferences, namely No Dictatorship of the Present and No Dictatorship of the Future.4 In Sect. 4 we offer results that identify which of the conditions used by Koopmans (1960) to axiomatize discounted utilitarianism is particularly questionable from an ethical perspective. The condition in question, referred to as Indepe (...truncated)