Abstract
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 Chichilnisky’s “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.
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Alcantud J.C.R., García-Sanz M.D.: Paretian evaluation of infinite utility streams: an egalitarian criterion. Econ Lett 106, 209–211 (2010)
Arrow K.J.: Social Choice and Individual Values. Wiley, New York (1951)
Asheim G.B.: Unjust intergenerational allocations. J Econ Theory 54, 350–371 (1991)
Asheim G.B., Mitra T.: Sustainability and discounted utilitarianism in models of economic growth. Math Soc Sci 59, 148–169 (2010)
Asheim, G.B., Mitra, T., Tungodden, B: A new equity condition for infinite utility streams and the possibility of being Paretian. In: Roemer, J., Suzumura, K. (eds.) Intergenerational Equity and Sustainability, pp. 55–68. Basingstoke: Palgrave Macmillan (2007)
Asheim G.B., Tungodden B.: Resolving distributional conflicts between generations. Econ Theory 24, 221–230 (2004a)
Asheim, G.B., Tungodden, B.: Do Koopmans’ postulates lead to discounted utilitarianism? Discussion Paper 32/04, Norwegian School of Economics and Business Administration (2004b)
Atkinson A.B.: The strange disappearance of welfare economics. Kyklos 54, 193–206 (2001)
Banerjee K.: On the equity-efficiency trade off in aggregating infinite utility streams. Econ Lett 93, 63–67 (2006)
Basu K., Mitra T.: Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian. Econometrica 32, 1557–1563 (2003)
Basu K., Mitra T.: Utilitarianism for infinite utility streams: a new welfare criterion and its axiomatic characterization. J Econ Theory 133, 350–373 (2007)
Birchenhall C.R., Grout P.: On equal plans with an infinite horizon. J Econ Theory 21, 249–264 (1979)
Blackorby C., Donaldson D., Weymark J.A.: Social choice with interpersonal utility comparisons: a diagrammatic introduction. Int Econ Rev 25, 327–356 (1984)
Bleichrodt H., Rohde K.I.M., Wakker P.P.: Koopmans’ constant discounting for intertemporal choice: A simplification and a generalization. J Math Psych 52, 341–347 (2008)
Bossert W., Sprumont Y., Suzumura K.: Ordering infinite utility streams. J Econ Theory 135, 579–589 (2007)
Burniaux, J.-M., Martins, J.O.: Carbon leakages: A general equilibrium view. Econ Theory (this issue) (2010)
Chichilnisky G.: An axiomatic approach to sustainable development. Soc Choice Welfare 13, 231–257 (1996)
Chichilnisky, G.: Sustainable markets with short sales. Econ Theory (this issue) (2010)
Chichilnisky G., Heal G.M., Beltratti A.: The green golden rule. Econ Lett 49, 175–179 (1995)
Chipman, J.S., Tian, G.: Detrimental externalities, pollution rights, and the “Coase Theorem”. Econ Theory (this issue) (2010)
Dasgupta, P.S., Heal, G.M.: The optimal depletion of exhaustible resources. Rev Econ Stud (Symposium) 3–28 (1974)
Dasgupta P.S., Heal G.M.: Economic Theory and Exhaustible Resources. Cambridge University Press, Cambridge (1979)
Debreu G.: Topological methods in cardinal utility theory. In: Arrow, K.J., Karlin, S., Suppes, P. (eds) Mathematical Methods in the Social Sciences, pp. 16–26. Stanford University Press, Stanford (1960)
Diamond P.: The evaluation of infinite utility streams. Econometrica 33, 170–177 (1965)
Dutta, P.K., Radner, R.: Capital growth in a global warming model: Will China and India sign a climate treaty? Econ Theory (this issue) (2010)
Figuieres, C., Tidball, M.: Sustainable exploitation of a natural resource: a satisfying use of Chichilnisky’s criterion. Econ Theory (this issue) (2010)
Fleurbaey M., Michel P.: Transfer principles and inequality aversion, with application to optimal growth. Math Soc Sci 42, 1–11 (2001)
Fleurbaey M., Michel P.: Intertemporal equity and the extension of the Ramsey criterion. J Math Econ 39, 777–802 (2003)
Gorman W.M.: Conditions for additive separability. Econometrica 36, 605–609 (1968a)
Gorman W.M.: The structure of utility functions. Rev Econ Stud 35, 367–390 (1968b)
Hammond P.J.: Equity, Arrow’s conditions and Rawls’ difference principle. Econometrica 44, 793–804 (1976)
Hara C., Shinotsuka T., Suzumura K., Xu Y.: Continuity and egalitarianism in the evaluation of infinite utility streams. Soc Choice Welfare 31, 179–191 (2008)
Heal G.M.: Valuing the future: Economic theory and sustainability. Columbia University Press, New York (1998)
Heal G.M.: Intergenerational welfare economics and the environment. In: Mäler, K.-G., Vincent, J. (eds) Handbook of Environmental Economics, North-Holland, Amsterdam (2005)
Karp, C., Zhang, J.: Taxes versus quantities for a stock pollutant with endogenous abatement costs and asymmetric information. Econ Theory (this issue) (2010)
Koopmans T.C.: Stationary ordinal utility and impatience. Econometrica 28, 287–309 (1960)
Koopmans, T.C.: Intertemporal distribution and optimal aggregate economic growth. In: Ten Economic Studies in the Tradition of Irving Fisher. New York: Wiley (1967)
Koopmans, T.C.: Representation of preference orderings with independent components of consumption. In: McGuire, C.B., Radner, R. (eds.) Decision and Organization: A Volume in Honor of Jacob Marschak, 2nd edn, pp. 57–78 [previously published in 1972]. Minneapolis: University of Minnesota Press (1986a)
Koopmans, T.C.: Representation of preference orderings over time. In: McGuire, C.B., Radner, R. (eds.) Decision and Organization: A Volume in Honor of Jacob Marschak, 2nd edn, pp. 57–78 [previously published in 1972]. Minneapolis: University of Minnesota Press (1986b)
Koopmans T.C., Diamond P.E., Williamson R.E.: Stationary utility and time perspective. Econometrica 32, 82–100 (1964)
Krautkraemer J.A.: Optimal growth, resource amenities and the preservation of natural environments. Rev Econ Stud 52, 153–170 (1985)
Lauwers L.: Rawlsian equity and generalised utilitarianism with an infinite population. Econ Theory 9, 143–150 (1997)
Lauwers L.: Intertemporal objective functions: Strong Pareto versus anonymity. Math Soc Sci 35, 37–55 (1998)
Lauwers, L.: Intergenerational equity, efficiency, and constructibility. Econ Theory (this issue) (2010)
Lecocq, F., Hourcade, J.-C.: Insights from a theoretical analysis of negotiation mandates: Unspoken ethical issues in the climate affair. Econ Theory (this issue) (2010)
Mitra T.: Stationary Paretian SWF: An Example. Cornell University, Mimeo (2008)
Ostrom, E.: Nested externalities and polycentric institutions: must we wait for global solutions to climate change before taking actions at other scales? Econ Theory (this issue) (2010)
Rawls J.: A Theory of Justice. Harvard University Press, Cambridge (1971)
Rezai, A., Foley, D.K., Taylor, L.: Global warming and economic externalities. Econ Theory (this issue) (2010)
Solow, R.M.: Intergenerational equity and exhaustible resources. Rev Econ Stud (Symposium), 29–45 (1974)
Svensson L.-G.: Equity among generations. Econometrica 48, 1251–1256 (1980)
Szpilrajn E.: Sur l’extension du l’ordre partiel. Fundam Math 16, 386–389 (1930)
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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, Universität Heidelberg, Universität Osnabrück, Université catholique de Louvain and Université de Montréal. 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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Asheim, G.B., Mitra, T. & Tungodden, B. Sustainable recursive social welfare functions. Econ Theory 49, 267–292 (2012). https://doi.org/10.1007/s00199-010-0573-7
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DOI: https://doi.org/10.1007/s00199-010-0573-7