Pivato, Marcus (2008): Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions.

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Abstract
We define an intergenerational social welfare function Sigma from R^N (the set of all infinitehorizon utility streams) into *R (the ordered field of hyperreal numbers). The function Sigma is continuous, linear, and increasing, and is welldefined even on unbounded (e.g. exponentially increasing) utility streams. This yields a complete social welfare ordering on R^N which is Pareto and treats all generations equally (i.e. does not discount future utility). In particular, it is what Chichilnisky (1996) calls a `sustainable' preference ordering: it is neither a `dictatorship of the present' nor a `dictatorship of the future'.
We then show how an agent with no `pure' time preferences may still `informationally discount' the future, due to uncertainty. Last, we model intergenerational choice for an exponentially growing economy and population. In one parameter regime, our model shows `instrumental discounting' due to declining marginal utility of wealth. In another regime, we see a disturbing `Paradox of Eternal Deferral'.
Item Type:  MPRA Paper 

Original Title:  Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions 
Language:  English 
Keywords:  intergenerational choice; intertemporal choice; infinitehorizon; nondiscounted; sustainable; hyperreal; nonstandard real numbers; nonstandard analysis; 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice; Clubs; Committees; Associations D  Microeconomics > D9  Intertemporal Choice and Growth > D90  General Q  Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q0  General > Q01  Sustainable Development 
Item ID:  7461 
Depositing User:  Marcus Pivato 
Date Deposited:  06. Mar 2008 07:16 
Last Modified:  21. Feb 2013 03:04 
References:  Anderson, R. M., 1991. Nonstandard analysis with applications to economics. In: Handbook of mathematical economics, Vol. IV. NorthHolland, Amsterdam, pp. 21452208. Araujo, A., 1985. Lack of Pareto optimal allocations in economies with infinitely many commodities: the need for impatience. Econometrica 53 (2), 455461. Arkeryd, L. O., Cutland, N. J., Henson, C. W. (Eds.), 1997. Nonstandard analysis. Vol. 493 of NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences. Kluwer Academic Publishers Group, Dordrecht, theory and applications. Bewley, T., 1970. Equilibrium theory with an infinitedimensional commodity space. Ph.D. thesis, UC Berkely. Borkar, V. S., 1995. Probability theory. Universitext. SpringerVerlag, New York, an advanced course. Brown, D. J., Lewis, L. M., 1981. Myopic economic agents. Econometrica 49 (2), 359368. Campbell, D. E., 1990. Intergenerational social choice without the Pareto principle. J. Econom. Theory 50 (2), 414423. Candeal, J. C., Indurain, E., Uriarte, J. R., 1992. Some issues related to the topological aggregation of preferences. Soc. Choice Welf. 9 (3), 213227. Caplin, A., Leahy, J., 2004. The social discount rate. Journal of Political Economy 112 (6), 12571268. Chichilnisky, G., 1996. An axiomatic approach to sustainable development. Soc. Choice Welf. 13 (2), 231257. Chichilnisky, G., Heal, G., 1997. Social choice with infinite populations: construction of a rule and impossibility results. Soc. Choice Welf. 14 (2), 303318, topological social choice. Cowen, T., Parfit, D., 1992. Against the social discount rate. In: Laslett, P., Fishkin, J. S. (Eds.), Justice between age groups and generations. Philosophy, Politics, and Society. Yale UP, New Haven, CT, pp. 14461. Efimov, B. A., Koshevoy, G. A., 1994. A topological approach to social choice with infinite populations. Math. Social Sci. 27 (2), 145157. Fishburn, P. C., 1970. Arrow's impossibility theorem: concise proof and infinite voters. J. Econom. Theory 2, 103106. Kirman, A. P., Sondermann, D., 1972. Arrow's theorem, many agents, and invisible dictators. J. Econom. Theory 5 (2), 267277. Lauwers, L., 1993. Infinite Chichilnisky rules. Econom. Lett. 42 (4), 349352. Lauwers, L., 1997a. A note on weak infinityChichilnisky rules. Soc. Choice Welf. 14 (2), 357358, topological social choice. Lauwers, L., 1997b. Topological aggregation, the case of an infinite population. Soc. Choice Welf. 14 (2), 319332, topological social choice. Lauwers, L., Van Liedekerke, L., 1995. Ultraproducts and aggregation. J. Math. Econom. 24 (3), 217237. Lind, D., Marcus, B., 1995. An introduction to symbolic dynamics and coding. Cambridge UP, New York. Muthoo, A., 1999. Bargaining theory with applications. Cambridge UP, Cambridge, UK. Rashid, S., 1987. Economies with many agents: An approach using nonstandard analysis. Johns Hopkins University Press, Baltimore, MD. von Weizacker, January 1967. Lemmas for a theory of approximate optimal growth. Review of Economic Studies 34.1 (97), 143151. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/7461 