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Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions

  • Pivato, Marcus

We define an intergenerational social welfare function Sigma from |R^|N (the set of all infinite-horizon utility streams) into *|R (the ordered field of hyperreal numbers). The function Sigma is continuous, linear, and increasing, and is well-defined 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'.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7461.

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Date of creation: 05 Mar 2008
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Handle: RePEc:pra:mprapa:7461
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  1. Chichilnisky, Graciela, 1995. "An axiomatic approach to sustainable development," MPRA Paper 8609, University Library of Munich, Germany.
  2. Efimov, Boris A. & Koshevoy, Gleb A., 1994. "A topological approach to social choice with infinite populations," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 145-157, April.
  3. Esteban Induráin & José Ramón Uriarte & Juan Carlos Candeal, 1997. "Some issues related to the topological aggregation of preferences: addendum (*)," Social Choice and Welfare, Springer, vol. 14(2), pages 359-361.
  4. repec:cup:cbooks:9780521576475 is not listed on IDEAS
  5. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
  6. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
  7. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
  8. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
  9. Araujo, Aloisio, 1985. "Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience," Econometrica, Econometric Society, vol. 53(2), pages 455-61, March.
  10. Brown, Donald J & Lewis, Lucinda M, 1981. "Myopic Economic Agents," Econometrica, Econometric Society, vol. 49(2), pages 359-68, March.
  11. Lauwers, Luc, 1993. "Infinite Chichilnisky rules," Economics Letters, Elsevier, vol. 42(4), pages 349-352.
  12. Andrew Caplin & John Leahy, 2000. "The Social Discount Rate," NBER Working Papers 7983, National Bureau of Economic Research, Inc.
  13. Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
  14. Chichilnisky, G. & Heal, G.M., 1995. "Social Choice with Infinite Populations: Construction of a Rule and Impossibility Results," Papers 95-19, Columbia - Graduate School of Business.
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