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Sustainability, optimality, and viability in the Ramsey model

  • Noël Bonneuil
  • Raouf Boucekkine

The Ramsey model of economic growth is revisited from the point of view of viability compared to optimality. A viable state is a state from which there exists at least one trajectory in capital, consumption, and reproduction that remains in the set of constraints of minimal consumption and positive wealth. There exists a largest set of viable states, including all others, called the viability kernel. This concept is an interesting addition to those of equilibria and optimal paths. Viability is first presented with a constraint of minimal consumption, then with an additional criterion of economic sustainability in the sense of the Brundtland commission, which amounts to requiring a non-decreasing social welfare. The comparison of viability kernels with or without sustainability shows how much consumption should be reduced and when. One strong mathematical result is that the viable-optimal solution in the sense of inter-temporal consumption is obtained on the viability boundary of an auxiliary system. Varying preference, technological, and demographic parameters randomly over simulated viability kernels with and without the Brundtland criterion help identify the determinants of the non-emptiness of the viability kernel and of its volume: technological progress works against population growth to favor the possibility for a given state of being viable or viable-sustainable.

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Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2009_34.

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Date of creation: Nov 2009
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Handle: RePEc:gla:glaewp:2009_34
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  1. Graciela Chichilnisky, 1997. "What Is Sustainable Development?," Land Economics, University of Wisconsin Press, vol. 73(4), pages 467-491.
  2. Giuseppe De Marco & Maria Romaniello, 2006. "Dynamics of Mixed Coalitions Under Social Cohesion Constraints," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 39-62.
  3. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  4. Chichilnisky, Graciela & Beltratti, Andrea & Heal, Geoffrey, 1994. "The environment and the long run: A comparison of different criteria," MPRA Paper 7907, University Library of Munich, Germany.
  5. Bonneuil, Noel, 1994. "Capital Accumulation, Inertia of Consumption and Norms of Reproduction," Journal of Population Economics, Springer, vol. 7(1), pages 49-62.
  6. Arnaud Valence, 2005. "Demand Dynamics in a Psycho-Socio-Economic Evolving Network of Consumers," Mathematical Population Studies, Taylor & Francis Journals, vol. 12(3), pages 159-179.
  7. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, vol. 11(02), pages 272-289, April.
  8. Saint-Pierre, Patrick & Bonneuil, Noel, 2008. "Beyond Optimality : Managing Children, Assets, and Consumption over the Life Cycle," Economics Papers from University Paris Dauphine 123456789/6869, Paris Dauphine University.
  9. van Geldrop, Jan & Withagen, Cees, 2000. "Natural capital and sustainability," Ecological Economics, Elsevier, vol. 32(3), pages 445-455, March.
  10. Kenneth Arrow & Partha Dasgupta & Lawrence Goulder & Gretchen Daily & Paul Ehrlich & Geoffrey Heal & Simon Levin & Karl-Göran Mäler & Stephen Schneider & David Starrett & Brian Walker, 2004. "Are We Consuming Too Much?," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 147-172, Summer.
  11. Bonneuil, Noel & Saint-Pierre, Patrick, 2008. "Beyond optimality: Managing children, assets, and consumption over the life cycle," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 227-241, February.
  12. Alain Ayong Le Kama & Katheline Schubert, 2007. "A note on the consequences of an endogenous discounting depending on the environmental quality," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00206326, HAL.
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