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Sustainability, optimality, and viability in the Ramsey model

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  • Noël Bonneuil
  • Raouf Boucekkine

Abstract

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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Bibliographic Info

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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Keywords: Viability theory; Optimization; Sustainability; Ramsey model;

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References

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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. van Geldrop, Jan & Withagen, Cees, 2000. "Natural capital and sustainability," Ecological Economics, Elsevier, vol. 32(3), pages 445-455, March.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Bonneuil, Noel, 1994. "Capital Accumulation, Inertia of Consumption and Norms of Reproduction," Journal of Population Economics, Springer, vol. 7(1), pages 49-62.
  10. 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.
  11. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
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Cited by:
  1. Krawczyk, Jacek B & Pharo, Alastair & Simpson, Mark, 2011. "Approximations to viability kernels for sustainable macroeconomic policies," Working Paper Series 1531, Victoria University of Wellington, School of Economics and Finance.
  2. Tanguy Isaac, 2013. "Sustainability is compatible with decreasing social welfare," Economics Bulletin, AccessEcon, vol. 33(2), pages 1116-1125.
  3. Jacek Krawczyk & Alastair Pharo & Oana Serea & Stewart Sinclair, 2013. "Computation of viability kernels: a case study of by-catch fisheries," Computational Management Science, Springer, vol. 10(4), pages 365-396, December.
  4. Krawczyk, Jacek B & Pharo, Alastair S, 2011. "Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems," Working Paper Series 1878, Victoria University of Wellington, School of Economics and Finance.

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