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Easter Island’s collapse: a tale of a population race

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  • David Croix
  • Davide Dottori

Abstract

We study different extended formulations for the set (formule) in order to tackle the feasibility problem for the set (formule). Here the goal is not to find an improved polyhedral relaxation of conv(X+), but rather to reformulate in such a way that the new variables introduced provide good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. For the case that A has one row a we analyze the reformulations in more detail. In particular, we determine the integer width of the extended formulations in the direction of the last coordinate, and derive a lower bound on the Frobenius number of a. We also suggest how a decomposition of the vector a can be obtained that will provide a useful extended formulation. Our theoretical results are accompanied by a small computational study.
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  • David Croix & Davide Dottori, 2008. "Easter Island’s collapse: a tale of a population race," Journal of Economic Growth, Springer, vol. 13(1), pages 27-55, March.
    • Handle: RePEc:kap:jecgro:v:13:y:2008:i:1:p:27-55
    DOI: 10.1007/s10887-007-9025-z
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    1. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
    2. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    3. Harford, Jon D., 2000. "Methods of pricing common property use and some implications for optimal child-bearing and the social discount rate," Resource and Energy Economics, Elsevier, vol. 22(2), pages 103-124, May.
    4. Hirshleifer, Jack, 1991. "The Technology of Conflict as an Economic Activity," American Economic Review, American Economic Association, vol. 81(2), pages 130-134, May.
    5. Lasserre, Pierre & Soubeyran, Antoine, 2003. "A Ricardian model of the tragedy of the commons," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 29-45, January.
    6. D'Alessandro, Simone, 2007. "Non-linear dynamics of population and natural resources: The emergence of different patterns of development," Ecological Economics, Elsevier, vol. 62(3-4), pages 473-481, May.
    7. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    8. Barry Rolett & Jared Diamond, 2004. "Environmental predictors of pre-European deforestation on Pacific islands," Nature, Nature, vol. 431(7007), pages 443-446, September.
    9. Maxwell, John W. & Reuveny, Rafael, 2005. "Continuing conflict," Journal of Economic Behavior & Organization, Elsevier, vol. 58(1), pages 30-52, September.
      • John W. Maxwell & Rafael Reuveny, 2004. "Continuing Conflict," Working Papers 2004-27, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    10. Pezzey, John C. V. & Anderies, John M., 2003. "The effect of subsistence on collapse and institutional adaptation in population-resource societies," Journal of Development Economics, Elsevier, vol. 72(1), pages 299-320, October.
    11. Brander, James A & Taylor, M Scott, 1998. "The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use," American Economic Review, American Economic Association, vol. 88(1), pages 119-138, March.
    12. Dalton, Thomas R. & Coats, R. Morris & Asrabadi, Badiollah R., 2005. "Renewable resources, property-rights regimes and endogenous growth," Ecological Economics, Elsevier, vol. 52(1), pages 31-41, January.
    13. Anderies, John M., 2000. "On modeling human behavior and institutions in simple ecological economic systems," Ecological Economics, Elsevier, vol. 35(3), pages 393-412, December.
    14. R. Morris Coats & Thomas R. Dalton, 2000. "Could institutional reform have saved Easter Island?," Journal of Evolutionary Economics, Springer, vol. 10(5), pages 489-505.
    15. Ehrlich, Isaac & Lui, Francis T, 1991. "Intergenerational Trade, Longevity, and Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 1029-1059, October.
    16. Grossman, Herschel I & Kim, Minseong, 1995. "Swords or Plowshares? A Theory of the Security of Claims to Property," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1275-1288, December.
    17. Hirshleifer, Jack, 1995. "Anarchy and Its Breakdown," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 26-52, February.
    18. Nils-Petter Lagerlöf, 2006. "The Galor-Weil Model Revisited: A Quantitative Exercise," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 116-142, January.
    19. Rafael Reuveny & John W. Maxwell, 2001. "Conflict and Renewable Resources," Journal of Conflict Resolution, Peace Science Society (International), vol. 45(6), pages 719-742, December.
    20. F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 329-331.
    21. Jon D. Erickson & John M. Gowdy, 2000. "Resource Use, Institutions, and Sustainability: A Tale of Two Pacific Island Cultures," Land Economics, University of Wisconsin Press, vol. 76(3), pages 345-354.
    22. Münster, Johannes & Staal, Klaas, 2005. "War with Outsiders Makes Peace Inside," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 75, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    23. Reuveny, Rafael & Decker, Christopher S., 2000. "Easter Island: historical anecdote or warning for the future?," Ecological Economics, Elsevier, vol. 35(2), pages 271-287, November.
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    1. Malthus se baña en el Pacífico: el misterioso caso de la Isla de Pascua
      by David Cuberes in Nada Es Gratis on 2019-09-26 05:00:25

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    15. Davide Fiaschi, 2009. "Natural Resources, Social Conflict and Poverty Trap," Discussion Papers 2009/82, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
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    More about this item

    Keywords

    Fertility; War; Bargaining power; Collapse; Natural resources; J13; O13; J52;
    All these keywords.

    JEL classification:

    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
    • J52 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Dispute Resolution: Strikes, Arbitration, and Mediation

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