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


  • David Croix


  • Davide Dottori



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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Suggested Citation

  • 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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    References listed on IDEAS

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    1. de la Croix, David & Gosseries, Axel, 2012. "The natalist bias of pollution control," Journal of Environmental Economics and Management, Elsevier, vol. 63(2), pages 271-287.
    2. Lagerlöf, Nils-Petter, 2014. "Population, technology and fragmentation: The European miracle revisited," Journal of Development Economics, Elsevier, vol. 108(C), pages 87-105.
    3. Mariani, Fabio & Pérez-Barahona, Agustín & Raffin, Natacha, 2010. "Life expectancy and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 798-815, April.
    4. Lagerlöf, Nils-Petter, 2013. "Violence and property rights," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 312-328.
    5. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2014. "Egalitarianism under population change: Age structure does matter," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 86-100.
    6. Dao, Nguyen Thang & Dávila, Julio, 2013. "Can geography lock a society in stagnation?," Economics Letters, Elsevier, vol. 120(3), pages 442-446.
    7. Han, Yutao & Pieretti, Patrice & Zanaj, Skerdilajda & Zou, Benteng, 2014. "Asymmetric competition among nation states: A differential game approach," Journal of Public Economics, Elsevier, vol. 119(C), pages 71-79.
    8. Luca Marchiori & Patrice Pieretti & Benteng Zo, 2008. "Brain Drain, Remittances, and Fertility," Economie Internationale, CEPII research center, issue 115, pages 9-42.
    9. Chan, Kenneth S. & Laffargue, Jean-Pierre, 2016. "Plunder and tribute in a Malthusian world," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 138-150.
    10. Marc Germain, 2012. "Equilibres et effondrement dans le cadre d'un cycle naturel," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 55(4), pages 427-455.
    11. 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.
    12. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2010. "Life span and the problem of optimal population size," Working Papers halshs-00536073, HAL.
    13. Pierre PECHER, 2013. "Ethnic conflict, power dynamics and growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2014008, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    14. de la Croix, David & Gobbi, Paula E., 2017. "Population density, fertility, and demographic convergence in developing countries," Journal of Development Economics, Elsevier, vol. 127(C), pages 13-24.
    15. He, Qichun, 2011. "Weather, fertility, and land: land curse in economic development in a unified growth theory," MPRA Paper 35420, University Library of Munich, Germany.
    16. Nagase, Yoko & Uehara, Takuro, 2011. "Evolution of population-resource dynamics models," Ecological Economics, Elsevier, vol. 72(C), pages 9-17.
    17. López, Ramón & Schiff, Maurice, 2013. "Interactive dynamics between natural and man-made assets: The impact of external shocks," Journal of Development Economics, Elsevier, vol. 104(C), pages 1-15.
    18. Sam Tang, 2008. "Scientific Research and Growth Volatility," Economics Discussion / Working Papers 08-11, The University of Western Australia, Department of Economics.

    More about this item


    Fertility; War; Bargaining power; Collapse; Natural resources; J13; O13; J52;

    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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