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Malthusian Trap and Endogenous Population

Listed author(s):
  • Hung, Nguyen Manh


  • Makdissi, Paul

In this paper, we develop a model in which human being constitutes the sole asset and is a production factor which can be combined with a fixed factor, say land, to produce a homogeneous commodity. Saving, so to speak, can only be made through having children, the number of which is an endogenous decision to the household. We show that the economy will run into the Malthusian equilibrium with high population and subsistent per capita consumption only when the initial population is large enough. Otherwise, the steady state equilibrium with lower population and higher per capita consumption than the Malthusian outcome will prevail. Also, we have identified the persistent Malthusian equilibrium - or Malthusian trap - and demonstrate that the economy can escape from this unappealing long run situation either through a suitable technological shift or an appropriate subsidy of the child-rearing cost. Our results are then extended to the stochastic framework where the time rate of population change undergoes a process of Brownian motion. The probability distribution of the steady state is well determined, and saving via the number of offsprings, as with the standard capital model, incorporates a precautionary component. Nous développons un modèle dans lequel l'être humain constitue le seul actif et est un facteur de production accumulable qui peut être combiné avec un autre facteur en quantité fixe, la terre, pour produire un bien homogène. L'épargne dans un tel modèle ne peut se faire que sous la forme d'enfants dont le nombre est une décision endogène pour le ménage. Nous démontrons que l'économie ne converge vers un équilibre malthusien avec un niveau de population élevé et un niveau de consommation de subsistance que si la population initiale est suffisamment nombreuse. Autrement, un état stationnaire avec une population moins nombreuse et une consommation per capita plus élevée prévaudra. Nous avons de plus identifié l'équilibre malthusien persistant - ou piège malthusien - et démontré que l'économie peut s'échapper de cette situation de long terme via un choc technologique suffisamment important ou via un subside approprié du coût d'élever des enfants. Nous étendons nos résultats … un cadre stochastique où le taux de croissance de la population est sujet … un mouvement brownien. La distribution … l'état stationnaire est déterminé et l'épargne via le nombre d'enfants, tout comme dans les modèles d'accumulation de capital standard, inclut une composante de précaution.

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Paper provided by Université Laval - Département d'économique in its series Cahiers de recherche with number 9705.

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Date of creation: 1997
Handle: RePEc:lvl:laeccr:9705
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  1. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
  2. Eckstein, Zvi & Wolpin, Kenneth I., 1985. "Endogenous fertility and optimal population size," Journal of Public Economics, Elsevier, vol. 27(1), pages 93-106, June.
  3. Assaf Razin & Efraim Sadka, 1995. "Population Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262181606, January.
  4. Gary S. Becker & Robert J. Barro, 1988. "A Reformulation of the Economic Theory of Fertility," The Quarterly Journal of Economics, Oxford University Press, vol. 103(1), pages 1-25.
  5. Bourguignon, Francois, 1974. "A particular class of continuous-time stochastic growth models," Journal of Economic Theory, Elsevier, vol. 9(2), pages 141-158, October.
  6. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, May.
  7. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
  8. Nerlove, Marc & Razin, Assaf & Sadka, Efraim, 1986. "Some Welfare Theoretic Implications of Endogenous Fertility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 3-31, February.
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