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Non-Existence of Steady State Equilibrium in the Neoclassical Growth Model with a Longevity Trend


  • Mikkel Nørlem Hermansen

    () (Department of Economics and Business, Aarhus University, Denmark)


Longevity has been increasing in the developed countries for almost two centuries and further increases are expected in the future. In the neoclassical growth models the case of population growth driven by fertility is well-known, whereas the properties of population growth caused by persistently declining mortality rates have received little attention. Furthermore, the economic literature on the consequences of changing longevity has relied almost entirely on analysis applying a once and for all change in the survival probability. This paper raises concern about such an approach of comparison of steady state equilibrium when considering the empirically observed trend in longevity. We extend a standard continuous time overlapping generations model by a longevity trend and are thereby able to study the properties of mortality-driven population growth. This turns out to be exceedingly complicated to handle, and it is shown that in general no steady state equilibrium exists. Consequently analytical results and long run implications cannot be obtained in a setting with a realistic demographic setup.

Suggested Citation

  • Mikkel Nørlem Hermansen, 2011. "Non-Existence of Steady State Equilibrium in the Neoclassical Growth Model with a Longevity Trend," Economics Working Papers 2011-04, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2011-04

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    References listed on IDEAS

    1. Bhattacharya, Joydeep & Qiao, Xue, 2005. "Public and Private Expenditures on Health in a Growth Model," Staff General Research Papers Archive 12378, Iowa State University, Department of Economics.
    2. D. Gale Johnson, 2000. "Population, Food, and Knowledge," American Economic Review, American Economic Association, vol. 90(1), pages 1-14, March.
    3. d'Albis, Hippolyte, 2007. "Demographic structure and capital accumulation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 411-434, January.
    4. repec:ebl:ecbull:v:9:y:2004:i:3:p:1-10 is not listed on IDEAS
    5. Rosa Aísa & Fernando Pueyo, 2004. "Endogenous longevity, health and economic growth: a slow growth for a longer life?," Economics Bulletin, AccessEcon, vol. 9(3), pages 1-10.
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    More about this item


    Longevity; Population growth; Overlapping generations models; Steady state equilibrium; Existence;

    JEL classification:

    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical

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