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“How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012)

Author

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  • Stefan Felder

    () (University of Basel
    University of Duisburg-Essen)

Abstract

Abstract Samuelson’s (Int Econ Rev 16(3):531-538, 1975) serendipity theorem states that the “goldenest golden rule” steady-state equilibrium can be obtained by a competitive two-period overlapping generation economy with capital accumulation, provided that the optimal growth rate prevails. De la Croix et al. (J Popul Econ 25:899-922, 2012) extended the scope of the theorem by showing that it also holds for risky lifetime. With this note, we introduce medical expenditure as a determinant of the probability of surviving to old age to prove the theorem. The original as well as all extended versions of the serendipity theorem, however, fail to prove that second-order conditions are satisfied in general. Still, unlike De la Croix et al. (J Popul Econ 25:899-922, 2012), we can exclude the existence of corner solutions where the probability of reaching old age is zero or one. The zero survival probability case becomes irrelevant if the option to randomize between death and life utility is taken into account. Survival with certainty is ruled out if the marginal cost of survival is increasing. Hence, the optimal survival probability represents an interior solution. Furthermore, we show for the optimal survival probability that the value of a statistical life is positive and equal to its marginal cost.

Suggested Citation

  • Stefan Felder, 2016. "“How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012)," Journal of Population Economics, Springer;European Society for Population Economics, vol. 29(3), pages 957-967, July.
  • Handle: RePEc:spr:jopoec:v:29:y:2016:i:3:d:10.1007_s00148-016-0587-y
    DOI: 10.1007/s00148-016-0587-y
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    References listed on IDEAS

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    1. Michel, Philippe & Pestieau, P, 1993. "Population Growth and Optimality: When Does Serendipity Hold?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 6(4), pages 353-362, November.
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    3. David Croix & Pierre Pestieau & Grégory Ponthière, 2012. "How powerful is demography? The Serendipity Theorem revisited," Journal of Population Economics, Springer;European Society for Population Economics, vol. 25(3), pages 899-922, July.
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    More about this item

    Keywords

    Longevity; Health expenditure; Overlapping generations; Value of a statistical life;

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • H42 - Public Economics - - Publicly Provided Goods - - - Publicly Provided Private Goods
    • H75 - Public Economics - - State and Local Government; Intergovernmental Relations - - - State and Local Government: Health, Education, and Welfare
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • J17 - Labor and Demographic Economics - - Demographic Economics - - - Value of Life; Foregone Income

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