Journal of Population Economics

, Volume 30, Issue 2, pp 621–646 | Cite as

Optimal fertility under age-dependent labour productivity

  • Pierre Pestieau
  • Gregory Ponthiere
Original Paper


In the so-called Rapport Sauvy (1962), the French demographer Alfred Sauvy argued that Wallonia’s fertility rate was socially suboptimal, and recommended a 20 % rise of fertility, on the grounds that a society with too low a fertility leads to a low-productive economy composed of old workers having old ideas. This paper examines how Sauvy’s intuition can be incorporated in the Samuelsonian optimal fertility model (Samuelson, Int Econ Rev 16:531–538, 1975). We build a four-period OLG model with physical capital and with two generations of workers (young and old), the skills of the latter being subject to some form of decay. We characterize the optimal fertility rate and show that this equalizes, at the margin, the sum of the capital dilution effect (Solow effect) and the labour age-composition effect (Sauvy effect) with the intergenerational redistribution effect (Samuelson effect). Numerical simulations show that it is hard, from a quantitative perspective, to reconcile Sauvy’s recommendation with facts. This leads us to examine other potential determinants of optimal fertility, by introducing technological progress and a more general social welfare function.


Optimal fertility Age structure Labour productivity Overlapping generations Social optimum 

JEL Classification

E13 E21 J13 J24 



The authors would like to thank Alessandro Cigno, David de la Croix, Thomas Baudin, and Pierre Mohnen, as well as two anonymous referees for their comments. We are also grateful to the participants of the XXIemeCongrès des Economistes Belges de Langue Française in Liege.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CORE and Paris School of EconomicsUniversity of LiegeLiegeBelgium
  2. 2.Paris School of EconomicsUniversity Paris East (ERUDITE)ParisFrance
  3. 3.Institut Universitaire de FranceParisFrance

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