Optimal fertility under age-dependent labor productivity

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 seminal Samuelsonian optimal fertility model (Samuelson 1975). For that purpose, we build a 4-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 labor age-composition effect (Sauvy effect) with the intergenerational redistribution effect (Samuelson effect). Finally, we develop a numerical example, and examine how Sauvy’s recommendation can be reconcilied with facts