Fertility Choice and Semi-Endogenous Growth: Where Becker meets Jones

We introduce fertility choice into an R&D-based semi-endogenous growth model so that the economy’s long-run growth rate is again fully en-dogenously determined. The ultimate growth engine is located in the population equation of the model (“people reproduce in proportion to their number”), and R&D carries sustained population growth forward to GDP growth. We indicate the problems stemming from the fact that in the considered class of models, population size ought to enter the utility functional multiplicatively. In particular, we show that second order optimality conditions need not hold and flow utility is required to be positive (levels of utility matter). A simplified “Barro–Becker– Jones ” model which we put forward, reconciles these problems, yields an asymptotic long-run fertility rate along an asymptotic BGP, and is open to further generalizations