Family Expansion and Capital Accumulation of a Dynasty

We consider a unified framework that combines two strands of previous literature on overlapping generations growth models of endogenous fertility and savings: one strand incorporating two-period lived agents with life-cycle utility functions and the other strand incorporating one period lived agents with dynastic utility functions. In this framework, we study the long-run effects of unfunded social security on fertility and savings. We provide complete characterization of optimal path in terms of the life-cycle felicity index and the degree of altruism towards all the future offsprings, exhibiting either monotonicity of the standard growth model, fluctuations of the Easterlin (1987) hypothesis or convergence in finite period.