Rate of Growth of Population and Aggregate Saving in the Basic Life-Cycle Model

In this paper we explore the impact of the life-cycle dynamics of family composition on the aggregate propensity to save and on the relationship between the latter and the rate of growth of population, in the hypothesis of life-cycle behaviour. We depart from Modigliani-Brumberg's basic model by assuming that the household, rather than the individual, is the relevant economic unit. In this framework we point out that in an economy with a steadily growing population the aggregate propensity to save is a function of several demographic parameters and, in particular, of the timing of births (T) and of the number of children generated by each household (f). We then explore the impact of T and f on the co-movements of the rate of growth of population and of the aggregate propensity to save. We show that, when the change of the rate of growth of population is brought about by a change of the number of children generated by each household, the aggregate propensity to save and the rate of growth of population move in the same direction, as suggested by Modigliani-Brumberg, unless the timing of births is very low and the number of children generated by each household relatively high. On the contrary, when the rate of growth of population changes because the timing of birth changes, the aggregate propensity to save and the rate of growth of population move in opposite directions unless the number of children generated by each household is very close to two and therefore the rate of growth of population very close to zero.