Influence of instantaneous fertility decline to replacement level on population growth: an alternative model

If age-specific birth rate mx of a stable population drop abruptly to mx/Ro, where Ro is the net reproduction rate, then, according to Keyfitz, the size of the ultimate stationary population relative to that at the beginning of the process is given by I = beoo(Ro - 1)/(rmuRo), where b and r are the birth rate and the rate of growth, respectively, of the stable population, eoo the life expectancy at birth, and mu the average age at childbirth in resulting stationary population. Noting that the decline in mx need not necessarily be uniform, investigation has veen carried out to examine the effect on I when fertility decline is more rapid at higher ages. In particular, the effect of the reduced age-specific rates such as mxe-rx (which also produces a stationary population) has been analyzed, and simplifications of the results carried out separately for three different models of the net maternity function. It has also been shown the when mx drops abruptly to some m* x, where the form of m*x need not be specified except for the restriction that the resulting population will be stationary, the value of the index can be approximately obtained from I* = beoo (1 - rmu/2), where mu is the average age at childbearing of theinitial stable population.