Abstract

If age-specific birth rates m, of a stable population drop abruptly tomx/R0, whereR0 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 byI =be00R0 − 1)/(rμR0, whereb andr are the birth rate and the rate of growth, respectively, of the stable population,e00 the life expectancy at birth, andμ the average age at childbirth in the resulting stationary population. Noting that the decline inmx need not necessarily be uniform, investigation has been carried out to examine the effect on Iwhen fertility decline is more rapid at higher ages. In particular, the effect of the reduced age-specific rates such asmxerx (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 that when m, drops abruptly to somemx*, where the form ofmx* need not be specified except for the restriction that the resulting population will be stationary, the value of the index can be approximately obtained fromI* =be00 (1 -/2), whereμ is the average age at childbearing of the initial stable population.

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