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

If age-specific birth rates m, of a stable population drop abruptly tom _x/R ₀, whereR ₀ 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 =be ⁰ ₀ R ₀ ? 1)/(rμR ₀, whereb andr are the birth rate and the rate of growth, respectively, of the stable population,e ₀ ⁰ the life expectancy at birth, andμ the average age at childbirth in the resulting stationary population. Noting that the decline inm _x 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 asm _xe^? 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 that when m, drops abruptly to somem _x ^*, where the form ofm _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 fromI ^* =be ₀ ⁰ (1 -rμ/2), whereμ is the average age at childbearing of the initial stable population.