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In this paper a method to investigate the dependence of age structure and growth rate on a given sequence of fertility and mortality schedules under the conditions of unchanging mortality and absence of migration is discussed. The method consists in projecting an arbitrary population classified by age to the ends of successive periods assuming that a given age pattern of mortality will remain without change and that a given sequence of fertility schedules will repeatedly operate on the population in a cyclical fashion. It is shown that after a sufficiently large number of repetitions of the cycle, the shifts in age structure between the ends of successive periods and the changes in the growth of the different age groups from one period to the next show a cyclical pattern. Formulas are derived expressing the above changes in terms of a sequence of k growth multipliers, k being the number of schedules in the fertility sequence, and the survival rates in the mortality schedule. A numerical illustration of the theory is given using fertility data from Finland.

On the dependence of age structure on a sequence of mortality and fertility schedules: An exposition of a cyclical model of population change