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Demography

, Volume 8, Issue 1, pp 71–80 | Cite as

On the momentum of population growth

  • Nathan Keyfitz
Article

Abstract

If age-specific birth rates drop immediately to the level of bare replacement the ultimate stationary number of a population will be given by (9):
$$\left( {{\textstyle{{b\mathop e\limits^ \bullet {}_0} \over {r\mu }}}} \right)\left( {\frac{{R_0 - 1}}{{R_0 }}} \right)$$
multiplied by the present number, where b is the birth rate, r the rate of increase, \(\mathop e\limits^ \bullet _0 \) the expectation of life, and R 0 the Net Reproduction Rate, all before the drop in fertility, and μ the mean age of childbearing afterwards. This expression is derived in the first place for females on the stable assumption; extension to both sexes is provided, and comparison with real populations shows the numerical error to be small where fertility has not yet started to drop. The result (9) tells how the lower limit of the ultimate population depends on parameters of the existing population, and for values typical of underdeveloped countries works out to about 1. 6. If a delay of 15 years occurs before the drop of the birth rate to replacement the population will multiply by over 2. 5 before attaining stationarity. The ultimate population actually reached will be higher insofar as death rates continue to improve. If stability cannot be assumed the ultimate stationary population is provided by the more general expression (7), which is still easier to calculate than a detailed projection.

Keywords

Underdeveloped Country Matical Curve Girl Child Stable Assumption Fixed Regime 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Population Association of America 1971

Authors and Affiliations

  • Nathan Keyfitz
    • 1
  1. 1.Department of DemographyUniversity of CaliforniaBerkeley

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