An economist's non-linear model of self-generated fertility waves

Summary

Standard one-sex linear models of Lotka or Bernardelli always approach asymptotically an exponential growth mode with stable age distribution. Realistic non-linear models need not possess this property. The present analysis uncovers a possibly realistic ease where an existent mode of balanced growth is ‘unstable‘, giving way when slightly perturbed to an asymptotic every-other generation limit cycle of determinable amplitude, and which is stable. The nonlinear model utilizes the hypothesis of R. A. Easterlin that age-specific fertility will tend to be lower for age classes that are relatively swollen in total number. By virtue of the law of diminishing returns, wages and feeling of security will tend to be low for such swollen groups. A possible rebound in fertility in the 1980s is implicit in the Easterlin hypothesis.

Additional information

Notes on contributors

Paul A. Samuelson

I owe thanks for financial aid to NIH Grant # 1 RO1 HD-09081-01 and Hiroaki Nagatani and Joel Yellin for research assistance that eliminated many errors.