To grow or to fluctuate – optimal demographic paths

Wrzaczek, S., Feichtinger, G., Fent, T., & Novak, A. (2026). To grow or to fluctuate – optimal demographic paths. Mathematical Population Studies 1-27. 10.1080/08898480.2026.2652292.

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Abstract

This paper establishes a rigorous foundation for population policy by applying intertemporal optimization theory to derive the optimal trade-off between population growth (or decline) and age-structure fluctuations caused by fertility rate changes. The model is based on the McKendrick-von Foerster partial differential equation, with an objective functional representing the discounted adaptation costs associated with the net reproduction rate. To enhance analytical tractability, we assume concentrated vitality rates. Our findings suggest that, over short-time horizons, an initial under- or overshooting of the net reproduction rate is optimal, while over longer horizons, an oscillating net reproduction rate emerges as the best trajectory. Numerical simulations using a stylized population structure illustrate how variations in the net reproduction rate influence the total population dynamics and age-group distributions over time. This study highlights the critical role of optimization in designing adaptive and sustainable population policies.

Item Type:	Article
Research Programs:	Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM) Economic Frontiers (EF)
Depositing User:	Luke Kirwan
Date Deposited:	20 Apr 2026 08:11
Last Modified:	20 Apr 2026 08:11
URI:	https://pure.iiasa.ac.at/21488

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