Why a Population Converges to Stability

Arthur, W.B. (1980). Why a Population Converges to Stability. IIASA Research Report. IIASA, Laxenburg, Austria: RR-80-019

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A central theorem in mathematical demography tells us that the age distribution of a closed population with unchanging fertility and mortality behavior must converge to a fixed and stable form. Proofs rely on ready-made theorems borrowed from linear algebra or from asymptotic transform theory, notably the Perron-Frobenius and the Tauberian theorems. But while these are efficient and expedient, they give little insight into the mechanisms that forces the age distribution to converge.

This paper proposes a simple argument for convergence. An elementary device allows us to view the birth sequence as the product of an exponential sequence and a weighted smoothing process. Smoothing progressively damps out the peaks and hollows in the initial birth sequence; thus the birth sequence gradually becomes exponential, and this forces the age distribution to assume a fixed and final form.

Item Type: Monograph (IIASA Research Report)
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:47
Last Modified: 27 Aug 2021 17:09
URI: https://pure.iiasa.ac.at/1247

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