在過去文獻中所提到的老化定義只是單就年齡的相對分配而言，但並未對社會中的最適年齡結構進行分析。舉例說明，開發中國家或是人口轉型初期的社會多面臨著較高的生育率，因此該社會的人口年齡結構太過年輕化，這對於整個國家或是勞動市場的勞動生產力而言未必是件好事。但如果該社會能適時適量地降低其人口成長率(如：控制生育率)，卻可能對該社會有很大的助益；然而就人口年齡結構而言，該社會卻步向老化的方向。因此，我們要賦予人口老化一個比較明確的定義，那就是：該社會何時步入老化的境界，必須視其人口結構是否已趨於一個較不利的狀況，而這個臨界點便是該社會的最適人口成長率。故如何詮釋出社會的最適人口成長率將是本文主要的研究目的。 　 我們根據Chu ( 1997) 利用「一階隨機優勢」的概念先定義出何謂「老化」，而後證明在某些經濟目標之下："高於最適人口成長時的人口老化，將使此經濟目標有所改善；而低於最適人口成長時的人口老化，將會使此經濟目標惡化。"我們可針對不同的經濟目標進行分析，如：人口扶養比、個人所得分配或是租稅負擔等。

Previous literature has defined “population aging” only based on the relative age distribution of a nation’s population, let alone the discussion regarding an optimal age distribution for a nation. For example, many developing countries have relatively high birth rates, by definition they are relatively “young” countries, which may be harmful in terms of the productivity for a nation as a whole. These countries may be better off economically by effectively lowering their birth rate and facing an “aging” problem. Therefore, we have to redefine the “aging”, not by looking at the age distribution, but by looking at when the age structure starts to have a negative economical impact to the society; at which we call it the optimal population growth rate. The research is to propose a theoretical framework, which can provide an analytical model of finding an optimal population growth path for a society. The research will use Chu' s (1997) first-degree stochastic dominance analytical framework to define “aging” and prove that a society can improve some economic objectives (for example, dependency ratio, individual income distribution, tax burden etc.) by effectively reducing the birth rate, when the population growth is above the optimal level. On the other hand, a society's economic objective would deteriorate when aging occurs at the time that population growth is below the optimal level.