On the stability of the steady state when population is decreasing
On the stability of the steady state when population is decreasing
复制标题
论人口减少时稳态的稳定性
DOI：
10.1007/bf01284388
复制
发表时间：
1985
期刊：
影响因子：
--
通讯作者：
A. Ritschl
中科院分区：
文献类型：
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作者：
A. Ritschl
由于当今许多发达国家面临人口规模下降的问题，人们认为，经济增长理论应该普遍化，以便解释经济对变化的适应，特别是对人口负增长的适应。在单一部门增长模型中，假定经济行为者以与其收入成正比的比例从资本存量中撤资，Samu el son（1975）得出了撤资与劳动力下降之间的平衡。与此同时，对于这种不储蓄是否会在竞争市场中发生，人们提出了质疑(参见Wagner （1981), Kurz(1982)）。最近，确实有证据表明萨缪尔森均衡是不稳定的(见Schmitt-Rink (1984)；Cigno（1981,1984）也得到了类似的结果：一旦被推离其均衡值，资本与劳动力的比率就会移动得更远，而不是回到该值。本文旨在表明，这种不稳定性可以归因于所采用的储蓄函数的形状，因此不是新古典理论本身的缺陷。在对储蓄假设进行修正的基础上，得到了对所有人口变化率都能产生稳定均衡的广义模型。在人口零增长的情况下，就会达到工资高而利润率降至最低的稳定状态，正如J. St. Mill（1848）所描述的那样。
As many advanced countries of today face a decline in population size, it is felt that the theory of economic growth should be generalized such as to explain the economic adaption to changing, especially to negative rates of population growth. In a one-sector growth model where economic actors are as-sumed to dissave from their capital stock in constant proportion to their income, Samu el son (1975) derives an equilibrium between disinvestment and labour force decline. Meanwhile, doubts have been raised as to whether such dissaving could occur in competitive mar-kets (see Wagner (1981), Kurz (1982)). Recently, it has indeed been shown that Samuelson's equilibrium is unstable (see Schmitt-Rink (1984); similar results are obtained by Cigno (1981, 1984)): Once having been pushed off its equilibrium value, the ratio of capital to labour moves even farther away instead of returning to that value.This paper aims to show that this instability can be ascribed to the shape of the savings function employed and is hence no defi-ciency of neoclassical theory itself. On modifying the savings hypothesis, a generalized model is obtained which yields stable equilibria for all rates of population change. With zero population growth, a stationary state is attained where wages are high and the profit rate has fallen to a minimum, just as described by J. St. Mill (1848).