期刊名称：Discussion Paper / Département des Sciences Économiques de l'Université Catholique de Louvain
印刷版ISSN：1379-244X
出版年度：2011
卷号：1
出版社：Université catholique de Louvain
摘要：We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. Linear production functions in the labor input and standard rearing costs are also considered. First, we study under which conditions the successive cohorts will be given the same consumption per capita. We show that this egalitarian rule is optimal whatever the degree of altruism when life spans are infinite. However, when life spans are finite, this rule can only be optimal in the Benthamite case, i.e. when the degree of altruism is maximal. Second, we prove that under finite life spans the Millian welfare function leads to optimal extinction at finite time whatever the lifetime. In contrast, the Benthamite case is much more involved: for isoelastic utility functions, it gives rise to two threshold lifetime values, say T0 < T1: below T0, finite time extinction is optimal; above T1, balanced growth paths are optimal. In between, asymptotic extinction is optimal. Third, optimal consumption and population dynamics are given in closed-form.
关键词：Optimal population size, Benthamite Vs Millian criterion, finite lives, optimal extinction
