Population dynamics and utilitarian criteria in the Lucas-Uzawa Model

详细信息	查看全文 | 推荐本文 |

• 作者：Simone Marsiglio^a ; ^c ; ^{simone.marsiglio@sp.unipmn.it} ; Davide La Torre^b ; ^{davide.latorre@unimi.it}
• 关键词：O40 ; O41 ; J13
• 刊名：Economic Modelling
• 出版年：2012
• 期刊代码：7_02649993
• 类别：eco
• 出版时间：July, 2012
• 卷：29
• 期：4
• 页码：1197-1204
• 文件大小：248 K

摘要

This paper introduces population growth in the Uzawa-Lucas model, analyzing the implications of the choice of the welfare criterion on the model's outcome. Traditional growth theory assumes population growth to be exponential, but this is not a realistic assumption (see Brida and Accinelli, 2007). We model exogenous population change by a generic function of population size. We show that a unique non-trivial equilibrium exists and the economy converges towards it along a saddle path, independently of population dynamics. What is affected by the type of population dynamics is the dimension of the stable manifold, which can be one or two, and when the equilibrium is reached, which can happen in finite time or asymptotically. Moreover, we show that the choice of the utilitarian criterion will be irrelevant on the equilibrium of the model, if the steady state growth rate of population is null, as in the case of logistic population growth. Then, we show that a closed-form solution for the transitional dynamics of the economy (both in the case population dynamics is deterministic and stochastic) can be found for a certain parameter restriction.