具有内生寿命模型中的多重增长路径与分歧

The Multiple Growth Paths and Bifurcations in the Model with Endogenous Lifetime

本文将S-形生存概率函数引入Chakraborty内生寿命模型,研究模型的动态特征.文中证明描述模型的离散动力系统至少存在一个非零平衡,至多存在三个非零平衡点,并在给的参数下出现鞍结点分歧.在出现三个非零平衡点的情形下,较高人均资本处的平衡处的生存概率较高,而较低人均资本处的生存概率较低,这两个平衡点是稳定的;处于这两个平衡点之间的平衡点是不稳定的.此时,模型描述的经济具有多重增长路径,并出现"贫困陷阱".

In this paper, S-shaped function of probability of surviving is integrated into the Chakraborty＇s endogenous probability of surviving model and the dynamics of this model is analyzed.It is proved that the discrete dynamical system which describes the model has at least one nonzero equilibrium and at most three nonzero equilibria and undergoes saddle-node bifurcation under some given parameters. When the system has three nonzero equilibria, the equilibrium with highest per capita capital has highest surviving probability and the equilibrium with lowest per capita capital corresponds to lowest surviving probability and both equilibria are stable; The equilibrium between the the equilibrium with highest and lowest per capita capital is unstable when the model has three equilibria. Therefore, the economy described by them model has multiple growth pathes and appears ＂poverty trap＂.