论知识的资本依赖动力学
On Capital Dependent Dynamics of Knowledge
摘要：
我们研究的动力系统理论的增长模型的动力学。我们分析了知识的某些形式及其对经济增长的影响。我们假设知识的变化率取决于物质资本和人力资本的变化率。首先，我们研究了具有常数储蓄的模型。还考虑了优化的家庭行为的模型。我们证明了知识的变化率仅取决于物质资本的变化率的模型可以简化为二维自治动力系统的形式。详细讨论了所有可能的演化路径和解在相空间中的稳定性。我们得到，在资本依赖知识变化率的情况下，资本、消费和产出的增长率更大。
英文摘要：
We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of physical and human capital. First, we study model with constant savings. The model with optimised behaviour of households is also considered. We show that the model where the rate of change of knowledge depends only on the rate of change of physical capital can be reduced to the form of the two-dimensional autonomous dynamical system. All possible evolutional paths and the stability of solutions in the phase space are discussed in details. We obtain that the rate of growth of capital, consumption and output are greater in the case of capital dependent rate of change of knowledge.
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