Deterministic and Stochastic Three-Sector Dynamic Growth Model with Endogenous Labor Supply

This paper explores the stability of the stationary state for a dynamic growth model with wealth and human capital accumulation. Knowledge is created through research and learning-by-doing, while the time allocation between labor and leisure is endogenized. We analyze the model in both its deterministic and stochastic versions. First, we describe the deterministic model and analyze the stationary state. Second, using the stationary state, we define the stochastic perturbation and study the mean and squared mean values of the system states for the linearized model. Third, we prove that for certain parameters, the stationary state is asymptotically stable both in the deterministic and the stochastic model. Finally, we perform the comparative dynamic analysis for the propensities to save and to enjoy leisure, the tax rates used to finance research, and the knowledge utilization efficiency