Modeling The Minimum Time Needed To Economic Maturity

A general equilibrium model has been constructed in a stochastic endogenous growth economy with the capital-labor ratio driven by an Itô-Lévy diffusion process. In particular, formal definition of the minimum-time needed to economic maturity is identified in the model and closed-form solutions of optimal savings strategy and optimal tax rates are established when the representative agent is assumed to exhibit log preference and there is a benevolent government in the economy. Moreover, the minimum-time needed to economic maturity is explicitly derived in the sense of sub-game perfect Nash equilibrium and one can further proceed to comparative static analysis with respect to the relevant parameters of the underlying economy such as the subject discount factor, the initial level of capital stock per capita, the utility-optimal and sustainable terminal path level of capital stock per capita, the natural growth rate of population, and the exogenous level of government spending. Finally, it is worth emphasizing that we focus on underdeveloped economies such as China and the present exploration presents a baseline mathematical model for studying the optimal policies needed to reach economic maturity as soon as possible.