The Optimal Tax In Economic Growth Models

This paper establishes two classes of economic growth model and studies the problems of the optimal tax based on this model.The first class of model is the endogenous economic growth model that brings the government behaviors into the classical Ramsey-Cass-Koopmans model. In this model, we discuss the effect of tax policy on economic growth on the condition of market competitive equilibrium. Two chief conclusions are drawn: firstly, when the government has carried out steady tax policies, for consumers there exists unique optimal capital stock path along which economy can grow sostenuto and steadily; when the tax path given by the government converge to some constant tax rate, there still exists one capital stock path which can make the whole economy grow gradually and converge evenly to the optimal state. Secondly, the optimal tax path has turnpike property. That is, all optimal tax paths will converge to the gold rule tax rate (the tax rate which makes economy lie in the steady and optimal growth state), by which the government may adjust the tax policies. When the value of some term of tax plan the government has set down is far lower than (or far higher than) the gold rule tax rate, It benefits for economic growth to improve (or decrease) properly tax.The second class of model is stochastic equilibrium model. As is well known, the problems of economic growth are tied closely up with the government behaviors. However, in the documents about government optimal behaviors, determined models are the most popular, such as the classical Mirrlees model. From these models people have drawn a series of richtheories about public sector optimal mechanism. However, the government behaviors are always objected to the effect of many uncertain factors. Therefore, determined models can't reflect fully the economic behaviors in reality. In order to keep closer to the reality, this essay establishes a stochastic equilibrium model, which essence is the classical Mirlees tax model.Based on this model, we studies the simultaneous existence of the agent's optimal capital stock and income, the government's optimal tax and public expenditure (We call the combination as an equilibrium mechanism), This essay draws the equivalent proposition of equilibrium mechanism existing and converts the former problem into another problem of selecting public sector mechanism that only includes the government behavior. So the existence of such as the optimal tax has been showed. Here, the functional smooth property isn't required and what is only required is its continuity. The classical Mirrlees tax model is a particular example of this essay when the state is given. But there are minute differences that Mirrlees has taken the public spending as variables given exogenously and instead I regard it as endogenous variables that need be optimized and selected by government. Besides the existence, this essay also draws the conclusion that the optimal income tax function is lowers semicontinuous on a closed subset of the Hilbert space.