The Government Expenditure And Taxes Of Stochastic Models For Continuous Time

The government in the economy society plays an important role, it bears many responsibilities. Revenue and expenditure plans are very important aspects of the government work, they influence and restriction each other in the quantity. They also play an extremely important role in the operation and development of national economy. From the angle of the econometric, the research of taxes and government expenditures will help us further explores the essential relation between them and better optimized tax and service to economic construction.This first part introduces the problem and its significance, and the development of the theory of optimal taxes. The second part was introduced emphatically to some knowledge about economics and time series analysis which used in, including difference equations and several classic theorem, etc. It also introduced the related conclusions of the basic random process (Brownian movement). Finally, it introduces the utility function and general stochastic optimization method for establish and solution model. In the third part of the article, it introduces a discrete time optimal tax model which put forward by Robert J. Barro in 1979, and then it introduces the improve results after differentiation in government spending.In the fourth part, according to the theory of optimum decision-making consumption model (Ramsey model), from the angle of the government, a continuous random tax model was established in stochastic optimization method into random item within the framework of the model and to promote the continuous time. Then the optimal solutions were obtained in two kinds of utility function of use of stochastic analysis of related knowledge for the simplified model.