R & D Subsidy Policy In Dynamic Economic Analysis

The improvement of technology is important in economics growth and the development of economy. As the source of the improvement of technology, Research and Development (R&D) is also important in business. At the same time, market power in such field makes not enough incentive because for the risk contained in the process of R&D. So fiscal policy is made to drive the optimal input of such field. As some works show, such policy works effectively at the right way. It's reasonable to make some research about the process of how to make such kind fiscal policy.In this paper, we study mainly how government officer use his finite resource to take the capital into the R&D, furthermore, to maximize the social welfare. We limit and divide the tools into the tax policy including consume tax and capital tax, unproductive public input, productive public input as the feedback of the R&D.It will take a long period to make the R&D which contains some risk of failure, so we must make such policy in a dynamic way. As the general equilibrium,we can let the manufacturer as the consumer. So the consumer is the executive of the R&D. It also can't be ignorant about that the consumer can make reaction such policy in a rational way. As the result of such reaction, such process can be divided into two stages---a Stackelberg game played by the officer as the leader and the consumer as the follower. And such process can also be a dynamic Principle-Agent problem in which the officer is the Principle and the other is the agent. The problem of Moral Risk may arise because the agent can change the use of the grant of R&D from principle, and the officer knows it may happen according with how it is in real world.On the foundation of such characters lists above, we develop a dynamic model in this paper. Under the help of Stochastic Dynamic Program, it separates the two maximization problems in classical P-A problem as two dynamic optimization processes. And solve it as how the Stackelberg does. Through the Comparative-Static-Analyses (CSA) of the solutions, we study how the officer decides the tax collection and public input to motive the input of R&D, and achieves the goal of economics growth and social welfare maximization. We find that the growth of capital tax can motives the input of R&D, to make the economy growth faster by increase the consumer tax makes social welfare as sacrifice.Then we give the initial idea of how to make the constraint of join if the agent has the power of bargaining with the officer.