A Control Model Research On Economic Growth

Economic growth is extremely concerned by many people in various countries of the contemporary world. All the government regards it as an economic index at the time of making policy. The public generally thinks that economic growth is a prerequisite of the national welfare and prosperous economy, a good recipe curing economic diseases. Because economic growth is so important that more and more people put their attention into research on it. Therefore study in both economic growths has significance on theory and practice for our country's to grow economy at a speedy, steady and lasting pace.Many experts have made a lot of studying on economic growth. They set up their own theory and model by means of econometrics, or economic cybernetics and so on. They hope that they can reveal its mechanism and relations among factors with the help of mathematics tool describing and studying economic system quantitatively. Economic system is an evolutive complex system and is regarded as a birth and death system. According to the thought and method of system science, economic growth is studied qualitatively and quantitatively.Dynamic process of forming and operation of capital is regarded as a birth and death process. A continuous function with two variables is related to time as well as enlistment age of the capital. Stock of the capital and level of consumption are regarded as state variables of the economic system. Workforce and technological progress functions are regard as exogenous variables. Accumulation rate is used to control investment scale. A distributed parameter model of macroeconomic system is set up by way of cybernetics.Drawing lessons from research results of forefathers, and with different production functions as their feedbacks, a series of control models of macroeconomic system is set up. The models can be used to adjust and control the economic system by forming close ring control system of the dynamic development of the capital on one hand. On the other hand, the models can be used to study the economic growth by forming two variables dynamic production function. Then solution of the model's existence and uniqueness, and correlative natures with initial and boundary conditions are discussed, thus theoretical foundation of model for further research and calculation is established.Finally, interaction of technological progress and the economic growth is studied qualitatively and quantitatively. The result shows: Technological progress plays an important role in economic growth and has a secular trend of stably rising. The result is the same as that coming from C—D production function model. The model is proved from both theory and reality, and offers basis for economic policy making and macro adjusting and controlling in the future.The main innovation of this paper is as follows:(1) Economic system is regarded as an evolutive complex system on macroscopical level. Regarded as a birth and death system, economic growth is studied by utilizing the thought and method of systematic science. The thought and method is different from other research.(2) Set up a control model of macroeconomic system described with distributed parameter. A continuous function with one pair of variables is introduced, not only related to time of the capital but also to its enlistment age. The model portray economic system more carefully than other model that have only the variable of time. The model described by distributed parameter model can reflect the nonlinear characteristic of the complex system.(3) Different production functions are used as feedback in the system control. The close ring control system can adjust and control economic system, and make economic increase stably, continuously.(4) Result calculated with discrete model is basically the same as that using C —D production function. It illustrates sufficiently that technological progress has a secular trend of stable rises in economic growth. Realizing the long-term influence of technological progress in the economic growth more clearly.