The Study Of Nonlinear And Disequilibrium Cobweb Models

Usually, the stability of individual commodity market price fluctuation is studied based on supply-demand equilibrium, called as "Cobweb Model". The traditional cobweb models are presumed that the supply and demand curves are linear and supply is equal to demand. But in practical economic system, the two hypothesises are hard to reach. The "linear" hypothesis only can describe three kinds of economic movements, that is, convergence, divergence and the second cycle closed movement; but can't illustrate every kind of cycle movements and chaos, which are frequently happened. The "equilibrium" hypothesis can't describe the practical disequilibrium.So, in this paper, its main researches are to make use of both disequilibrium economics theory and chaotic economics theory to study the market price models; according to the economic movement, to improve the traditional cobweb models and set up nonlinear and disequilibrium cobweb models, which are more accurate, scientific, and able to describe practical economy; then to analyze commodity price fluctuation and stability on the established models with the change of the parameters; finally to draw some conclusions. These results are obtained by conducting strict mathematical inference. Therefore, the results are believable and consistent with the economic situation. The thesis is worthy of consulting not only for economic theory analysis but also for practical economic forecast. Thereby, this work is creative and meaningful.This thesis is scheduled as follows:Chapter One, Preface. Brief introduction of the ideas of the thesis and analysis method that includes the source of the title, theoretical significance and analysis method.Chapter Two, Fundamental knowledge and latest research of chaotic economics and disequilibrium economics. The main contents include: basic concepts of chaotic economics and disequilibrium economics with regards to the thesis; brief summary of the birth and development of chaotic theory; application achievements in economics of chaotic theory and disequilibrium theory.Chapter Three, Analysis on the generalized cobweb models. This chapter is one of the thesis's cores and keystones. The dynamic change and the stability of the generalized cobweb models such as Model One are studied, including setting up the models and giving the economic meanings; dynamic analysis on Model One and proving that the price array produced by Model One won't emerge above the third cycle movement and chaos; stability analysis on Model One and obtaining six theorems about the stability of equilibrium price.Chapter Four, Analysis on some specialized cobweb models. This is the second key part of the thesis. The main content is to study the stability of some cobweb models in which supply or demand curves are given nonlinear form. Researches on the stability are done and the existent conditions and stable regions about equilibrium price are obtained.Chapter Five, Application of Logistic equation in cobweb models. Evolutionmechanism of Logistic equation is studied, and is used in a kind of cobweb model. The stability and the characters are studied with the change of parameters. Finally the parameters' regions in which the economic system reaches the stability and the chaos are determined.Chapter Six, Analysis of Chinese marginal preference of consumption by the method of chaotic economics. In this chapter, chaotic economics theory is used to analyze the state of Chinese consumption system. Then a conclusion is drawn that Chinese consumption system is stable and the result is consistent with the economic situation.