Dynamic Analysis Of Several Classes Of Business Cycle Models With Time Delays

Today, in the world's financial crisis, laissez-faire of the economy has been questioned. The regulation of government policies and its supervision has become more and more important. Investment and taxes are two kinds of essential tools in the regulation of the government's policy, however, there exists time delay in every implementation process. These questions about the thorough knowledge of those time delay processes, how it affects the macroeconomic operation and how to avoid a long delay, have important theoretical value and practical value both in theoretical economics and positive economics. This paper, based on several business cycle models, considering time delay(wherever in capital accumulation or tax collection, whatever fixed or distributed time delay) into business cycle system, will explore the impacts of time lags on the economic system by employing Routh-Hurwitz criterion, stability switch theorem, Hopf bifurcation theory and so on. The essays is divided into six chapters.In the first chapter, this paper first reviews the history of researches on business cycles, several types of major dynamic business cycle models, then introduces the history of dynamic analysis methods of several business cycle models. At the same time, the innovations in this thesis are also briefly introduced in this chapter.In chapter two, by considering the dynamic macroeconomic model with fixed delayed time in capital accumulation, which is based on Samuelson-Hicks's dynamic multiplier-accelerator model, We show that the time lag can cause business cycles by applying linear stability method and Hopf bifurcation, and finally the numerical examples are given.In chapter three, on the basis of the model in chapter two, we consider the stochastic dynamic economic model with both time lag in capital accumulation and time lag in tax collection, then follow the method of Ruan & Wei and Nisbet's relative works, we can obtain that every fixed time delay and random variables will have an effect on the stability of economic system.In chapter four, we take into consideration a more realistic exponential distribution in the time delay of tax revenue, we introduce the exponetially distributed time delay, namely, there are different time delays in lots of heterogeneous organizations or companies, comparing with those homogeneous companies which have the same time delay. We prove that the distributed delayed time changes the stability of economic system, the fixed time delay will dominant the stability of the economic system. The numerical simulation is in accordance with theoretical results.In chapter five, while considering the discrete time lag in capital accumulation, we investigate generalized IS-LM model with four equations after adding the capital accumulation equation on the dynamic IS-LM model with the constraint of government expenditure. Through the application of Hopf bifurcation theorem, normal form method and the center manifold theory, we prove the existence, uniqueness, direction and stability of the business cycle.In chapter six, based on Gabisch & Lorenz and Boldrin's related essays of augmented IS-LM model, we then assume that the investment function will depend on the income in the past and also the capital stock in the past but with different past time, we construct the augmented IS-LM model with two fixed different time lags, dynamically analyze the impacts of the time lags on the dynamic model, in which we will analyze the direction and stability of the business cycle.