Research On Differential Dynamical Macro-finance Models With Non-symmetrical Information

Dynamical macro-finance models are efficient approaches to master macro-finance situation through the study of running laws and interrelations of macro-economic variables, which are quite useful for corresponding departments of a government to manage concrete macro-economy with the use of economic levers and directive plans. Aimed at problems of central bank's monetary policy and nominal stock of debt with non-symmetrical information, a kind of dynamical macro-finance model is built in this paper by analyzing public inflation expectations. Some dynamical and economic results are -obtained after extensive analyzing the models with system dynamic theory. Firstly, dynamical property at the equilibrium points of model (Ml) is discussed; a sufficient and necessary condition of the stability at equilibrium points is given out; the stable manifold and the unstable manifold of the simplified model are found. Secondly, the model (M2) has one parameter period solution when it has a pair of pure imagine eigenvalue and its period value is obtained. Moreover, the condition of occurring Hopf bifurcation and property of Hopf bifurcation at the bifurcation value are discussed. When an eigenvalue of the system is zero, the model experiences a transcritical bifurcation at the equilibrium points as the parameter varies through the equilibrium value. Thirdly, when money growth rate and stock of debt both keep steady, there may occur somecatastrophe phenomena of pubic inflation expectations if pubic inflation expectations are simulated by polynomial function.Finally, equilibrium values of games between policy makers and the public are found. Monetary policy effects are compared when policy makers adopt discretion or singleness policy. Monetary policy correlated to motivation of budget financing and nominal debt has inflation tendency and the tendency is endogenie. If money growth rate is higher, the public will increase their inflation expectations and higher inflation or inflationary spiral may happen, thereby money policy will be in hot water. Importance to keep away finance crisis is pointed out.