Global Stability and Dynamic Analysis for a Type of Macroeconomic Systems

Abstract

This paper aims at the dynamic properties of the proposed globally planned economic systems named after CPE proposed by Loo-Keng Hua who is one of the worldwide famous Chinese mathematicians. First, we give new existence conditions of growth balanced solution to the model. Second, we lead into the concept of stability for balanced output and carry out a theorem that deals with some equivalent conditions for judging a solution of output starting from the fact that any initial input can whether approach the existing balanced solution or not. Third, a new dynamic price system related to interest factors is proposed here and it is demonstrated that the new price equation is a much generalized one in comparison with the original price one which is only a special case of this new price equation. Also, relationships of the balanced solutions between the price and the output equation are investigated and the stability analysis is studied as well for the new price system. Finally, two examples are employed to illustrate the technical operation of input-output method and some new contributions of this article.