Research on applications of linear system theory in economics

Abstract

It is well known that the basic researches about linear systems are the most and the simplest ones and that linear systems are widely applied in many subjects including economics. Based on Input-Output Analysis, a country's economy can be considered as a complex system that could be described by mathematical and linear models. Then the linear economic models could be analyzed using linear system theory and Positive Eigenvector Method suggested by Luogeng Hua. For closed and dynamic economic system, the conclusion is that it is not stable but active. For a kind of open linear economic system, it is active if and only if the gross input coefficient should be bigger than a limit. However active economic system does not mean growing. To ensure the economic system growing, two conditions are necessary and sufficient. One is the gross input coefficient should be bigger than another limit, and the other condition is that it should be linear correlation between the original input structure and the positive right eigenvector of the direct consumption coefficient matrix. In an empirical analysis for China between 1987 and 2007, results are calculated for the biggest eigenvalues of the direct consumption coefficient matrices.