Solvability of the Economic Input-Output Equation by Time Irreversibility

• 作者: Shinji Miura
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: INPUT-OUTPUT EQUATION SOLVABILITY TIME IRREVERSIBILITY TIME PARADOX
• 年，卷（期）: 2014,（3）
• 页码范围: 143-155
• 页数: 13页
• 分类号: O1

摘要

This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leontief type, and discusses its solvability. The equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. This condition means that commodities which a part of the relevant society possesses are not all inputted to its inside. Moreover, if the process of input and output is time irreversible, each part of the relevant society satisfies the space-time openness condition. Therefore, the solvability of the equation is guaranteed by time irreversibility. This proposition seems to be relevant to the grandfather paradox which is a type of time paradox.