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Administrative Management Agency and Other Six Authorities of Japan (1970) The Work Report of Making the Modified Input-Output Table in 1960 and the Price Evaluation Table in 1965. Hitachi Kosoku Insatsu K.K., Hitachi. (In Japanese)

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• TITLE: Solvability of the Economic Input-Output Equation by Time Irreversibility

  AUTHORS: Shinji Miura

  KEYWORDS: Input-Output Equation, Solvability, Time Irreversibility, Time Paradox

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.4 No.3, August 26, 2014

  ABSTRACT: 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.