Solvability of the Economic Input-Output Equation by Time Irreversibility

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.

Money Circulation Equation Considering Time Irreversibility

“…If you compare this paper with Miura [13], you will notice that the proof for the solvability of the money circulation equation is similar to that of the economic input-output equation. However, the details are different.…”

“…Hence, E µ − Θ is a Z-matrix, which is defined as a square matrix in which the non-diagonal elements are all non-positive. Moreover, we can obtain 0 ψ Θ ≥ from Equations ( 6) and (13). Considering this with Equation ( 5), we find that ( )…”

“…Her work may be affected by the economic input-output theory invented by Wassily Leontief. 13 When she disclosed this equation, Hungary was still under a planned economy, and the central bank of Hungary had a monopolistic control of credit and money circulation. Under such a situation, while working at Hungarian Planning Office, she showed her money circulation equation in order to support an economic planning.…”