Solvability of the Economic Input-Output Equation by Time Irreversibility

Shinji Miura

doi:10.4236/alamt.2014.43013

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.

Highlights

IntroductionIf we trace the source of commodity inputted in the relevant space-time, it is only either outputted or carried
The purpose of this paper is to clarify a solvability condition of the economic input-output equation which was invented by Wassily Leontief
Economic input-output analysis is affected by equilibrium economics, which is the mainstream of contemporary economics

Summary

Introduction

If we trace the source of commodity inputted in the relevant space-time, it is only either outputted or carried. We call this the disposal comprehensibility principle. If we trace the result of commodity outputted in the relevant space-time, it is only either inputted or becomes surplus. Ρk refers to the quantity of commodity disposed from output to input, and βk refers to the quantity of commodity disposed from output to surplus Considering both the disposal comprehensibility and exclusivity principle, Yk = ρk + βk for ∀k ∈ N is satisfied. The relationships between the disposal quantities and other quantities are summarized in the following table

Result

Formalization of the Economic Input-Output Equation

Solvability Condition of the Economic Input-Output Equation