Abstract
The essence of money circulation is that money continues to transfer among economic agents eternally. Based on this recognition, this paper shows a money circulation equation that calculates the quantities of expenditure, revenue, and the end money from the quantity of the beginning money. The beginning money consists of the possession at term beginning, production and being transferred from the outside of the relevant society. The end money consists of the possession at term end, disappearance and transferring to the outside of the relevant society. This equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. Moreover, if money is transferred time irreversibly, each part of the relevant society satisfies the space-time openness condition. Hence, the solvability of the equation is guaranteed by time irreversibility. These solvability conditions are similar to those of the economic input-output equation, but the details are different. An equation resembling our money circulation equation was already shown by Mária Augustinovics, a Hungarian economist. This paper examines the commonalities and differences between our equation and hers. This paper provides the basis for some intended papers by the author.
Highlights
Simon Newcomb, who was an American economist in the nineteenth century, said: “A piece of money changes hands without end, since every person who receives it expects, unless in exceptional cases, to pay it out again to some one else.”1How to cite this paper: Miura, S. (2014) Money Circulation Equation Considering Time Irreversibility
Any money expended, received as revenue and included in the end money seems to come from the beginning money, which consists of the possession at term beginning, production and transferred from the outside
If the money circulation equation has a unique solution, each expenditure quantity can be calculated from the expenditure rate, the distribution rate and the beginning money
Summary
Simon Newcomb, who was an American economist in the nineteenth century, said: “A piece of money changes hands without end, since every person who receives it expects, unless in exceptional cases, to pay it out again to some one else.”. If we trace the source of money expended in the relevant space-time, it is only either received as revenue or included in the beginning money We call this the disposal comprehensibility principle. If we trace the result of money received as revenue in the relevant space-time, it is only either expended or included in the end money. Ρk refers to the quantity of money disposed from revenue to expenditure, and βk refers to the quantity of money disposed from revenue to the end money Considering both the disposal comprehensibility and exclusivity principle, Yk = ρk + βk for ∀k ∈ N is satisfied. The relationships between the disposal quantities and others are summarized in the following table
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