Unified money circulation equation and an analogical explanation for its solvability

The equation of exchange is well-known as a quantitative expression of money circulation, but it has a defect in that the relation between the velocity of money and the situation of economic agents is not clear. This paper attempts to found the velocity which pays attention to movement of money. For that purpose, this paper shows a money circulation equation in which agents of the whole society are unified. If this equation has a unique solution, the velocity of money is reduced to the expenditure rate of the whole society. Thereby, the defect of the equation of exchange can be remedied. Our attempt can be interpreted as connecting the velocity of money with the multiplier analysis. Success or failure of the trial depends on its solvability. This solvability problem of the money circulation equation is closely related to the missing problems of the monetary budget constraint. This paper also attempts to explain the missing problems in the case of the budget constraint of the whole society. This paper explains that a time irreversible disposal solves those problems by using an analogy