Money circulation and debt circulation: A restatement of quantity theory of money

Both money and debt are products of credit creation of banks. Money is always circulating among traders by facilitating commodity transactions. In contrast, debt is created by borrowing and annihilated by repayment as it is matured. However, when this creation- annihilation process is mediated by banks which are constrained by a credit capacity, there exists continuous transfer of debt among debtors, which can be defined as debt circulation. This paper presents a multi-agent model in which income determination, credit creation, and credit transaction are integrated. A hypothetical economy composed of a banking system and multiple traders is proposed, in which the traders are allowed to borrow money from the bank once their expenditure cannot be financed by their own funds. In order to demonstrate the circulations of money and debt from the micro view, the authors track the transfer processes of them and collect their holding times respectively. When the traders could afford their expenditures, only money circulation can be observed. However, as they are forced to borrow, the money circulation is accelerated and debt circulation emerges. Both distributions of holding times of money and debt are found to take exponential form due to the random nature of exchanges. The velocity of money circulation is determined by the expending behavior of traders, while the velocity of debt circulation is associated with the repayment behavior of debtors. Consequently, the aggregate income can be decomposed into two parts: one comes from money circulation and the other from debt circulation.