Monetary Theory of Macro Accounting for Supply Chain Finance

We present a monetary theory where money is taken primarily as a medium of debt repayment and not as a medium of exchange. Money and products are exchanged in reciprocal contracts of disposals of property rights within two-sided obligation contracts. Money demand arises because production takes time and producers need to pay suppliers of resources before they are paid at markets for their products. Accordingly, money is part of monetary systems of macro accounting for supply chain finance where producers are exchanging their products for money in order to repay loans of investments. We take advantage of two legal principles of separation and abstraction in order to clarify the concepts of obligations, debts, claims, disposals, property rights or money. Monetary systems exist to organise the division of labour at the micro level of economies. At the meso level of banking money helps to organise the sharing of risks from investments. At the macro level monetary systems help to distribute the product of the common productive effort (GDP). We analyse macro (aka quadruple accounting) systems composed as parallel bookings in one or more micro (aka double) accounting systems of the agents exchanging products and money in networks of obligations created by contracts. We use the Bill of Exchange (BoE) as the financial instrument to unify views on paper, gold and fractional monetary systems and to understand how to book money creation at central banks. We propose to keep track of invariances of accounting systems over micro, meso and macro levels of economies by sheaf theory and homology theory to detect and resolve inconsistencies as the mathematical foundation of monetary policy. We discuss open games as an implementation technology for monetary macro accounting (MoMa) systems in reduced form (Markov) models and for the analysis of data for a structural analysis by models of belief formation or multi-agent systems. We also discuss industrial applications of our monetary theory.