Graph representation of balance sheets: from exogenous to endogenous money

A graph representation of the financial relations in a given monetary structure is proposed. It is argued that the graph of debt-liability relations is naturally organized and simplified into a tree structure, around banks and a central bank. Indeed, this optimal graph allows to perform payments very easily as it amounts to the suppression of loops introduced by pending payments. Using this language of graphs to analyze the monetary system, we first examine the systems based on commodity money and show their incompatibility with credit. After dealing with the role of the state via its ability to spend and raise taxes, we discuss the chartalist systems based on pure fiat money, which are the current systems. We argue that in those cases, the Treasury and the central bank can be meaningfully consolidated. After describing the interactions of various autonomous currencies, we argue that fixed exchanged rates can never be maintained, and we discuss the controversial role of the IMF in international financial relations. We finally use graph representations to give our interpretation on open problems, such as the monetary aggregates, the sectoral financial balances and the endogenous nature of money. Indeed, once appropriately consolidated, graphs of financial relations allow to formulate easily unambiguous statements about the monetary arrangements.