Endogenizing the provision of money: Costs of commodity and fiat monies in relation to the value of trade

We consider the problem of including the costs and value of the institutions that define money and support trade, within the framework of economic optimization. We compare monetary systems mediated by durable commodity monies, versus pure fiat monies, in order to understand the separation and eventual independence of the institutionally-created value of money from the values of underlying traded goods. We treat the emergence of monetary function as a problem in mechanism design, modeled by minimal strategic market games that overcome a generalized Jevons failure when agents must commit ahead of time to specialist resource production. We consider in particular the problem of defining closures with respect to both money flows and labor-allocation and trading decisions, and show that minimal models require many of the fundamental institutions of banking and contract enforcement found in real economies, in order to define a self-policing system. We define costs, value, and the efficiencies of the institutions that support trade in terms of a natural money-metric welfare function, and compare the characteristics of commodity and fiat monies by these measures. Through careful treatment of the stock/flow distinction in repeated-game settings, we find that commodity money, even when its value derives heavily from its institutional role, remains defined by its flow characteristics, in contrast to fiat money, for which the control function is defined inherently in terms of stock variables. Our notation is somewhat nonconventional for economics but to do justice to econo-physics concepts such as scaling and dimensional analysis and to stress the distinction between stocks and flows, we believe this notation is justified. We provide a full listing of notation in .