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Existence and efficiency of general equilibrium with commodity money is investigated in an economy where N commodities are traded at N(N−1)/2N(N−1)/2 commodity-pairwise trading posts. Trade is a resource-using activity recovering transaction costs through the spread between bid (wholesale) and ask (retail) prices. Budget constraints, enforced at each trading post separately, imply demand for a carrier of value between trading posts. Existence of general equilibrium is established under conventional convexity and continuity conditions while structuring the price space to account for distinct bid and ask price ratios. Commodity money flows are identified as the difference between gross and net inter-post trades.

It is well-known that the Arrow–Debreu model of Walrasian general equilibrium cannot account for money. Professor Hahn (1982) writes “The most serious challenge that the existence of money poses to the theorist is this: the best developed model of the economy cannot find room for it. The best developed model is, of course, the Arrow–Debreu version of a Walrasian general equilibrium. A first, and …… difficult …… task is to find an alternative construction without …… sacrificing the clarity and logical coherence …… of Arrow–Debreu.” This paper pursues development of foundations for a theory of money based on elaborating the detail structure of an Arrow–Debreu model. The elementary first step is to create a general equilibrium where there is a well-defined demand for a medium of exchange—a carrier of value between transactions. This is arranged by replacing the single budget constraint of the Arrow–Debreu model with the requirement that the typical household or firm pays for its purchases directly at each of many separate transactions. Transactions take place at commodity-pairwise trading posts. Then a well-defined demand for media of exchange (commodity monies, not necessarily unique) arises endogenously as an outcome of the market equilibrium. The use of media of exchange is particularly evident when the structure of demands is characterized by an absence of double coincidence of wants (Jevons, 1875). Media of exchange are characterized as the carrier of value between transactions (not fulfilling final demands or input requirements themselves), the difference between gross and net trades1. Related general equilibrium models with transaction cost include Foley, 1970, Hahn, 1971, Hahn, 1973, Kurz, 1974, Starrett, 1973 and Starr, 2003c. The trading post model is intended to provide a parsimonious2 addition to the Arrow–Debreu model sufficient to generate a theory of money. The monetary structure of trade is shown to be a consequence of the price theory general equilibrium, not a separate assumption.

This essay creates a parsimonious model where a medium of exchange (commodity money) is an outcome of the (slightly augmented) Arrow–Debreu general equilibrium. The monetary structure of trade is a result of the price theory general equilibrium. Monetary trade is not a separate assumption; monetary exchange is an outcome, a direct implication of the general equilibrium when there are multiple distinct budget constraints facing each agent. The trades of firms and households in a trading post economy may be characterized by many separate transactions, each fulfilling a separate budget constraint. In an economy of N commodities there are N ( N − 1) / 2 trading posts, one for each pair of goods. The trading post model reformulates the budget so that each of many separate transactions fulfills its own budget constraint. This treatment generates a demand for carriers of value (media of exchange) moving among successive trades ( Starr, 2003a,b ). Virtually the same axiomatic structure ( Arrow and Debreu, 1954 ) that ensures the existence of general equilibrium in the model of a unified market without transaction costs yields existence of equilibrium and a well-defined demand for media of exchange in this disaggregated setting. Trading post equilibria are Pareto efficient when they are simply the elaboration of an underlying Walrasian equi- librium, an inessential trading post economy; see also Hahn (1973) . However, the multiplicity of separate budget constraints and the additional transaction costs incurred or avoided may skew the allocation and pricing (an essential trading post equilibrium). Then the equilibrium cannot be supported by a Walrasian price structure and the allocation will be Pareto inefficient; see also Starrett (1973) . The price system is informative not only about scarcity and desirability. It also prices liquidity. Transaction costs generate a spread between bid and ask prices at each trading post. The bid–ask spread tells firms and households which goods are liquid, easily traded without significant loss of value, and which are illiquid, unsuitable as carriers of value between trades, Menger (1892) . The multiplicity of budget constraints creates the demand for liquidity; the bid–ask spreads signal its supply. When liquidity is too expensive (example 10.5.2 ), media of exchange will not be used. When liquidity is inexpensive and helpful in achieving a Pareto improving allocation (example 10.3.1 ), media of exchange will be actively traded in equilibrium. The trading post model endogenously generates a designation and a flow of commodity money(ies). The existence of (commodity) money and the monetary structure of trade is an outcome of the general economic equilibrium. Money is not a separate assumption; it is a result of the equilibrium allocation.