Walrasian General Equilibrium Foundations of Monetary Theory
Chapter 11: Commodity Money Equilibrium in a Convex Trading Post Economy
11. Commodity money equilibrium in a convex trading post economy1 Sufficient conditions for existence of general equilibrium with commodity money in the trading post model of Chapter 3 are developed in this chapter. N commodities are traded at 1 N (N 2 1) commodity-pairwise 2 trading posts. Trade is a resource-using activity located in optimizing firms recovering transaction costs through the spread between bid and ask prices. Budget constraints, enforced at each trading post separately, imply demand for a carrier of value between trading posts. General equilibrium exists under conventional convexity and continuity conditions while structuring the price space to account for distinct bid and ask prices. Commodity money flows are identified as the difference between gross and net inter-post trades. 1 THE ABSENCE OF MONEY IN THE ARROW2DEBREU MODEL It is well known that the Arrow2Debreu model of Walrasian general equilibrium cannot account for money. One of the leading achievements of the Arrow2Debreu model is to characterize and demonstrate existence of the general equilibrium under a broad array of weak sufficient conditions. Though this volume presents a variety of examples of general equilibrium in the trading post model, they are just examples. Is there a family of weak sufficient conditions so that the trading post model has an equilibrium? Is there then a role for medium of exchange, a commodity money? What is the problem with the Arrow2Debreu model? Why can it not account for money? There are two big reasons. One is that all trade takes place at...
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