2000-25r University of California, San Diego Department of Economics Why Is There Money? Endogenous Derivation of 'money' as the Most Liquid Asset: a Class of Examples

The monetary character of trade, the existence of a common medium of exchange, is derived as an outcome of the economic general equilibrium in a class of examples. Two constructs are added to an Arrow-Debreu general equilibrium model: market segmentation with multiple budget constraints (one at each transaction) and transaction costs. The multiplicity of budget constraints creates a demand for a carrier of value between transactions. A common medium of exchange, money, arises endogenously as the most liquid (lowest transaction cost) asset. Government-issued fiat money has a positive equilibrium value due to its acceptability in payment of taxes. Scale economies in transaction cost account for uniqueness of the (fiat or commodity) money in equilibrium. The monetary structure of trade and the uniqueness of money in equilibrium can thus be derived from elementary price theory. Why Is There Money? Endogenous Derivation of 'Money' as the Most Liquid Asset: A Class of Examples Revised October 30, 2001 Ross M. Starr University of California, San Diego I. Money in Walrasian General Equilibrium Consider three commonplace observations on the character of trade in virtually all economies: (i) Trade is monetary. One side of almost all transactions is the economy's common medium of exchange. (ii) Money is (virtually) unique. Though each economy has a 'money' and the 'money' differs among economies, almost all the transactions in most places most of the time use a single common medium of exchange. 1 This paper has benefited from seminars and colleagues' helpful comments at the University of California Santa Barbara, University of California San Diego, NSF-NBER Conference on General Equilibrium Theory at Purdue University, Society for the Advancement of Behavioral Economics at San Diego State University, Econometric Society at the University of Wisconsin Madison, SITE at Stanford University, Federal Reserve Bank of Kansas City, Federal Reserve Bank of Minneapolis, Midwest Economic Theory Conference at the University of Illinois Urbana Champaign, University of Iowa, Southern California Economic Theory Conference at UC Santa Barbara, Midwest Macroeconomics Conference at University of Iowa, University of California Berkeley, European Workshop on General Equilibrium Theory at University of Paris I, Society for Economic Dynamics at San Jose Costa Rica, World Congress of the Econometric Society at University of Washington, Cowles Foundation at Yale University, and from comments of Meenakshi Rajeev. Remaining errors are the author's. 1 (iii) 'Money' is government-issued fiat money, trading at a positive value though it conveys directly no utility or production. Where economic behavior displays such uniformity, a general elementary economic theory should be able to account for the universal usages. But each of these three observations contradicts the implications of a frictionless Walrasian general equilibrium model. This essay presents elementary structure in that model sufficient to derive points (i), (ii), and (iii) as outcomes. In doing so, this essay responds to a challenge expressed by Tobin (1980) Barter would restrict transactions to "double coincidences of wants" ... [This] insight tells us why the social institution of money has been observed throughout history even in primitive societies. An insight is not a model, and it does not satisfy the trained scholarly consciences of modern theorists who require that all values be rooted, explicitly and mathematically, in the market valuations of maximizing agents... Social institutions like money are public goods. Models of general equilibrium --competitive markets and individual optimizing agents---are not well adapted to explaining the existence and quantity of public goods... General equilibrium theory is not going to explain the institution of a monetary ... common means of payment. Thus the examples below are intended to satisfy our 'trained scholarly consciences' and to show that a general equilibrium model can explain endogenously from price theory the institution of a common monetary means of payment. The price system itself designates 'money' and guides transactors to trade using 'money.' The model emphasizes complete 2 A bibliography of the issues involved in this inquiry appears in Ostroy and Starr (1990). In addition, note particularly Banerjee and Maskin (1996), Hellwig (2000), Howitt (2000), Howitt and Clower (2000), Iwai (1996), Kiyotaki and Wright (1989), Marimon, McGrattan and Sargent (1990), Rey (2001) and Young (1998). The treatment of transaction costs in this essay (as opposed to the recent focus in the literature on search and random matching equilibria) resembles the general equilibrium models with transaction cost developed in Foley (1970), Hahn (1971), and Starrett (1973). The structure of bilateral trade here however is more detailed, with a budget constraint enforced on each transaction separately, so that the Foley, Hahn, and Starrett models do not immediately translate to the present setting. 2 markets and complete information. The examples --as distinct from random matching models --include no uncertainty in transactors searching for matching trades. It is well known that a frictionless Arrow-Debreu model cannot accomodate a role for money. This essay is intended as a partial counterexample, demonstrating that minimal friction in trade is sufficient to induce the existence of money as a result, not an assumption. Indeed prices specify which good acts as 'money.' The monetary structure of the economy is derived from elementary price theory in a class of examples. Use of a common medium of exchange, a commodity money, is an outcome of the market equilibrium. Starting from a (non-monetary) Arrow-Debreu Walrasian model, the monetary quality of the economic equilibrium is derived through the addition of two constructs: market segmentation with multiple budget constraints (one at each transaction) and transaction costs. Transaction costs imply differing bid and ask prices for each good. Commodity money arises endogenously (without government intervention or designation as legal tender) as the most liquid (lowest transaction cost or narrowest bid/ask spread) asset. Fiat money --issued by government --derives its positive value from acceptability in payment of taxes; it becomes the common medium of exchange from its low transaction cost. Uniqueness of (fiat or commodity) money, uniqueness of the common medium of exchange in equilibrium, follows from scale economy in transaction costs. There is a fourth, less commonplace, observation that turns out to be a significant guide to modeling: (iv) In a monetary economy, even transactions displaying a double coincidence of wants are transacted with money. Because transactions involving a double coincidence of wants are relatively rare, this characterization of trade is less obvious. Nevertheless, University of California faculty whose children are enrolled at the University pay the student fees in money, not in kind; Ford employees buying a Ford car pay for the car in money, not in kind; Albertson's supermarket checkout clerks acquiring groceries pay for their food in money, not in kind. 3 Confirmed in telephone conversation with public relations offices at Ford and Albertson's. The public relations officers the author spoke to expressed some surprise at the notion that academic economists entertained the view that these trades would be made 3 This observation suggests that the focus on the absence of double coincidence of wants --as distinct from transaction costs --as an explanation for the monetization of trade may miss a significant part of the underlying causal mechanism. Section III of the paper presents the model of segmented markets with linear transaction costs without double coincidence of wants, in a class of examples. Commodity money is endogenously chosen in market equilibrium as the lowest transaction cost (narrowest bid/ask spread) commodity. Section IV demonstrates that the absence of double coincidence of wants is essential to monetization of trade in a linear model by considering the same problem with full double coincidence of wants. The result is a nonmonetary equilibrium. Section VI considers a (nonconvex) transaction technology with scale economies. The examples there demonstrate that uniqueness of money (uniqueness of the endogenously chosen medium of exchange) results from scale economies in transaction costs. Further, Section VI demonstrates that scale economies in transaction cost account for monetization of trade with a unique 'money' even when there is full double coincidence of wants. Section VII considers government-issued fiat money whose value is supported by acceptability in payment of taxes. In a linear transaction cost model, fiat money's (assumed) low transaction cost makes it the common medium of exchange. Alternatively, in a nonlinear model, scale economies in transaction cost and government's large scale ensure that fiat money is the unique common medium of exchange. Distinguishing Models of Money: Random Matching/Search versus General Equilibrium with Transaction Cost Random matching/search models of monetary economies, typified by Kiyotaki and Wright (1989, 1991) and by Trejos and Wright (1993, 1995), endogenously generate a medium of exchange function. They have recently been the most prominent and successful formal models to do so. They display distinctive elements differing from monetary general equilibrium models, Starrett (1973), Ostroy and Starr (1974), Iwai (1996), including this essay. Random matching models do not represent organized markets. Agents meet to trade in isolation, recognizing that subsequent opportunities to