SPDAs and GICs: Like Money in the Bank? (p. 2) Richard M. Todd Neil Wallace
Acceptability, Means of Payment, and Media of Exchange (p.18) Nobuhiro Kiyotaki Randall Wright Federal Reserve Bank of Minneapolis Quarterly Review Vol. 16, No. 3
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Acceptability, Means of Payment, and Media of Exchange*
Nobuhiro Kiyotaki Randall Wright Visitor Adviser Research Department Research Department Federal Reserve Bank of Minneapolis Federal Reserve Bank of Minneapolis and Professor of Economics and Professor of Economics University of Minnesota University of Pennsylvania
Arguably the most important function of money is its role ductive input, at least potentially. A fiat money is an ob- as a medium of exchange. Wicksell ([1906] 1967, p. 15) ject used as a medium of exchange that will never be used defined a medium of exchange to be "an object which is as a consumption good or a productive input. More pre- taken in exchange, not on its own account, ... not to be cisely, Wallace (1980) defines fiat money to be money consumed by the receiver or to be employed in technical that is intrinsically useless and inconvertible. Intrinsic use- production, but to be exchanged for something else within lessness refers to the property that the object will never be a longer or shorter period of time." He further defined a used as a consumption good nor as a production good, general medium of exchange to be an object "which is while inconvertibility refers to the fact that it is not backed habitually, and without hesitation, taken by anybody in by something that has intrinsic worth. Von Mises ([1912] exchange for any commodity" (Wicksell [1906] 1967, p. 1934) provides an early discussion of the threefold classi- 17). Related notions include a means of payment, which fication of economic objects into consumption goods, pro- is an object used to pay for purchases and settle debts, and duction goods, and media of exchange. Many objects, in- a general means of payment, which is an object that can cluding any commodity money, for example, can play always be used to pay for any purchase or settle any debt. more than one role; but fiat money by definition is only There could be circumstances where the concepts of a medium of exchange and never a consumption or pro- means of payment and media of exchange differ. For ex- duction good. ample, there could be legal restrictions that imply taxes A natural question is, What makes an object more or are payable in some object, which would make it a means less desirable as a medium of exchange? A related but of payment, at least for tax purposes, but this would not different question is, What makes an object more or less necessarily mean that it is accepted as a medium of ex- likely to become a medium of exchange? Textbook dis- change by private agents. Nevertheless, for the purposes cussions describe many of the intrinsic properties of ob- of this essay, we will ignore such circumstances and use jects that make them desirable media of exchange or mon- the terms means of payment and media of exchange in- ey, such as storability, recognizability, durability, divisibil- terchangeably. We are mainly interested in which sorts of ity, and so on. In addition to these intrinsic properties, objects will be used as media of exchange and in what Menger (1892) also emphasized what he called "saleabili- circumstances. Objects and Circumstances *This essay is reprinted, with the publishers' permission, from The New Palgrave A commodity money is an object used as a medium of ex- Dictionary of Money and Finance, ed. Peter Newman, Murray Milgate, and John Eat- change that also has use as a consumption good or a pro- well; London: Macmillan Press, New York: Stockton Press. © Macmillan Press 1992.
18 Nobuhiro Kiyotaki, Randall Wright Acceptability
ty," or what we call acceptability. We define the accept- agents with consumption goods and the rest of the agents ability of an object here to be the probability that it is with an intrinsically worthless object that we call money. accepted in exchange by other agents at a given price. Let M be the fraction of agents endowed with money, and (Whether or not an object is accepted can depend on the assume for simplicity that this money object is also indi- amount offered—for example, it may be difficult to buy visible and that each agent endowed with it is endowed a package of cigarettes in England with U.S. dollars at the with exactly one unit. Agents meet bilaterally and at ran- official exchange rate, although perhaps not if one is will- dom once each period and trade if and only if it is mu- ing to pay a sufficient dollar price—but we will ignore tually advantageous. However, there is a transaction cost this here by taking price as given; see Lippman and in terms of disutility, denoted by 8, that is incurred by the McCall 1986.) receiver whenever that agent accepts any consumption When an object is more readily acceptable to other good in trade. For simplicity, there is no transaction cost people in the economy, it is more likely that each individ- to accepting money here, but this is not essential. (See ual will desire it and accept it as a medium of exchange. Kiyotaki and Wright 1991.) The implication is that the property of acceptability can We seek Nash equilibria in trading strategies, in which have a self-reinforcing nature. Of course, acceptability de- each agent chooses whether to trade or not in order to pends on time, place, and circumstance and is not con- maximize the expected discounted utility of consumption stant. For example, it is hard to buy cigarettes late at night net of production and transaction costs, taking the trading with a large-denomination U.S. bill even in the United strategies of other agents as given. Here we focus on States. Also, things that serve as fiat or commodity money steady-state equilibria, where things do not change over in one place or time need not serve as money at other time, and also on symmetric equilibria, where no agent or places or times, as history illustrates. good is treated differently from any other. A property of These observations lead to the conclusion that accept- such an equilibrium is that agents trade one commodity ability may not actually be a property of an object as for another commodity if and only if the latter is one of much as it is a property of social convention. In more their consumption goods. The reason is that, when other technical economic language, we would say that the ac- agents are treating goods symmetrically, the acceptability ceptability of an object is a property of an equilibrium, or of all goods is the same, and therefore there is no advan- perhaps a property of an object in a particular equilibrium. tage to trading one good for another if the latter is not going to be consumed. Since there is a transaction cost, An Example agents therefore never exchange one good for another un- Our next goal is to present a simple example of a theoreti- less they are going to consume it. cal economic model that determines acceptability endoge- Hence, in the equilibria under consideration, commodi- nously and illustrates these points. The model is based on ties will never be used as media of exchange, and there- Kiyotaki and Wright 1991 and forthcoming, where the fore there will be no commodity money; however, fiat interested reader can find several elaborations and applica- money could still potentially act as a medium of exchange, tions. (A survey of related models can be found in Ostroy and this will be the focus of our attention here. (Commod- and Starr 1990.) ity money is analyzed in a related framework in Kiyotaki Consider an economy with a large number of infinitely and Wright 1989.) Additionally, the fact that individual lived agents and a large number of perfectly storable con- agents do not accept commodities that they do not con- sumption goods, with the property that each agent con- sume means that the acceptability of any consumption sumes a fraction x of the goods and each good is con- good is x, since x is the probability with which any good sumed by a fraction x of the agents. Assume that all goods is one that a random agent consumes. Thus, when two are produced by equal numbers of agents, but that agents agents with commodities meet, a barter transaction will be do not produce goods that they themselves consume. consummated if and only if there is a "double coincidence These goods are all indivisible and come in units of size of wants," as Jevons (1875) put it, in the sense that each one. When an agent consumes one unit of a consumption of the two agents is willing to consume the commodity good, the agent receives utility u and immediately pro- which the other is trying to trade. A double coincidence duces a new good at a cost in terms of disutility c. Note happens with probability x2. The thing to be determined that agents cannot produce without first consuming. is the acceptability of money—that is, the probability with At the initial date, we randomly endow some of the which money is accepted.
19 To analyze this, suppose a representative agent accepts = x, then Vm = Vc; that is, when money is just as accept- money with probability n when others accept it on aver- able as commodities, the payoffs from trading with money age with probability fl. We will determine the agent's and from bartering are equal. In this case, the individual payoff from following this strategy and then find the is indifferent to accepting money and could choose any n agent's optimal choice of 71, or best response, given FL between 0 and 1. Let Vc and Vm denote the payoffs, respectively, when the Therefore, there are exactly three equilibria in the mod- agent has a commodity and when the agent has money at el: n = 0, II = 1, and n = x. In the first case, money is the end of each period, and let (3 denote the discount not acceptable; in the second, it is a generally acceptable factor between periods. When the agent has a commodity, medium of exchange; and in the third, it is a partially he or she acquires a consumption good next period if and acceptable medium of exchange. Although the intrinsic only if the agent meets someone else with a commodity properties of money are the same in each case, expecta- and a double coincidence occurs, which happens with tions as to acceptability have a self-fulfilling tendency, probability (l-M)x2. This yields utility U = u - 8 - c which influences whether or not money serves as a medi- (which we assume is positive) from consumption net of um of exchange and whether it is generally or only par- transaction and production costs. Further, the agent ends tially acceptable. Notice also how the use of money helps next period with money if he or she meets another agent to alleviate the difficulty of pure barter. When n = 1, a with money and both sides agree to trade, which occurs double coincidence is not required to acquire consumption with probability MXK, and ends next period with a com- goods; one can first sell produced goods for money and modity in all other instances. Hence, the payoff to having then use the money to buy consumption goods. Especially money and trying to barter is when x is small, as it will be when there are many highly specialized commodities in existence, for example, the use 2 (1) VC = p{(l -M)X U + MxnVm + (l-Mxn)Vc}. of a generally acceptable money can entail a substantial increase in the efficiency of exchange. Similarly, when our representative agent has money, he Intrinsic Properties or she acquires a consumption good next period if and only if the agent meets someone with a commodity and The above example illustrates one way in which the use the two agents agree to trade, which occurs in this case of a medium of exchange and its acceptability can be de- with probability (l-M)xYl. Further, our agent ends next termined endogenously in a model. Acceptability is not period with a commodity with this same probability and actually a property of the object, but depends on which with money otherwise, since the only way an agent with equilibrium we are in. However, this is not to say that money can ever acquire a commodity is to trade for one intrinsic properties of objects are unimportant. Suppose, consumption good, consume, and produce. (It can be for example, there is a per-period storage cost of holding shown that agents never trade money for commodities that money, denoted by k. For small positive k, there are still they do not consume in equilibrium.) Hence, the payoff to three equilibria, as described above, except now the equi- having a commodity is given by librium where money is only partially acceptable has n > x because money's acceptability has to increase to com- pensate for the deterioration in its fundamental properties. (2) V = m-M)xU{UWc) + [1 - (l-M)xTl]Vm}. m Thus, even if the flow return on money (which is -k in By manipulating these two equations, it is easy to ver- this example) is less than that on real commodities (which is zero in this example), there are still equilibria in which ify the following results. First, ifY\
20 Nobuhiro Kiyotaki, Randall Wright Acceptability
References
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