American Economic AssociationMoney and Barter in General Equilibrium with Transactions Costs Author(s): Jürg Niehans Source: The American Economic Review, Vol. 61, No. 5 (Dec., 1971), pp. 773-783 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1813141 Accessed: 20-08-2014 15:40 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org This content downloaded from 158.170.25.240 on Wed, 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions tion activities. because it simplifies the notation and corresponds nmore 2 See John R. Sanmuelson.25. treated as if it were of the same kind as the Each year is assumed to be the same as utility of consumer goods or factors of pro. consumltion was there assumne(dto b)e given indel)en- dently of monetary arranigemiients. that money is held to "bridge the gap" lated to speculation and uncertainty. for exanmple. It will be evenitually we want to explain. can ifldee(I be built oni the traded against money. R'osenstein-Rodan. namely full shown that this theory is able to explaini monetization. It also fails to provide an explicit extent the model is dynamic. exchanged. It is often argued. to this money. The theory does not permit us to tionary. /773 This content downloaded from 158. Hicks.240 on Wed. in this respect the model is sta- duction. that there is a separate trading post for rangements. General Features of the Model tized. The analysis could well he conducted in terimisof exchange between individuals (see. excluding capital accumulation explain why an economy uses money and growth. Within each year things are rather than barter. that a theory of money. any other. however. mwarkettheory. ()f course. It also gives an ex.the two are now plicit analysis of the (indirect) utility of joilitly determiinied. TI'he fiiianicial support l)y National Science chainge theory is richer in economiiic conteInt than a Foundation Grant GS-2217 is gratefully acknowledged. because this is what concept of transactions costs. money arising from the exchanige process. ranging from barter to full I The present miiodelis a further (levelopmiientof the monetization. Money and Barter in General Equilibrium with Transactions Costs By JURG NIEHANS* In this paper. The exchange and to monetary theory1 is generalized by the storage of goods will be the oiliy produc- explicit introduction of transactions costs. which can not be analyzed satisfactorily in Individuals are assumed to be endowed terms of equilibrium theory. terest. valid for economic in each market a certain commodlity is e(quilibrium. 4 the use of the market concept is not really neces- The discussion will be restricte(d to a pure sary. and there is no credit. in- The neoclassical theory of general mone.2 However. closely to the neoclassical app)roach. This dy- analysis of the services of money in saving namic element provides a rationale for the resources used up in the exchange process. Johns Hopkins 1969 and 1970 articles). or time preference. and 2) the utility of money can be Let time be divided into years and days.my * Department of political economiiy. I'. between receipts and payments. the neoclassical approach exchange economy."4 We from the complementary point of view that cannot start by assuming. Exchange transactions costs. 1. While in transactions costs. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions . as the result of differences approach I used in my 1969 and 197/0 articles. We rather have to assume the emergence of dlifferent exchanige ar. This paper is written takes place in (lifferent "markets. therefore. that money is making it possible to formalize the notion essentially a dynamic phenomenon. re. These quantities can be con- argument is true only in the absence of sumed. an individual ex- University. with certaini quantities (sometimes zero) there is always the qualification that this of each good. or stored. holding of stocks.170. N. including cash balances.3 tary equilibrium is based on the twin as- sumptions that 1) the economy is mone. The latter aplproach was choseni here ISee the recent restatement by Paul A. nor how it chooses its subject to change from (lay to day. all change arrangement. some of these cannot expect. lating storage to different resource inputs.1 nonmonetary commodities are ex. title of ownership has to be transferred in certain prescribed forms. This content downloaded from 158. Again it would be pos- triples. Under given conditions. At one post. loss. that the market markets will usually turn out to be inac. etc. In a fully monetized economy.) tions are made with respect to variable but from their transfer from one owner to transactions costs: another. measured and marked. interest payments. reflecting wastage. n-tuples of goods. there is no upper limit to steady-state stocks. little affected by the number of shares.25. trans. pp. between the two sides. We kets. In prin. the transfer may have to be 8 In a more complete analysis. . I protection. volume of transactions in a given actions costs vary with the quantity trans. In the present costs are defined as those costs which context fixed transactions costs will there- arise not from the production of goods fore be disregarded. the goods have to be inspected. is nothing that could be said at the present It is an essential feature of the model time beyond what was already indicated in that exchange causes costs. Another part may be fixed: The There are also costs for the holding of resource costs of a stock transaction is stocks. there are thus (q/2) (q. In the present cases (like trees) physical growth. etc. have to be a negative yield or a positive cost. quadruples. these costs would also recorded etc. Costs may For the present purposes we shall assume arise because the parties have to communicate. tation in terms of competitive prices. 6 The term is a catchall for different items. . ciple. The following assump- (including transportation. Transactions the above mentioned paper. a that storage costs consist simply in a title search may be necessary. For and sold.8 These storage costs showed in an earlier paper7 that fixed introduce another element of production into the model. 722 ff). The sum of these components will duce these uncertainty elements in an explicit way.240 on Wed. In part. there could also be trading posts for ify a technology. Meltzer). and so on. contracts have to be shrinkage of stocks by a certain percentage drawn up. otherwise 7 See Niehans (1969. therefore. in others (like bonds) context it is both impossible and unnecessary to intro. far-reaching consequences for the welfare ing (1/2) (q-1) (q-2) trading posts are implications of general equilibrium. the present purpose a one-factor produc. reflecting in some Karl Brunner and Allan H.774 THE AMERICAN ECONOMIC REVIEW each pair of goods. market. relating the transfer of a certain good to 3) they are the same for goods bought the required inputs of many factors.1) mar. . apples are transactions costs give rise to an integer traded against nuts. While the existence q. There are good reasons for classifying include subjective time preference.6 It will be assumed for simplicity 1) They are counted separately for the that all transactions costs are expressed in two goods exchanged in a given terms of "work. maintenance.5 For prices have no straightforward interpre- q goods. 4) they do not depend on the aggregate tion function is sufficient. while a part of them many of these items as search or information costs (see would be offset by positive yields. there deserted. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions .170. involve almost twice the costs of the trans- fer of one. at another apples are programming problem whose shadow exchanged against pears. the remain. thus excluding a potentially ferred: The transfer of two houses may important externality. of fixed transactions costs may thus have changed against money only." measuring the time and transaction with no interdependence trouble in making transactions. mechanism provides for an optimal ex- tive. it would be possible to specify for 2) they depend both on the transactor each transaction a production function and the good. It is assumed that transactions costs on such higher-order markets sible to specify production functions re- are prohibitive-as in reality they usually are. for which we have to spec- I In principle. packing. t-1sh) With given endowments. . market prices. -= = 1/ltpkh ty hk tzhk (though possibly zero) at every trading post. where trans. T days. Denote tSh to be the stock of to be paid for the holding of a certain good h held on day t and yh the daily stock. . tSh = 0sh (h 1 . t .25. costs. q of q. of transferring one unit of good h. this is in- which is assumed to have convex isoquants tended to be a stationary model. tyhk) + (tsh .9 This conceptualization of holding holding costs per unit of such stocks. . . these constraints can be written actions costs are assumed to be paid out of q-1 the qth good. If Ch is the cost. . . Correspondingly. . . . in. measured in units tions. k transactions costs and storage costs. . k . goods and 1 . . E (tZhk . the T(q. Substituting for tZhk. . terminal and positive marginal utility for at least stocks are required to be equal to initial stocks: I For services (including work) storage costs must be assumed to be infinite or in any case prohibitive. any de. for the year as a whole. each day of the year: mand for money results from transactions q motives. For costs means that capital is visualized as each good except the qth. The individual is endowed tXq _ (tpkkq tykq . txh = E (tpkh tykh . The question is under what condi. t-lsh) + yh tSh = tCh The model outlined in the preceding section will now be specified in detail. k + ayh t5 h = tjCh (h = h dividuals are supposed to schedule their exchange transactions and stocks in such a Purchases and sales at a given trading post way that the utility of the resulting con. It can tyhk. This rate may be different for one commodity. in. but it is sold against k on day t will be denoted assumed to be constant over time. We The T resource constraints for q include begin with the optimization problem of an additional terms reflecting transactions individual faced with given market condi. the resource working capital in the form of inventories.240 on Wed. General price equilibrium will be reached when prices tzkh ty kh are such that demand and supply are equal tphk =. . constraint states that consumption minus while problems of time preference.. h. Suppose there are 1 . TXq) Since.1) resource tions this equilibrium will be one of barter constraints can be written and under what circumstances a good will q emerge in the role of money.1. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions . tXhl . k ing in the market and carrying stocks from _ (3) + ( tSq t-lSq) + yq tSq one day to another the individual maxi- q q mizes the differentiable utility function of + E E (Ch + ck tphk) tyhk = t-q consumption x. while tZkh iS the quantity of k bought be interpreted as an own-rate of interest against h. tyqk) with resources txl . TCq. By trad. . . tyhk) (2) I II. NIEHANS: MONEY AND BARTER 775 per period.q) This content downloaded from 158. credit.170. h k h ( 1) U = U (IXIJ . net purchases plus addition to stocks plus terest. tXh . The quantity of good h different individuals and goods. Individual Optimization + (tsh . Ixh ... are related through the exchange ratio or sumption pattern is maximized. and capital goods are not storage costs equals the endowment for touched upon. trading posts may not be frequented by like other stocks. In Otxh symbols. but determined endogenously by For a problem of this type Kenneth the optimizing calculus. y) marginal value or opportunity cost. (I. p..25. all flows and stocks must be dividual may well be both a buyer and a nonnegative: seller of the same good. as func. L. The inequality sign implies that a good. p. U / 0& cave objective function and linear con. in view z = z(x. The analysis of the approach to tiplier tXh can be interpreted as the mar- equilibrium stocks is outside the scope of ginal value or opportunity cost of resource this paper. tions. many It should be emphasized that initial stocks. laUT tXh < txh > 0 0 transaction costs.10 The Kuhn-Tucker conditions What we have described is a non-linear relating to consumption are programming problem with a quasi-con. Also. exchange flows and stocks. him at all. . ever.240 on Wed.776 THE AMERICAN ECONOMIC REVIEW T q q_ L= U(IX17 . dividual. With respect to the first term of the ing to that of neoclassical theory. (4) tions of endowments. If a good is consumed at all. p.170. once that the Kuhn-Tucker conditions are they are attained at the beginning of a necessary and sufficient for a maximum. how. The model thus Arrow and Alain Enthoven have shown determines those initial stocks which. tyhk)+ tSh . supply conditions note that in the Lagrange function contrary to the neoclassical model. give the individual no reason These conditions are obtained from the to plan for a change in initial stocks next Lagrange function shown above. market prices. t--15h + ly 5h -tch t h k- T _ q q + E tx[q E E (ch + ck tphk) tyhk (h. its marginal x = x(x. that is. E (tpkh tyk. c. q.tXh tXh =0 straints.. k 4h) t h k In addition. p. y) wealth. The mul- year. c. using vector notation. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions . \9 txh ) tion. Balinski and William Baumol who also give the required qualifica- and storage costs. k = 1 . Its solution determines consump. E E t\h tXh . h on day t. may have a positive marginal value even if it has no direct utility. On the other hand. c. that the resulting functions do not 11The implied conditions for market demand can be have a homogeneity property correspond. _. TxQ) . an in. This content downloaded from 158. tphk tyhk appears with multiplier tXk. given year. The problem is thus a straightforward There is another set of conditions for generalization of the neoclassical problem market supply1" of utility maximization under a budget constraint for a world with transactions 10This statement is based on M. y) utility in consumption is equalized to its y = y(x.. are not given to the in. c. though at different txh > 0 tyhk 0. It should be noted. obtained from the supply conditions together with the definition of prices. (h tsh2O = 1*q) trading posts. against different other goods. . and storage costs. y) of its services in exchange or as a store of s = s (x. tXh . Trade can take place along the straight 12 Alternatively. tion that equilibrium in n.1) markets for each tXk tphk _. on the other hand. tSh > 0 matically satisfied for the other.240 on Wed. and stock in Figure 1. value of good h held in stock for one day. (8) could be rearranged to say that the marginal stock value. finally. k = 1 . It will be zero. found in neoclassical models. In particular.12 and stocks for all individuals are deter- The condition means that in equilibrium. . (t = 1 . . .tXh tXq(ch+ tphk)] tyhk = 0 prices on the (q/2) (q. Denoting individuals by subscripts.tXh(ch+ ck tphk) < 0 of T days. in general. capitalized at the storage cost line through E whose slope measures the rate. and erties can be made to result from special marginal flow values tXh are equalized over assumptions. If holding costs are "real" and a "monetary" part. zation problem of trader 1 is represented sumption. defined by the given endowments. tXh(l yh) < 0. two traders and two goods (and thus one market). the shown below how the neoclassical prop- marginal stock values go to zero. Market Equilibrium can be illustrated graphically. by the definition of prices.1 markets implies equi- taneously without violating the stationarity condition. we obtain However. in contrast to the marginal flow value tXh consumption. it is auto- t+l\h . NIEHANS: MONEY AND BARTER 777 k [txk tphk -t. There- The first inequality can be written fore. If none of the familiar homogeneity properties the gain is smaller. stocks are held at satiation levels. tXh + we thus obtain the set of Tq(q. we may call it the marginal stock value.. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions .13 be zero. must not exceed the marginal flow value. time. This content downloaded from 158. demand. Note that E is the no-trade functions for each of n individuals.14 The number (8) t+lXh .170. The point. only half of the above equilibrium conditions are independent. h. become en- dogenous variables. tXh < ah tXh of independent equilibrium conditions The expression on the left is the marginal thus matches the number of prices. For negative holding costs or posi.\qck nt hk nEt hk thi This is the counterpart to the familiar E s = E condition that relative prices are equal to the marginal rate of substitution. this aspect III. It is important to realize that for some tive yields there is no equilibrium. h k) For stocks. Once equilibrium prices are known. The result is a if a stock is held at all. market demand and supply. supply. For one day. marginal loss because of storage costs. no stocks are held. 13 Mathematically this shows up in the fact that for 14 This is the counterpart to the neoclassical proposi- yh<O. (8) cannot be satisfied for all time periods simul. librium in the nth market. These prices have to yhk> 0 satisfy the requirement that aggregate de- The first inequality can be rearranged mand equal aggregate supply for each to read good. It should be from holding it for a day is just equal to the noted that this system has. Holding costs act as an effective brake on the system cannot be dichotomized into a stock accumulation. T. mined simultaneously.25. if this - t+l\htXXh(l + yh)] tSh = 0 condition is satisfied for one of the goods 7 + traded at a given trading post. the marginal gain general equilibrium of barter. The optimi- We now assume that we know the con.1) condi- t\qCh (6) ttphk < tions tXk . t. q. further markets the equilibrium trade volume may accumulation always pays. 12 FIGURE 3 FIGURE 1 rium was initially at the no-trade point E. this prices only. This re- The intersection of these curves then de- sults in market demand and supply repre- termines the direction of trade. The measuredby the vertical distance between kink in each consumption frontier. The supply are summarizedby the offer curves consumption frontier is AEB. XI B 1 z.170. for traders 1 and 2 in Figure 2. all markets may be active.240 on Wed. However. as illustrated in Figure 3. a pl2 below min p'2 or above 21 21 max p"l would make the price line intersect the offer curve of trader 1 either in the third or first quadrant.25. and the quantities ex- With a change in market price. any price within this (shaded) will lead to a change in market demand range making the desired exchange zero and/or supply. market price. It may happen. however. if any. if the equilib- for both traders. If transac. FIGURE 2 respectively (but not necessarily the offer curve of 2). we can generally determinea range of along the flat segments AE and EB. In a multimarket sys- tem. that trade line and the consumption frontier market equilibrium is at the no-trade will swivel around E. it is clear that it may stay there for some market price of good 1 in terms of good 2. the sented by the differencebetween T and E. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions .z2 yi ~~~T xi 2 21 21 g od x. commodity bundle resulting from trade is The results for market demand and not fully available for consumption. various sets of markets can be made inactive by choosing appropriate configu- 12 Z1 ly12 '2 A12 Y 12 rations of transactions cost rates. due to the consumption frontier and the trade transactions costs. they are origin represents the no-trade point. The trader will maximize utility by the respective offer curve at the origin. where the tions costs are paid out of good 2. This content downloaded from 158. ceterisparibus. If the initial con- point. choosing consumption pattern C. range of prices. implying 15 As the figure is drawn. In one 1' 2 case. A similar graph could be However.'5 21 21 This two-person one-market example p12 shows that the no-trade solution is more 2 likely. In this sumption equilibrium was somewhere case. the higher the trans- actions cost rate. in view of transactions costs the drawn for the second trader. both the changed.Y2 y1 . is reflected in a kink of line. -.778 THE AMERICAN ECONOMIC REVIEW good 2 max pl2 A \ ~min p1I2 2 xX2 A E 12 12 ______________y12 12 Z1I. exchange. some of transactions cost rates. Xq(Cg + Ckpgk)] name of money. others nonmonetary. system with direct barter only. It is derived from the more general indirect. replacing indirect by direct plaining the emergence of different ex. 2Cgp hgXq tions costs in some particular way. the transactions cost other good. similar to a tax on exchange. There is no general rea. It is re- mine which trading posts are active under garded as commonplace that such a sys- a given set of conditions. we shall now try to derive special (and in some obtain the marginal gain from using the indirect route sense limiting) cases by varying transac. But even if tastes and goods are bought for resale. because with the given exchange IV. enough to make this negative. will ments. there is always a rate high enough to make this would be the case of a fully monetized it preferable to eliminate that medium of economy. In the latter cases. In general. (phgpgk .240 on Wed. can be the most efficient trading pattern avail- made to emerge by varying the pattern of able. sufficiently similar. be it direct or model. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions .17 In the course of this process we change arrangements. NIEHANS: MONEY AND BARTER 779 that every good is traded against every an indirect exchange. including cases of both direct barter all trade. ginal gain from the corresponding indirect exchange son to expect that any one good will uni. with g as medium of exchange is versally or even widely be used as a me. barter. The first term represents the value of the gains in k from We first assume that wherever there is using the more favorable indirect prices. based on a simplified model. with given tastes and endow.170. transactions costs. costs. phk) (xk . From this general case we Deducting the first expression from the second. Barter and Commodity Money technology. tem is wasteful. This is not generally true. though. In another case. embodied in a particular set Different exchange arrangements. The same individual to trade to satisfy any of their needs. It is logically conceivable that some trading posts will be active. Xq(ch + cgphg) dium of exchange and thus deserve the + phg[xkpgk . There is clearly some cg high (1969). others even small transactions costs will shut off idle. Ck q) . This is so. phgxg . In a second experiment we assume that the timeless aspects of this proposition will transactions cost rates are increased wher- be considered in the context of a one-period ever there is any exchange. creasing transactions costs can reduce the ferent range of applications. In the present section. it may well be monetary. if tastes and endowments are and indirect exchange. while the second term measures 16 For numerical illustrations of different monetary the value of the additional transactions costs on the arrangements. this will tend to lower model presented above by simply omitting the volume of market exchange. time superscripts and stocks. This content downloaded from 158.The result is likely to be result is complete self-sufficiency of in- a complex network of exchange in which dividuals. because the rise in transactions Suppose. in- may use several such media.25. net of addi- tional transfer costs. AS . see Niehans medium of exchange. we start out by assigning arbitrary make it relatively more profitable to con- positive values to transaction cost rates in sume one's own endowment. it is thus one of the will sooner or later arrive at an exchange principal functions of the model to deter. all markets rate on the respective medium of exchange are deserted except those where one par.Xh . From the point of view of ex. each in a dif. and different 17 The square bracket in equation (5) is the marginal individuals will often use different sets of gain from the direct sale of one unit of hifor k. thus serving as endowments are such that individuals have media of exchange. It is clear that ticular good is traded against other goods. A possible a random fashion. The mar- exchange media."6 in part. is progressively increased. Xk - creasing the c's.21 Once consistency is assured. As a consequence. commodity.20 The availability of just one change rate for any two commodities good with zero transactions costs is equals the quotient of their prices in enough to guarantee consistency of the terms of a third good. it can be proved as 18 Consider (3). a neoclassical duce all transactions costs to zero.170. phm < = and pmk < ___ Xm . pp. whence nq q h k hk hk nq A + Xh ChXq p hm pmk <X -_. disregarding time subscripts and follows. CkXq i h ki since aggregate market purchases and sales cancel in But for the two legs of the indirect exchange equilibrium." been criticized for being essentially a bar- By increasing transactions cost rates. oranges. domly assigned transactions cost rates.19 The price we pay for these tem. change. instead of for particular goods. The exchange are traded against nuts. choice of the medium (or media) of ex- sufficiency as we want. = not take place. general equilibrium system. the price of h in terms of the Ak .780 THE AMERICAN ECONOMIC REVIEW volume of trade to any level we care to simplifications is that exchange flows at the specify. Equations (4) Finally.25. we start out by (pkNy. However. It is clear that for a given endowment with Xh + chXq Xm + c-Xq work the y's can be forced down to any level by in. the bring society as close to individual self. Its ally the smallest trace of market exchange basic shortcoming is rather that the choice would use up all of society's work. again disregarding and thus. ence.pmk q < phk there is only a direct supply of /i against k. leaving all others sistent in the sense that the direct ex. From the point of view of monetary this amount at the given transactions cost theory the neoclassical system has often rates specify a "trade possibility frontier. As a consequence. whence tion violates equation (6). thus maximizing the amount nate. contrary to the consistency postulate. we may re. the same type of argument shows that the direct transac- But the double sum is identically zero. x7h) . which means that the indirect exchange does q q q E phN(xh . denoted m. these traders will goods. E E . stocks ancl letting xq=0. market equi- This content downloaded from 158._ _ EE E (C + Cip)yi =E i XAk . tions this criticism does not seem valid. starting again from the ran- and (6) show that for all nonzero flows. CmMXq CkXq 19Consider equations (2) and (3). are matters of economic indiffer- Going to the other extreme. this ter theory. (6) holds as an equality. Suppose. If. The result is But we already know that the inequality sign holds in this case. equilibrium price system in the sense de- the resource constraints can be expressed fined above. only h the indirect route will be used. it is irrelevant to what extent apples available for transactions.kh phNyhk) 0 h h k assuming that the indirect exchange takes place.240 on Wed. The result is the familiar budget assume the position of middlemen in the exchange sys- constraint. on the other hand. Suppose no work is directly con. time subscripts and stocks and redefining /i to include q (since there are no transactions costs). prices will now equal the marginal rates of we reduce these rates to zero for one substitution. If yhk>0. the model reduces to a neoclassical sis of monetization and monetary services. In this system is unable to give an explicit analy- case. 21 In case this is not evident. in the case of monetary exchange. unchanged. In the E phN(xh_xh) =0 same way it can be shown that with phnpynk > phk. 720 ff). until fin. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions . The price system will be con. in terms of any one of the goods. Multiply the Xh + ChXq phmpmk < _ -_ constraint for hi by phN. or gold programs which can be maintained with dust. and added over all ders. Adding over individuals phmpyk<phk. In the light of these considera- frontier can be made to shrink. various trading posts become indetermi- sumed. arbitrarily 20 If transactions costs are lowered for particular tra- chosen as numeraire. It follows that with phn. CkXq numeraire. for cm= 0. For an example see Niehans (1969. renmembering that pkhphN = pkN."8 By between barter and monetary exchange increasing transactions costs we can thus and. and add over commodities. of course. where hiis suplplied in the direct barter market. resulting in a pat- cal model. for phmpmk>p1k. however.240 on Wed. not apply. all current supplies being used up by trans- pk(Xk . some of the most fundamental aspects of monetary trading posts may just as well money.25 his accounts in each market separately. cluding the time dimension.26 The current endow- tute for the !'s fromiiall other conistraintsinto the imioniey constraint. if a good with zero transactionis costs is even if it can be transferred without cost. thus taking the 23"Anelemiientof indeterminacy is still left inasmuch place of wsorkin the present model. stocks and vidual were under Ino constraint to balance storage costs.170. Their utility is librium requires that every supply of Ii against k be of a purely indirect nature.:ly of k takes its way through other miiarkets. To provide such an analysis we be closed down.The the respective transactionis and storage same is true. with transactions costs as a nonclassical component. that the k k commodity wx-hich is used as money is. the result is the 24 One could construct a timeless flow imiodelwhere budget constraint moniey is supplied in positive amounts wNithoutbeing consumed. By assigning low enough values to sup. This would require. Second. A timeless flow model is unable to ex- sumption are always lower for m. In for money in a nmodelwith predetermined consumption. = 0 actions costs. should happen to imieet. the current travel along the indirect route. the non. but with a determinate moine. First.let all nonmonetary eral medium of exchange. [ or the timiieless case. E. the one usecl up in making transactions.22 We are thus close to a neoclassi. while the corresponding costs. the miore general case wvith nonzero transactions costs see Niehans (1970).}k) + (x"rM -_ V) + E p7Ck A _k . available. on money.24 It thus precludes an analysis of instead of monetary exchange. and these by as. NIEHANS: MONEY AND BARTER 781 further conclusions can be drawn.25.xamining equation (6) for flows in this (lirection. however. All non. tern of exchange flows and stocks without tary exchange network. being (lerived matche(d by a corresp)onding sup)lv of k against Ii. there will never zero flows of new supply and consump- be an advantage in using direct barter tion. at the same time. Token Money in the various markets. it is inefficient to use any other is not nieutral and the quantity theory of good as medium of exchange.are indifferenit between direct 25 lor illustrative computations of the stock demand barter and twvocompensating monetary exchanges. that even in this case In contrast to the timeless case. It is monetary goocls will thus flow directly also unable to explain the use of a token from the initial resource owner to the money circulating in given quantity with final consumer. money (in the sense of proportionate ef- modity m will thus be elevated to the fects of the money supply on prices) does status of the general medium of exchange. being goods may now be exchanged ancl held in currently supplied and consumed. we only have to compare transactions costs V. plain the stock demand for money. the supply of k xv-ill Since they are not consumed. b)e a token money. We are thus confronted endowments are all used up by storage wziththe typical arbitrage situation. an Suppose we start again by assigning aggregate budget constraint is all that positive random values to transactions matters. As a stock even though they fail to appear in anybody's utility function. Third. called money. if they highly artificial assumption. 22 Identifv onie good as imionev. it is always possible to nmakeone of follows that there can be no equilibrium with inconsis- these goods. this is. the money of this section. with the reverse signl. This will then transactions in e(luations (2) and (3) vanish andl substi. again designated m. With consistent prices. The com. certain money is still commodity money. noted. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions . the gen- tent nrices. it from their efficiency as media of exchange. 26 If the endowment flows of a token money are posi- This content downloaded from 158. turns out that for phmpmk<phk. not so. consecluence. This is clearlv a as the hungry tailor and the shiverinig baker. and storage cost rates. all commodity have to return to the complete model in- flows can again be arranged as if the indi.23 It should be any particular monetary characteristics. It costs. to apply the model to those other resource constraints. Within its confines. The nomenon of "seignorage" for a stationary economy can now be thought to be economy. neutrality. a doublina of the money prices of other goods tpkm7 and of money flows tyrlh. 3) includes the just high enough to make attrition equal to the new supply. (flow) value. but While for each money user at given prices now made determinate by transaction such a money has a positive marginal costs on nonmonetary goods. Since tions costs. the money floNws are doul)led cases in which the cost of holding assets while the price of money in terms of goods is cut in half. there must still be some storage costs to make the vides full integration of monetary and model stationary over the year.=0.28 The absence of direct storage costs.--h+XqCh. In all impossible. physical shrinkage. it reads tXmtph. could be constructed by money for which there are no current suitable assumptions about transactions endowment flows.For mean t. Inspection of the programming the marginal stock value of money mea- problem shows that the system then be. a general increase of all monetary endowments in VI. even if I product of X. in addition solute money prices and individual cash to being token money. In this case prices Nvill value theory. preference. and in money prices tpkm foi all t and ing case envisaged in the neoclassical k. If desired. the economy is satiated with cash given monetary resources tx7 for all i and balances. holding costs must be zero transactions cost approach is able to deal (ym= 0).27We thus end up with neutral money. leaving their product unchanged. let us suppose there is a token moinetization. providing a general eqjui- utility and transactions costs for money librium theory of exchange. neutral money of the neoclassical theory 27 In the resource constraint for in. Concluding Remark the same proportion will leave everybody's In this paper the neoclassical system utility unaffected. The main deficiency of sumption. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions .170. as a limiting case.. 2) gives an explicit analysis be such that the resulting demand for money stocks is of the services of money. satiation with cash halances (loes not 28 Consider equation (6) for the money price of Ih. and storage costs. all tXm moving inversely was extended to include transactions and to money prices. has zero transac. with zero con. An analysis of inter- transactions costs in the constraint for (Iare not affected either. otherwise the terminal stock effectively with three basic problems of monetary theory inasmuch as it 1) pro- tive. a doubling of t. that is tm.. This content downloaded from 158. 29 Of course. the present model is the neglect of time bling of stocks.hat the marginal flowTvalue of monev tAtl goes ctm=0. Within this thus appear as the crucial assumptions for framework. while the commod. barter and further on to various forms of Finally. the spondingly.240 on Wed.782 THE AMERICAN ECONOMIC REVIEW ments with token money cover the phe.29 This is the highly special limit- t. This fixes the equilibrium values of ab- We now assume that money. Corre.25. but i do not have the power to replace it.. If there is some attrition of the equipped with an arbitrary stock of such a money stock. am satiated with cash balances. WVith unchanged cannot reasonal)ly be interpreted as a commodity flows and zero transactions costs on money. approach to monetary equilibrium. various exchange systems. sured by t+l'Xrn tXm is now zero (see equa- comes homogeneous of degree zero in the tion (8)). measured by tXm. could not equal the initial stock. if not ities exchanged for money t1h4mt are unchangedl. those who are able to supply 'perfect money" the flow of replacement money obtain a n t mr steady stream of other goods and services M=Al sSi t = O .-7 1 will he reflectedl in a dou.. the system can now ranging from no exchange to multilateral be dichotomized in the neoclassical way. T from those who wear out the money. This makes it difficult. balances at every moment of time. All that matters is the to zero--the loss of a (lollar is always a loss.and tph which does not change. 3." J. 35." 240-83." K. Banking. J. Baumol. 29. N. Oct. July P. Hicks. Stuid. Aug." Schiweizerische Zeitschrift fuir Volks- M. J. 1. Arrow and A. 1933. and J. financial intermediation. 1. in Nonlinear Programming and its Economic 129-48. Rosenstein-Rodan. 1936." Rev. This content downloaded from 158.. Brunner and A. Finance. L.. "The Dual wirtschaft und Statistik. H. 706-26. K. Enthoven. "Money in a Static Theory of Op- timal Payments Arrangements.170. Investigations of Demand and Supply Func. "What Classical and Neo- tions for Money. J. "Some Further Economica. P. Feb." J. classical Monetary Theory Really Was. thus require a further extension of the 441-55. R. "The Coordination of 1968. 20 Aug 2014 15:40:49 UTC All use subject to JSTOR Terms and Conditions . 1-15. 257-80. "Quasi-Con. Balinski and W. model. will Zeitsclzrift fur Nationalakonomie. 1969. Nov. C. the General Theories of Money and Price. Niehans. May 1964. 4. credit. June 1970.25. 779-800. Can. Econ. Interpretation. REFERENCES Credit. "Die Geldnachfrage in einer dynam- cave Programming. Meltzer. 237-56. Money. "Gleichgewicht und Konjunktur. tems. Samuelson." Econzornetrica. 106. A. NIEHANS: MONEY AND BARTER 783 est. 19. J." the rules for an optimal money supply. ischen Optimierungstheorie des Zahlungssys- 1961. Econi. 1968.240 on Wed.