Integration of Market Exchange and money circulation Gang gon March. 1995 I want to thank Edward Nell, David Colander, John Eatwell and Thomas Palley for their comments and suggestions on the early draft of paper Dept of Economics, Graduate Faculty, New School for Social Research, 65 Fifth Ave, New York, NY 10003
Integration of Market Exchange and Money Circulation Gang Gong* March, 1995 I want to thank Edward Nell, David Colander, John Eatwell and Thomas Palley for their comments and suggestions on the early draft of paper. * . Dept. of Economics, Graduate Faculty, New School for Social Research, 65 Fifth Ave., New York, NY 10003
Integration of Market Exchange and money circulation Integration of Market Exchange and Money Circulation Abstract loney as a medium of exchange is circulated along with market exchanges. The process of market exchanges can be viewed as a sequence of trades with the starting point to be an autonomous demand. Money in this process is naturally integrated with the proceeding of market exchanges. Its circulation is now closed, continuous and dynam ics. This further provides some implications to post Keynesian macroeconomics Much study on monetary economics follows the Walras-Hicks-Patinkin tradition to treat money as a stock. Typically, the demand-supply principle is used to determine the money stock equilibrium along with the commod ity equilibrium. However, money as a medium of exchange is also a flow. It is circulated among different agents. In economics literature. there is also a circulation approach that follows Wicksell's trad ition to study the macroeconomic operation ulation of Wicksell's trad ition does not provide much micro-insides of money circulation. Money as a medium of exchange is circulated along with the proceeding of market exchanges, and therefore the study on money circulation should be integrated with the study on the trading process Without concerning its macroeconomic implication, attempts, with vary degree of success, have also been made to formalize the money circulation along with a trad ing process. Such a trad ition follows the pioneer works by Ostroy (1973)and Ostroy and Starr (1974). The trading supposed to be decentralized, sequential and executed in pairs. Recently, Diamond's"search rocess"(Diamond 1982, 1984)is often used to formalize this idea. 2 1. For recent literature along this line, see, e. g, Deleplace and Nell ed (1995) 2. For the review, see Ostroy and Star(1990). For a more recent study, see Kiyotaki and Wright (1993)
Integration of Market Exchange and Money Circulation 2 Integration of Market Exchange and Money Circulation Abstract: Money as a medium of exchange is circulated along with market exchanges. The process of market exchanges can be viewed as a sequence of trades with the starting point to be an autonomous demand. Money in this process is naturally integrated with the proceeding of market exchanges. Its circulation is now closed, continuous and dynamics. This further provides some implications to post Keynesian macroeconomics. Much study on monetary economics follows the Walras-Hicks-Patinkin tradition to treat money as a stock. Typically, the demand-supply principle is used to determine the money stock equilibrium along with the commodity equilibrium. However, money as a medium of exchange is also a flow. It is circulated among different agents. In economics literature, there is also a circulation approach that follows Wicksell's tradition to study the macroeconomic operation based on the circulation of money.1 Wicksell's tradition does not provide much micro-insides of money circulation. Money as a medium of exchange is circulated along with the proceeding of market exchanges, and therefore the study on money circulation should be integrated with the study on the trading process. Without concerning its macroeconomic implication, attempts, with vary degree of success, have also been made to formalize the money circulation along with a trading process. Such a tradition follows the pioneer works by Ostroy (1973) and Ostroy and Starr (1974). The trading is supposed to be decentralized, sequential and executed in pairs. Recently, Diamond's "search process" (Diamond 1982, 1984) is often used to formalize this idea.2 1 . For recent literature along this line, see, e.g., Deleplace and Nell ed. (1995). 2 . For the review, see Ostroy and Starr (1990). For a more recent study, see Kiyotaki and Wright (1993)
Integration of Market Exchange and money circulation This paper presents my own contribution to the subject of money circulation. Along the line of Ostroy-Starr-Diamond, I first consider a market exchange process that might be called the multiplier" process presented in(Gong,, 1995). This process shares many similar properties as in those search models, except perhaps only the starting point. It has been known that the starting point of a search process is often unclear, and therefore exchanges are executed often in disordered and random fashion. 3 In the multiplier process, the starting point is further specified and therefore exchanges proceed orderly I will show that such a trad ing process is naturally integrated with a process of money circulation and satisfies Clower,'s "cash in ad vance"constraint(Clower, 1967). By this inward looking of money circulation, I then can show how outwardly money is circulated among different types of agents. 4 One will find that the money circulation is now closed, continuous and dynamics. Finally, the implication to the some issues in post Keynesian macroeconomics will be d iscuessed in this context The necessity of a special trader Suppose the mythical auctioneer had adjusted all necessary prices to their equilibrium and hence stepped down from his stage. It now remains for the trade to be executed. At that moment traders are supposed to possess the information, given by the auctioneer, how much they should supply and how much they can demand at the equilibrium price. To whom should they supply, and from whom should they demand? These are the problems with which the aforementioned models of trading process usually start. However even if traders have found their partners, a problem still remains Indeed, the search process often appears to be a stochastic process describ led by a certa in probability distribution such as a poisson distribution as in Diamond (1982, 1984)and Kiyotakiand Wright(1993) 4. The notion of"in ward-"and"outward-looking"is copied from Ostroy (1989), with the meanings to be the micro insides and macro-outsides respetively
Integration of Market Exchange and Money Circulation 3 This paper presents my own contribution to the subject of money circulation. Along the line of Ostroy-Starr-Diamond, I first consider a market exchange process that might be called the "multiplier" process presented in (Gong,, 1995). This process shares many similar properties as in those search models, except perhaps only the starting point. It has been known that the starting point of a search process is often unclear, and therefore exchanges are executed often in a disordered and random fashion.3 In the multiplier process, the starting point is further specified and therefore exchanges proceed orderly. I will show that such a trading process is naturally integrated with a process of money circulation and satisfies Clower's "cash in advance" constraint (Clower, 1967). By this inward - looking of money circulation, I then can show how outwardly money is circulated among different types of agents.4 One will find that the money circulation is now closed, continuous and dynamics. Finally, the implication to the some issues in post Keynesian macroeconomics will be discuessed in this context. The Necessity of a Special Trader Suppose the mythical auctioneer had adjusted all necessary prices to their equilibrium and hence stepped down from his stage. It now remains for the trade to be executed. At that moment, traders are supposed to possess the information, given by the auctioneer, how much they should supply and how much they can demand at the equilibrium price. To whom should they supply, and from whom should they demand? These are the problems with which the aforementioned models of trading process usually start. However even if traders have found their partners, a problem still remains. 3 . Indeed, the search process often appears to be a stochastic process describled by a certain probability distribution, such as a poisson distribution as in Diamond (1982, 1984) and Kiyotaki and Wright (1993). 4 . The notion of "inward-" and "outward-looking" is copied from Ostroy (1989), with the meanings to be the microinsides and macro-outsides respetively
Integration of Market Exchange and Mo Circulation To see this issue, let's take Wicksell's famous ABC example(wicksell, 1936, ch. 3)in which, commod ity A is known to be desired by the owner of commod ity b, b by the owner of commod ity C, and C by the owner of A. Who should pay out first before he receives the money from other traders? For a regular trader, such as the owner of commod ity A(or B or C) who comes for both buying and selling, there is no meaningful reason why he should pay out first and let the others take the advantage that he creates so that they can receive his money first and pay their own later--not necessarily directly to him as in our ABC example. If the owner of A does not receive the money from the owner of C after he pays out first to the owner of B, he will be broken. Besides, there is no way to satisfy Clowers cash in advance constraint. But if no trader pays out first, or buys something first, how is the trade executed, or how is money circulated? This example indicates that to start the trade there must be a special trader who comes to the market only for paying without receiv ing, or only for buying without selling. We can expect that once such a trader come to the market other potential transactions can be carried out. Does this type of special traders exist in the real world? The multiplier process as a market Exchange process first remark that such special traders exist implicitly in some search models. For exampl Kiyotaki and Wright(1993)assume, "Initially, a fraction Mof the agents are each endowed with money while 1-M are each endowed with one real commodity. (p. 64)Clearly the M fraction of the agents can be regarded as our special traders, for they have nothing for trading except their money. In practice, they can be regarded as investors(and other autonomous demanders. )We find that an investor is exactly a special trader who comes to the market only for buying without selling Gong(1995) present a Keynesian multiplier exchange model, which shows how vario market exchanges are generated so long as an investor comes to the market. Since the money
Integration of Market Exchange and Money Circulation 4 To see this issue, let's take Wicksell's famous ABC example (Wicksell, 1936, ch. 3) in which, commodity A is known to be desired by the owner of commodity B, B by the owner of commodity C, and C by the owner of A. Who should pay out first before he receives the money from other traders? For a regular trader, such as the owner of commodity A (or B or C) who comes for both buying and selling, there is no meaningful reason why he should pay out first and let the others take the advantage that he creates so that they can receive his money first and pay their own later ⎯ not necessarily directly to him as in our ABC example. If the owner of A does not receive the money from the owner of C after he pays out first to the owner of B, he will be broken. Besides, there is no way to satisfy Clower's cash in advance constraint. But if no trader pays out first, or buys something first, how is the trade executed, or how is money circulated? This example indicates that to start the trade there must be a special trader who comes to the market only for paying without receiving, or only for buying without selling. We can expect that once such a trader come to the market, other potential transactions can be carried out. Does this type of special traders exist in the real world? The Multiplier Process as a Market Exchange Process I first remark that such special traders exist implicitly in some search models. For example, Kiyotaki and Wright (1993) assume, "Initially, a fraction M of the agents are each endowed with money while 1− M are each endowed with one real commodity." (p. 64) Clearly the M fraction of the agents can be regarded as our special traders, for they have nothing for trading except their money. In practice, they can be regarded as investors (and other autonomous demanders.) We find that an investor is exactly a special trader who comes to the market only for buying without selling. Gong (1995) present a Keynesian multiplier exchange model, which shows how various market exchanges are generated so long as an investor comes to the market. Since the money
Integration of Market Exchange and money circulation circulation presented here is exactly associated with this exchange model, it is necessary to describe it first The economy that we consider here is highly decentralized. However we could imagine a special place, perhaps called the"trader center", where all possible traders have to come to express their desired transactions. This idea does not mean, as Walras imagined, that all trad will get together"standing face to face. (Walras, 1954, p. 41)Moreover there is no need for a market manager or an auctioneer. Instead, we can imagine that the trade center is divided by various rooms(or plots), each correspond ing to a particular commod ity. We can suppose the room(or plot) is rented, either individually or jointly, by the producers who produce that correspond ing commod ity. In practice, the place of this kind is very much similar to, for example New York's Javits center, where various trade fairs take place. All these mean that although our economy is highly decentralized, it is also highly efficient in the sense that information can asily be transmitted, and therefore search for a potential trading partner is relatively easy Consider an investor who comes to, say, a construction market to express that he wants to buy a building and thus as a result, a contract (order) is made between him and a certain construction company. The manager of this company will calculate the inputs, including labor, steel, and other raw material, etc, needed for producing that building and hence a visit is arranged to these various input markets. This will generate a series of other exchanges (contracts). Continuously, those who sell their outputs to(or get contract with) the construction company as suppliers will also visit their own input markets as demanders. Therefore more exchanges will follow. We can expect that the process will continue until it moves to its endpoint The existence of such an endpoint ind icates that the sequence of reflections created by our initial investor will finally converge to zero. 5 6. A mathematical proof to this point has been provided in Gong(1995)
Integration of Market Exchange and Money Circulation 5 circulation presented here is exactly associated with this exchange model, it is necessary to describe it first. The economy that we consider here is highly decentralized. However we could imagine a special place, perhaps called the "trader center", where all possible traders have to come to express their desired transactions. This idea does not mean, as Walras imagined, that all traders will get together "standing face to face."(Walras, 1954, p. 41) Moreover there is no need for a market manager or an auctioneer. Instead, we can imagine that the trade center is divided by various rooms (or plots), each corresponding to a particular commodity. We can suppose the room (or plot) is rented, either individually or jointly, by the producers who produce that corresponding commodity. In practice, the place of this kind is very much similar to, for example, New York's Javits center, where various trade fairs take place. All these mean that although our economy is highly decentralized, it is also highly efficient in the sense that information can easily be transmitted, and therefore search for a potential trading partner is relatively easy. Consider an investor who comes to, say, a construction market to express that he wants to buy a building and thus as a result, a contract (order) is made between him and a certain construction company. The manager of this company will calculate the inputs, including labor, steel, and other raw material, etc., needed for producing that building and hence a visit is arranged to these various input markets. This will generate a series of other exchanges (contracts). Continuously, those who sell their outputs to (or get contract with) the construction company as suppliers will also visit their own input markets as demanders. Therefore more exchanges will follow. We can expect that the process will continue until it moves to its endpoint. The existence of such an endpoint indicates that the sequence of reflections created by our initial investor will finally converge to zero.5 6 . A mathematical proof to this point has been provided in Gong (1995)