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)
Integration of Market Exchange and money circulation We might call this endpoint an equilibrium. It is not the usual demand-supply equili is an equilibrium(in the Nash sense) correspond ing to our initial investment. In practice, an "end point "may never exist since more investors and other autonomous demanders will come in succession before the end of the reflections created by the previous investor. Furthermore, the time taken by the sequence of reflections due to a certain autonomous demand may be very long All these indicate that the trades. which seem to be carried in a disordered random fashion in our daily life, intrinsically proceed orderly: they are the reflections or multiplier effects due to certain (not necessarily one type of) prev ious autonomous demands-though it is always difficult, actually impossible, to distinguish which reflection (or exchange) is attributed to which autonomous demand We now turn to show that such a trad ing process is naturally integrated with a process of money circulation Money circulation, an Inward-looking in Real Market We may distinguish two types of inward-looking of money circulation: one is in the real market and the other in the financial market. Our previous discussion is about the market exchanges in the real market, from which we have known that an investor can be regarded as a starting point of a sequence of market exchanges. Since investment is only a paid-out, we thus can expect that the money is injected into the real market once the investment expenditure is paid out. Where the money comes from of the investor is related to the process of financial exchanges and hence turns out to be another inward-looking of money circulation. The circulation in financial market will be the subject of the next section. In this section, we assume that our supposed investor has enough money in his account for him to pay his investment expenditure The money circulation without financial exchanges can be imaged as in Figure(1)
Integration of Market Exchange and Money Circulation 6 We might call this endpoint an equilibrium. It is not the usual demand-supply equilibrium. It is an equilibrium (in the Nash sense) corresponding to our initial investment. In practice, an "endpoint" may never exist since more investors and other autonomous demanders will come in succession before the end of the reflections created by the previous investor. Furthermore, the time taken by the sequence of reflections due to a certain autonomous demand may be very long. All these indicate that the trades, which seem to be carried in a disordered random fashion in our daily life, intrinsically proceed orderly: they are the reflections or multiplier effects due to certain (not necessarily one type of) previous autonomous demands ⎯ though it is always difficult, actually impossible, to distinguish which reflection (or exchange) is attributed to which autonomous demand. We now turn to show that such a trading process is naturally integrated with a process of money circulation. Money Circulation, an Inward-looking in Real Market We may distinguish two types of inward-looking of money circulation: one is in the real market and the other in the financial market. Our previous discussion is about the market exchanges in the real market, from which we have known that an investor can be regarded as a starting point of a sequence of market exchanges. Since investment is only a paid -out, we thus can expect that the money is injected into the real market once the investment expenditure is paid out. Where the money comes from of the investor is related to the process of financial exchanges and hence turns out to be another inward-looking of money circulation. The circulation in financial market will be the subject of the next section. In this section, we assume that our supposed investor has enough money in his account for him to pay his investment expenditure. The money circulation without financial exchanges can be imaged as in Figure (1):
Integration of Market Exchange and money circulation investment firms tvh honey carve noone Figure 1: Money Cireulation, an Inward-looking in Real Market The payment of an investment, say I, can be thought of as being a starting point of the whole voyage of money circulation. This amount of money, which is also equal to vi, is flowed out from the account of the investor to that of the corresponding sellers. this will realize the production of the first round enterprises and hence a certain amount of profit will be generated. the enterprises may retain a part of profit in their deposit accounts as their own saving sf, which is therefore withdrawn from the circulation in the real market. The rest of the money, including the dividends p,, the payments to labor wi and the payments to the second round firms for purchasing material my, will be continuously circulated Among the m, m, is flowed into the account of the second round firms, and w, and p, into the account of the first round households as consumer income Again part of this income will be flowed into the account of the second round firms as the pay ments of consumption C1: and the other will be retained as consumer saving sh, in their deposit accounts and hence ithdrawn from the circulation Now the total amount of money flowed in to the accounts of the second round firms is m,+Cl which is also equal to v2. A part of them sf, will be retained and hence withdrawn from the circulation and the other will be continuously flowed out. he circulation process will continue. But since in each round, a certain amount of money is withdr awn from the circulation as saving, the actual money in the circulation will be continuously contracted. We can expect that if there is no further additional money (such as through investment) injected into the circulation, the money in the circulation will finally converge to zero. this implies that the total amount of saving- which is the money
Integration of Market Exchange and Money Circulation 7 The payment of an investment, say I, can be thought of as being a starting point of the whole voyage of money circulation. This amount of money, which is also equal to v1 , is flowed out from the account of the investor to that of the corresponding sellers. This will realize the production of the first round enterprises and hence a certain amount of profit will be generated. The enterprises may retain a part of profit in their deposit accounts as their own saving sf1 , which is therefore withdrawn from the circulation in the real market. The rest of the money, including the dividends p1 , the payments to labor w1 and the payments to the second round firms for purchasing material m1 , will be continuously circulated. Among the m, m1 is flowed into the account of the second round firms, and w1 and p1 into the account of the first round households as consumer income. Again part of this income will be flowed into the account of the second round firms as the payments of consumption c1 ; and the other will be retained as consumer saving sh1 in their deposit accounts and hence withdrawn from the circulation. Now the total amount of money flowed into the accounts of the second round firms is m c 1 + 1 , which is also equal to v2 . A part of them sf2 will be retained and hence withdrawn from the circulation and the other will be continuously flowed out. The circulation process will continue. But since in each round, a certain amount of money is withdrawn from the circulation as saving, the actual money in the circulation will be continuously contracted. We can expect that if there is no further additional money (such as through investment) injected into the circulation, the money in the circulation will finally converge to zero. This implies that the total amount of saving — which is the money
Integration of Market Exchange and Mo Circulation drawn from the circulation is equal to the total amount of investment which is the money injected into the circulation at the b Money circulation, an Inward-looking in Financial Market One can easily find that all transactions in the above process satisfy Clowers cash in advance constraint except the investment. Implicitly, I assume that the investor has enough money for his investment expend iture. Where does this money come from? This is a pro blem of how investment is financed. The financing process leads the money to flow out from the accounts of the corresponding financiers into that of the investors We have known that saving can be viewed as a withdrawn of money from the circulation in the real market. The savor- when add itional money is flowed into his account -may find he is now in excess balance. While hold ing some of his money still in his account for ord inary uses he will seek to dispose his excess money by paying out for buying assets. If he buys real assets, he is now investing; if he buys financial assets, he is financing other investors either d irectly or ind irectly. Here the"directly"means that the savor buys the new issued stocks or the financ ial assets sold by the investors who need cash. The "indirectly means that the savor buys the financial assets not sold by investors but by the financial traders who will use cash to buy other financial assets. When the latter engages in their own buying activity, they are again d irectly or indirectly financing other investors. We thus can expect that when the savor injects his idle cash into the financial market, the money will be circulated within the financial market for a while When it is circulated out, the money -must with the amount exactly the same as the original idle cash injected by the savor- will be flowed into the account of the investor Money circulation, an Outward-looking
Integration of Market Exchange and Money Circulation 8 withdrawn from the circulation — is equal to the total amount of investment — which is the money injected into the circulation at the beginning. Money Circulation, an Inward-looking in Financial Market One can easily find that all transactions in the above process satisfy Clower's cash in advance constraint except the investment. Implicitly, I assume that the investor has enough money for his investment expenditure. Where does this money come from? This is a problem of how investment is financed. The financing process leads the money to flow out from the accounts of the corresponding financiers into that of the investors. We have known that saving can be viewed as a withdrawn of money from the circulation in the real market. The savor — when additional money is flowed into his account — may find he is now in excess balance. While holding some of his money still in his account for ordinary uses, he will seek to dispose his excess money by paying out for buying assets. If he buys real assets, he is now investing; if he buys financial assets, he is financing other investors either directly or indirectly. Here the "directly" means that the savor buys the new issued stocks or the financial assets sold by the investors who need cash. The "indirectly" means that the savor buys the financial assets not sold by investors but by the financial traders who will use cash to buy other financial assets. When the latter engages in their own buying activity, they are again directly or indirectly financing other investors. We thus can expect that when the savor injects his idle cash into the financial market, the money will be circulated within the financial market for a while. When it is circulated out, the money — must with the amount exactly the same as the original idle cash injected by the savor — will be flowed into the account of the investor. Money Circulation, an Outward-looking
Integration of Market Exchange and money circulation We are now ready to present an outward-looking of money circulation. This can be shown as in Figure(2). Note that what we havent discussed is the role of bank. Since investors may also be financed from the bank, the money flow with respect to the bank should also be included.6 nterest vestors Figure 2: Money Circulation, an Outward-looking The circulation here is now closed. continuous and hence also d ynamics It is the investment that draws out the money from the account of the investor and circulated into the commodity and labor market for real exchanges. The corresponding result of this circulation is the generation of arious economic activities: production, employment, consumption and saving. The latter is flowed out and hence turns out to be a withdrawal from the circulation in the real market this withdrawn money -after deducting those that must be kept in the account for ordinary uses(the working capital)and those that must be flowed into the bank as loan return and interest payments will be re-pulled by financial exchanges into the of new investors. Therefore new economic activities will be generated when these new investments are paid out. Meanwhile the bank can also create money, the deposit money, through its loan to investors With the money circulation presented above, the inclusion of government and central bank is straightforward(see Figure 3) 6. For simplicity, l exclude the short-term loan that might be used to finance a firm s daily production process
Integration of Market Exchange and Money Circulation 9 We are now ready to present an outward-looking of money circulation. This can be shown as in Figure (2). Note that what we haven't discussed is the role of bank. Since investors may also be financed from the bank, the money flow with respect to the bank should also be included.6 The circulation here is now closed, continuous and hence also dynamics. It is the investment that draws out the money from the account of the investor and circulated into the commodity and labor market for real exchanges. The corresponding result of this circulation is the generation of various economic activities: production, employment, consumption and saving. The latter is flowed out and hence turns out to be a withdrawal from the circulation in the real market. This withdrawn money — after deducting those that must be kept in the account for ordinary uses (the working capital) and those that must be flowed into the bank as loan return and interest payments — will be re-pulled by financial exchanges into the account of new investors. Therefore new economic activities will be generated when these new investments are paid out. Meanwhile the bank can also create money, the deposit money, through its loan to investors. With the money circulation presented above, the inclusion of government and central bank is straightforward (see Figure 3). 6 . For simplicity, I exclude the short-term loan that might be used to finance a firm's daily production process
Integration of Market Exchange and money circulation Mot ccount of Goverme Implications to post Keynesian macroeconomics In this paper, I present a contribution to the issue of money circulation. The money circulation presented here is based on a market exchange process, called the multiplier process Such a process shares much similarity as in those of search process, but it goes a step further by introducing a special trader, call the autonomous demander. With this introduction, the exchanges need not be executed randomly and disorderly as in most search process models Money in such a process is naturally integrated with the proceed ing of market exchanges, and Clower's"cash in advance" constraint is always satisfied. Outwardly, the money circulation is now closed, continuous and dynamics The post Keynesian approach to economic theory builds on Keynes's General Theory in which the aggregate demand is decomposed into two parts: D, and D2.7 According to Keynes, D, the consumption, is induced by income, and therefore the aggregate demand is fundamentally determined by D,, the investment. As D, is determined(through an investment function), the aggre gate demand is also determined at a multiple of D2. Algebraically, if Y=C+1, and C=cY, then Y=/(1-c) As Davidson(1992) points out, "Since classical theory does not recognise the possibility of a D2 category Keynes's taxonomy prov ides an inherently more general theory. "(p. 458)
Integration of Market Exchange and Money Circulation 10 Implications to Post Keynesian Macroeconomics In this paper, I present a contribution to the issue of money circulation. The money circulation presented here is based on a market exchange process, called the multiplier process. Such a process shares much similarity as in those of search process, but it goes a step further by introducing a special trader, call the autonomous demander. With this introduction, the exchanges need not be executed randomly and disorderly as in most search process models. Money in such a process is naturally integrated with the proceeding of market exchanges, and Clower's "cash in advance" constraint is always satisfied. Outwardly, the money circulation is now closed, continuous and dynamics. The post Keynesian approach to economic theory builds on Keynes's General Theory in which the aggregate demand is decomposed into two parts: D1 and D2 . 7 According to Keynes, D1 , the consumption, is induced by income, and therefore the aggregate demand is fundamentally determined by D2 , the investment. As D2 is determined (through an investment function), the aggregate demand is also determined at a multiple of D2 . Algebraically, if Y = C + I , and C = cY , then, (1) Y = I (1− c) 7 . As Davidson (1992) points out, "Since classical theory does not recognize the possibility of a D2 category, Keynes's taxonomy provides an inherently more general theory." (p. 458)
