Keynes s revolving fund of finance and transactions in the Circuit

Transcription

1 Keynes s revolving fun of finance an transactions in the Circuit By Steve Keen 1 Keynes s primary motivation in writing Alternative theories of the rate of Interest an The ex-ante theory of the rate of interest was to counter attempts by Ohlin an others to recast his liquiity preference theory as no more than a supply an eman moel of the etermination of the rate of interest. This rearguar action was ultimately unsuccessful, given the profession s ultimate acceptance of Hicks s IS-LM analysis as a summary of the General Theory. However, it also ha a positive outcome, as tussling with Ohlin s arguments le Keynes to propose that investment finance was an aitional eman for money (Keynes 1937b: 247) to the General Theory s triumvirate of transactions, precautionary an speculative emans. Keynes s musings on the interplay between firms who wish to borrow to finance investment, an banks that provie that finance, is prescient of, an of course partly inspire, the Circuitist School s later contribution. But Keynes s less formal logic also reache some conclusions contrary to current Circuitist belief. Keynes was correct on these points, while recent Circuitist literature is in error. Notwithstaning this however, the contributions of Graziani et alia on the nature of a monetary economy are essential to the evelopment of a proper moel of Keynes s revolving fun of liqui finance (Keynes 1937c: 666). THE REVOLVING FUND Keynes ientifies three sources of confusion between himself an Ohlin, Hicks an Robertson (Keynes 1937b: ); the thir of these a confusion between the money neee to initiate an investment, an the money neee while investment is actually proceeing le to the evelopment of the concept of a finance eman for money: I procee to the thir possible source of confusion, ue to the fact (which may eserve more emphasis than I have given it previously) that an investment ecision (Prof. Ohlin s investment ex-ante) may sometimes involve a temporary eman for money before it is carrie out, quite istinct from the eman for active balances which will arise as a result of the investment activity whilst it is going on. (Keynes 1937b: 246) Keynes emphasizes that, if a planne investment is to be turne into an actual one, then the investor will have a nee for money that precees the investment itself: Planne investment i.e. investment ex-ante may have to secure its financial provision before the investment takes place; that is to say, before the corresponing saving has taken place There has, therefore, to be a technique to brige this gap between the time when the ecision 1 Associate Professor of Economics & Finance, University of Western Syney, Australia;

2 to invest is taken an the time when the correlative investment an saving actually occur. (Keynes 1937b: 246) This finance coul be secure either by new equity or new bank ebt. In either case, there will be an imbalance between the market s commitments to finance these ventures, an actual savings at that point in time, which generates a finance eman for money. Keynes argues that this shoul be consiere a fourth, aitional motive for esiring money in aition to the transactions, precautionary an speculative motives etaile in the General Theory: Investment finance in this sense is, of course, only a special case of the finance require by any prouctive process; but since it is subject to special fluctuations of its own, I shoul (I now think) have one well to have emphasise it when I analyse the various sources of the eman for money. (Keynes 1937b: 247) Keynes s iscussion of how this eman might be met strengthens Dow s case, that Keynes viewe the money supply as enogenous (Dow 1995). Though he observes that aitional finance eman for money might rive up the rate of interest which is consonant with a fixe, exogenously etermine money stock he also countenances that the banking system might meet this eman with an aitional supply which implies an enogenous process of money creation: Now, a pressure to secure more finance than usual may easily affect the rate of interest through its influence on the eman for money; an unless the banking system is prepare to augment the supply of money, lack of finance may prove an important obstacle to more than a certain amount of investment ecisions being on the tapis at the same time. (Keynes 1937b: 247; emphasis ae) Keynes continues that the ecision to supply money as finance for investment is an important eterminant of the level of economic activity. Thus while he rejecte the classical view that savings etermine investment, he argue that finance etermines investment, an investment in turn etermines savings. It is the supply of available finance which, in practice, hols up from time to time the onrush of new issues. But if the banking system chooses to make the finance available an the investment projecte by the new issues actually takes place, the appropriate level of incomes will be generate out of which there will necessarily remain over an amount of saving exactly sufficient to take care of the new investment. (Keynes 1937: 248) In making this case, Keynes also states unambiguously that banks control the supply of money: The control of finance is, inee, a potent, though sometimes angerous, metho for regulating the rate of investment (though much more potent when use as a curb than as a stimulus). Yet this is only another way of expressing the power of the banks through their control over the supply of money i.e. of liquiity. (Keynes 1937: 248) Money is thus an enogenous variable, with its etermination involving both the esire by firms to invest, an the willingness of banks to len. Keynes starts his

3 consieration of this process with a constant level of investment i.e., with a steay stream of investment projects coming forwar over time, so that the rate of change of aggregate investment with respect to time is zero. In this case, Keynes argues that a constant stream of investment can be finance by a fixe pool of money, which turns over continuously: If investment is proceeing at a steay rate, the finance (or the commitments to finance) require can be supplie from a revolving fun of a more or less constant amount, one entrepreneur having his finance replenishe for the purpose of a projecte investment as another exhausts his on paying for his complete investment. (Keynes 1937b: 247) This implies that a constant level of economic activity can be sustaine by a constant stock of money since investment in turn etermines the level of income, an a constant level of gross investment implies a constant capital stock. Rising investment, on the other han, implies rising capital an rising output, an here Keynes argues that there will be a rising eman for money for finance: if ecisions to invest are (e.g.) increasing, the extra finance involve will constitute an aitional eman for money (Keynes 1937b: 247). As note above, Keynes countenances that this eman coul put upwars pressure on the rate of interest, if banks i not generate more money. But it coul also lea to banks increasing the money supply if the banking system chooses to make the finance available. In tranquil times, banks woul willingly supply aitional finance when firms esire a rising level of investment, an this in turn woul cause rising incomes over time. The eman for money woul thus call forth its supply. Keynes conclues with observations about the tenency of economists to confuse finance an saving, an stocks an flows. Finance, he emphatically eclare, has nothing to o with saving. At the financial stage of the proceeings no net saving has taken place on anyone s part, just as there has been no net investment. Finance an commitments to finance are mere creit an ebit book entries, which allow entrepreneurs to go ahea with assurance. (Keynes 1937b: 247). Keynes s conjecture that confusion between stocks an flows was the source of important errors in monetary theory is worth quoting at length: It is possible, then, that confusion has arisen between creit in the sense of finance, creit in the sense of bank loans an creit in the sense of saving. I have not attempte to eal here with the secon. It shoul be observe that a confusion between the first an the last woul be one between a flow an a stock. Creit, in the sense of finance, looks after a flow of investment. It is a revolving fun which can be use over an over again. It oes not absorb or exhaust any resources. The same finance can tackle one investment after another. But creit, in Prof. Ohlin s sense of saving, relates to a stock. Each new net investment has new net saving attache to it. The saving can be use once only. It

4 relates to the net aition to the stock of actual assets. (Keynes 1937b: 247; emphasis ae) Keynes s concept of a finance eman for money thus provies a link between a flow of eman for creit money, an the stock of creit money that is neee to meet that flow eman, given the time lags in the economy. Unlike Keynes, the Circuitist School has attempte to eal with creit in the sense of bank loans. In so oing, they have reache several conclusions that implicitly or explicitly contraict Keynes. Keynes implicitly argues that capitalists coul make aggregate money profits, after borrowing money at positive rates of interest, when he speaks of one entrepreneur having his finance replenishe for the purpose of a projecte investment as another exhausts his on paying for his complete investment. In contrast, Circuitists explicitly allege that capitalists cannot make aggregate monetary profits, even if the rate of interest is zero: in the basic circuit approach (escribing a close economy with no government expeniture), firms in the aggregate can only obtain the wage bill they avance to workers (w N ) an, as a result, it is impossible for all firms to obtain money profits. (Bellofiore et al. 2000: 410) 1 Keynes argues that constant economic activity coul be supporte with a constant stock of money, regarless of how workers allocate their wages. Circuitists claim that a constant level of activity requires an increasing stock of money if workers save, since with part of the borrowe money save, firms are unable to repay their bank loans in full: If, as is likely to be the case, firms wish to continue their activities, they have to renegotiate bank loans equal to the net stock of money in aition to any lening necessary to start a new prouction process. (Fontana 2000: 35) Crucially, Keynes sees money turning over inefinitely in revolving fun of liqui finance so that money, once create, exists forever (though he i not consier the issue of bankruptcy). On the other han, in Circuitist literature, money is estroye when loans are repai: To the exten that bank ebts are repai, an equal amount of money is estroye (Graziani 2003: 29-30) In all these points of contraiction, Keynes is correct an the Circuitists are wrong, for the reason Keynes gave in 1937: Circuitists, like so many economists before them, have confuse stocks with flows. However, Circuitist insights into the nature of money, an of exchange in a monetary economy, play a crucial role in turning Keynes s accurate verbal insights into a workable mathematical moel of a monetary prouction economy. THE CANONICAL CIRCUITIST INSIGHTS The three key contributions of the Circuitist School are: The proposition that a true monetary economy cannot use a commoity as money;

5 The insight that exchanges in a monetary prouction economy are three-sie, single commoity transactions; an A logical efinition of money that is free of the customary confusions that arise from efining money in terms of ifferent types of bank eposits. The first proposition is erive from the simple observation that an economy using as money a commoity coming out of a regular process of prouction, cannot be istinguishe from a barter economy (Graziani 1989: 3). From this it follows that true money is a token, which in turn gives rise to two further conitions, that: the use of money must give rise to an immeiate an final payment an not to a simple commitment to make a payment in the future; an the use of money must be so regulate as to give no privilege of seigniorage to any agent. (Graziani 2003: 60) These conitions lea to the secon funamental insight, that all sales in a monetary economy involve three parties: a seller, a buyer, an a bank which transfers the requisite number of units of account from the buyer s account to the seller s. These in turn provie a efinition of money that enables it to be clearly istringuishe from creit another confusion that Keynes notes. Money is as a unit of account whose transfer is accepte as final payment in all commoity an service exchanges; creit, on the other han, enables a commoity or service exchange to occur, but involves a continuing ebtor-creitor relationship between the buyer an the seller. CIRCUITISTS AND CHARTALISTS The State plays no necessary role in the above efinition of money though Circuitists of course acknowlege the existence of fiat money, an generally accept the Chartalist or state theory of money position with respect to the origins of money an its moern legal framework (see for example Graziani 2003: 78-80). However, this School has attempte to buil moels which at the outset have no government sector nor any explicit role for the Central Bank (Graziani 2003: 26-32). In this sense, the Circuit approach conflicts with the Chartalist argument that It is thus impossible to separate the theory of money from the theory of the state (Wray 2000: 50). From the Circuitist point of view, the prouction an enforcement of a unit of account by a tax-levying state is an embellishment to its funamental concept of money. The Circuitist starting point of a pure creit economy is thus arguably closer to the essential nature of money, even if so-calle State Money is the universal norm toay, an even State enforcement of monetary obligations may be the only viable way to sustainably meet Graziani s anti-seignorage conition in the real worl. However, the failure to ate of Circuitists to prouce a coherent moel of enogenous money coul have implie that the Chartalist position was correct, in that a tax-levying state was inee an essential component of a functional moel of money. In fact, as I show below, a functional moel of a monetary prouction economy can be built without either a government sector or a central bank, so long as transfers between private bank accounts are accepte as making final settlement of ebts between buyers an sellers.

6 THE BASIC CIRCUITIST MODEL Graziani 2003 presents a canonical version of the Circuitist verbal moel of a monetary prouction economy. The moel is escribe as having four classes of agents the central bank, commercial banks, firms an wage earners (26-27) but espite this, the central bank is given no role in the moel itself. The actual moel therefore has only three agents. 2 The moel s monetary ynamics commence with A ecision... by the banks to grant creit to firms, thus enabling them to start a process of prouction (27). Graziani argues that the amount of creit emane by the firms (an supplie by the banks) equals the wage bill for the planne level of prouction. Using the borrowe money, capitalists pay workers an put them to work to prouce commoities. These are then sol, with consumer goos being sol to workers an investment goos to other capitalists (sales to bankers appear later). Spening by workers on consumer goos (an also purchases of corporate bons by workers) return money to the firms, who can then use this money to repay their ebt to banks. This repayment of ebt estroys money: To the exten that bank ebts are repai, an equal amount of money is estroye (29-30). The repayment of ebt closes the circuit, but this only happens If wage earners spen their incomes entirely (incluing on purchases of corporate bons). However if they on t, then ilemmas arise: If instea wage earners ecie to keep a portion of their savings in the firm of liqui balances, firms are unable to repay their bank ebt by the same amount. (30) The next cycle, if it involves an ientical scale of prouction, therefore requires new money, so that the money supply must increase to finance a constant scale of prouction. The new quantity of money in this secon circuit will be equal to the wage bill plus the new liqui balances set asie by wage earners at the en of the previous cycle (31). The above, however, omits the problem of interest on ebt! Graziani acknowleges this in contrast to some Circuitist papers that abstract from the problem, in a manner that is embarrassingly reminiscent of the neoclassical approach to logical conumrums (Bellofiore et al. 2000: 410 footnotes 8 an 9). It appears that firms are unable to pay interest: even in the most favourable case [corresponing to workers spening all their wages], the firms can only repay in money the principal of their ebt an are anyhow unable to pay interest. (31) The solution he proffers, in a monetary moel, is a real one, that banks are pai in commoities rather than money: the only thing they can o is to sell part of their prouct to the banks, which is tantamount to saying that interest can only be pai in kin (31). At least bankers get their hans on the physical loot: capitalists, it seems, en up with neither goos nor money. Money profits in the aggregate are zero, an profits earne by one firm may simply be the mirror image of inefficiencies an consequent losses incurre by other firms (32).

7 A DYNAMIC MODEL OF THE CIRCUIT Starting from precisely the same founation, I reach contrary conclusions on almost every point above, an conclue instea that Keynes s 1937 insights were correct. A constant level of prouction can be finance with a constant stock of money (see also Anresen 2006); firms can easily pay the interest on ebt with money; an firms in the aggregate earn money profits. Money is not estroye by the repayment of ebt (though bank eposits are estroye by loan repayment, an the stock of money available for transactions at any one time is reuce); workers can have positive bank balances without forcing firms to make losses; an, though it is relate to the wage bill, the initial amount borrowe is in fact far smaller. These contrary conclusions arise simply from applying the correct form of mathematical analysis to the Circuitist school s logical insights into the nature of a monetary prouction economy. The Circuit is funamentally ynamic, an can therefore only be properly unerstoo using ynamic analysis. Mathematical ynamics are essential here, partly because the interrelations between entities in a ynamic moel are easily mis-specifie in verbal analysis, an especially because it is easy, in a verbal exposition, to confuse stocks an flows. In what follows, I construct a skeletal ynamic mathematical moel of the Circuit, using balance sheets in which all entries are flows. The moel is, I stress, eliberately skeletal: causal factors of financial flows that are clearly variables in the real worl are treate as constants with the intention that these will inee be mae variables in a later moel. However, just as much is learnt in anatomy by stuying skeletons, much can be learnt about the actual monetary systems by stuying a stylize system in which the causes of financial instability are absent. Graziani s moel has three classes of agents firms, bankers, an workers. Since this is a monetary economy, all three classes have eposit accounts which I inicate as F D, B D an W D respectively. Prior to the making of a loan, all three accounts have zero balances, an firms ebt to banks F L is likewise zero (this is not a bank account as such: it oes not contain money, nor can money be pai into it, but it instea recors the outstaning obligation of the firms to the banks; it is, therefore, a recor of account). This ab initio situation is shown in Table 1. Bank Assets & Liabilities Time Assets Liabilities Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Initial values Table 1: Initial conitions prior to loan

8 In step one of the moel, banks make loans to the firms. Since this is creit money, a ebt obligation is create between the firms an banks along with the creation of money. Using L to signify the magnitue of the loan, this results in the situation shown in Table 2. This clearly emboies the irect an causal loans create eposits perspective of enogenous money. Bank Assets & Liabilities Time Assets Liabilities Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Start of loan Table 2: Loan issue L L 0 0 A loan generates an obligation to pay interest to the lener, while a eposit obligates the bank to pay interest to the epositor. I use r L for the rate of interest on loans an r D for the rate on eposits, (where r L >r D ). These obligations are shown in Table 3. Bank Assets & Liabilities Time Assets Liabilities Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Obligations initiate by loan +r L F L +r D F D 0 0 Table 3: Loan an eposit obligations We now move from the loan obligations to the flows which must occur out of accounts in the system since there is no other source of money. The firms must therefore pay the loan interest obligation out of their eposit account F D, while the bank must pay its eposit interest obligation out of its eposit account B D. The flows occur between these two eposit accounts, an the payment of loan interest is recore on the asset sie of the leger, so that the firms ebt remains constant at the level of the initial loan L. Since the interest payments flow between the firm an banker eposit accounts, the overall sum of eposit accounts also stabilises at L; but since r L >r D,

9 the balance shifts from the firms eposit account to the bankers over time. This ynamic is shown in Table 4. Bank Assets & Liabilities Flows Assets Liabilities SAM Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Sum Interest flows initiate by loan +r L F L - r L F L =0 Table 4: Payment of interest +r D F D - r L F L +r L F L - r D F D 0 0 Equation (0.1) states this incomplete system as a set of couple ODEs. It is obvious that the level of ebt will remain constant (at the initial value L), as will the sum of eposit accounts, but the money in the firms account will over time be transferre to the banks. At some point, firms eposit accounts will turn negative which is of course an unsustainable situation. F L = 0 F = r F r F D D D L L B = r F r F W D L L D D D = 0 (0.1) Figure 1 shows a simulation of this system. Given the set of example parameter values (L=100, r L =5%, r D =3%) while the outstaning loan an the sum of eposit accounts remain at 100 throughout, all the money has been transferre from the firms eposit account to the bankers after 30.5 years.

10 Given Initial values Flow ynamics Firm loan account F L ( 0) = L Firm eposit account F D ( 0) = L Bank eposit account B D ( 0) = 0 Worker eposit account W D ( 0) = 0 F L ( t) F D ( t) = B D ( t) = = W D ( t) r L F L ( t) r D F D ( t) r L F L ( t) = 0 r L F L ( t) r L F L ( t) r D F D ( t) F L F D B D W D Account Balances := Oesolve F L F D B D W D, t, Y Circuit Moel Step One: Interest payment only Firm Loan Firm Bank (RHS) Worker (RHS) Time F D ( Y) = 0 B D ( Y) = 100 W D ( Y) = 0 F D ( Y) + B D ( Y) + W D ( Y) = 100 Figure 1: Simulation of interest payment only moel in Mathca This outcome possibly explains why Circuitists have been loathe to acknowlege the nee to pay interest in their moels of the monetary circuit: the situation seems hopeless for firms. However, this is only because firms have not yet one anything with the borrowe money. In fact, it has been borrowe to finance prouction, which involves both buying inputs from other firms, an paying wages to workers. This in turn is one in orer to evoke a stream of purchases from other firms, workers an bankers from which the firms hope to make a net profit.

11 The issue of prouction, an the transactions enabling it an emanating from it, is another area of great confusion in Circuitist writings. The key confusion is one of stocks an flows, starting from the proposition that the size of the initial loan (the stock L) is equal to the wage payments neee to hire the workforce (a flow). Instea, the wage bill is relate, not to the initial loan, but to the rate of outflow of money from firms eposit accounts that is use to pay wages. Calling this rate of outflow w, an amount w.f D is transferre per unit of time (per year in this moel) from firms to workers as wages. Bank Assets & Liabilities Flows Assets Liabilities SAM Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Sum Wage flow to initiate prouction Table 5: Spening to finance prouction -w. F D +w. F D 0 The relationship between money an wages is thus not the creit initially grante [L, a stock] is totally turne into wages [w.f D, a flow] (Graziani 2003: 29). Instea, in this skeletal moel, wages equal a constant times the balance in the firms eposit account. 3 Given the relationship between the initial loan an the balance in the firms account, the annual wages pai can be substantially greater than the initial loan. With workers now having positive bank balances, they too are receipients of interest income. Though in the real worl workers normally get lower eposit rates than firms, for simplicity I will use the same rate of interest r D here. A flow of r D.W D is therefore eucte from the bankers account an eposite into the workers account.

12 Bank Assets & Liabilities Flows Assets Liabilities SAM Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Sum Interest income flows from wages Table 6: Incomes from prouction - r D. W D +r D. W D 0 To complete the moel, we have to inclue the flow of transactions from workers an bankers to capitalists that purchase the goos flowing (implicitly in this moel) in the opposite irection. Here I use ω for the rate at which spening flows from workers eposit accounts to firms, an β for the corresponing rate of spening by banks. The amounts ω WD an β BD are therefore eucte from workers an banks accounts respectively an creite to the firms account. The basic moel is finally complete, an as shown by the sum column of the Social Accounting Matrix, all transactions are properly accounte for an sum to zero so that money is neither create nor estroye. The components of the basic couple ODE moel can now be rea own the columns of the final 4 rows of Table 7.

13 Bank Assets & Liabilities Flows Assets Liabilities SAM Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Sum Interest flows initiate by loan 0 +r D.F D - r L.F L +r L.F L - r D.F D 0 0 Wage flow to initiate prouction -w. F D +w. F D 0 Interest income flows from wages - r D. W D +r D. W D 0 Flows from sale + ω W + β B Table 7: Transactions complete the basic moel D D β B D ω WD In couple ODE form, the moel is as shown in Equation (0.2). F L = 0 ( ) ( ω β ) ( ) β F = r F r F w F + W + B D D D L L D D D B = r F r F r W B D L L D D D D D W = w F + r W ω W D D D D D (0.2) The moel can now be simulate (see Figure 2; the aitional parameter values use here are w=3, ω = 26 an β = 0.5 ), an since it is a linear moel, its equilibrium can also be erive symbolically (see equation (0.3)) 0

14 100 Basic Circuit Moel 15 Account Balances Firm Loan Firm Bank (RHS) Worker (RHS) Time F D ( Y) = B D ( Y) = W D ( Y) = F D ( Y) + B D ( Y) + W D ( Y) = 100 Figure 2: Basic Circuit moel As is now obvious, the basic Circuitist moel with a single injection of enogenous money is consistent with sustaine economic activity over time contraicting the Circuitists since an increasing supply is not neee to sustain constant economic activity, an confirming Keynes 1937b (see also Anresen 2006). However, the amounts shown here are transaction account balances: we o not yet know whether these are compatible with sustaine incomes over time. L L ( ω rd ) ( β rl ) F L E ( ω ) ( β ) 100 w + rd rd FD E = ( ) = L rl rd BD E β rd W D E L w ( β r ) L ( w + ω rd ) ( β rd ) Income ynamics (0.3) Fortunately, two income flows are easily associate with particular transactions in equation (0.2): wages an interest income. Annual wages are equal to w F an gross bank interest income is rlf L ( an 5 per annum respectively in this simulation). Wages an interest income are thus positive an sustaine; what about profits? To reveal profits, we nee to consier what the term w represents. As well as being equivalent to wages, it also represents that part of the net surplus from prouction that accrues to workers. The net surplus in monetary terms itself epens on how rapily D

15 money investe in prouction returns to firms. In Marx s terms, it represents the time lag between extening M an receiving M+ (assuming, as I o in this skeletal moel, that the process occurs smoothly). This coul be a perio of, say, 4 months between financing prouction an receiving the complete procees of sale of output again something that woul be a variable in a more complex moel. There are thus two components to w: the share of the net surplus (in Sraffa s sense of the surplus, in which wages an profits are entirely pai out of the net surplus from the input-output process) from prouction going to workers, an the rate of turnover from M to M+, given by technical conitions of prouction an the time taken for the sale of physical commoities. I use s for the share of surplus accruing to the owners of firms (so that the share going to workers is thus 1-s), an P for the lag between M an M+. 4 We therefore have the relation given by equation (0.4): ( 1 ) w = s P (0.4) With w set to 3 in the simulation above, a hypothetical value of s of 0.4 (which correspons to a rate of surplus value in Marx s terms of 67%) yiels a value for P of 5 (which means that the lag between spening M an making M+ is 1/5 th of a year or 2.4 months). The monetary value of net output per annum is thus P.F D (which equals in equilibrium, given the parameter values in the moel) which is split between workers an the owners of firms in the ratio (1-s):s. In this ebt-finance only moel, the owners of firms then have to pay interest on their outstaning ebt to banks. Using Π, W an I to signify profits, wages an interest income respectively, the income flows of the moel in equilibrium are: L ( ω rd ) ( β rl ) ( ) ω β s P Π ( 1 s P + rd ) ( r ) E D IE = rd L = 5 W ( ω ) ( β ) E L r D rl ( 1 s) P (( 1 s) P + ω rd ) ( β rd ) (0.5) Firms thus o make net profits, which, though relate to the size of the initial loan, can be substantially larger than this amount (an profits are substantially larger than the servicing cost of ebt). Economic activity also continues inefinitely at an equilibrium level with a single injection of enogenous money: aitional money is not neee to sustain economic activity at a constant level. This contraicts Graziani s assertion that aitional money woul be neee if workers retaine positive bank balances (Graziani 2003: 31), but confirms Keynes s intuition that a revolving fun of a more or less constant amount can finance sustaine economic activity (Keynes 1937b: 248). The size of the initial loan L can also be relate to the equilibrium value of wages generate by the loan: (( 1 s) P + ω rd ) ( β rd ) ( 1 s) P ( ω r ) ( β r ) L = W = 100 E D L (0.6)

16 Two more issues remain to be consiere: the impact of ebt repayment, an the moelling of growth. Debt repayment an bank reserves Accoring to Graziani an almost all theorists in enogenous money the repayment of ebt estroys the money that was create with it (Graziani 2003: 29-30). I consier this by aing an aitional term R L to represent the repayment of ebt. If we relate this to the level of outstaning ebt 5, then the amount R L.F L is eucte from the firms only source of money, F D. Yet to where oes it go? Here Graziani s anti-seignorage conition comes into play: the use of money must be so regulate as to give no privilege of seigniorage to any agent (Graziani 2003: 60). This repayment therefore cannot be mae to the existing bankers eposit account B D, since banks use this account to finance spening on commoities. It must therefore go to a separate, capital account: the banks reserve account, which I call B R. Reserves, once create by the repayment of loans, will be re-lent. This amount will be eucte from the banks reserve account an eposite in the firms eposit account an a matching entry will be mae in the firms loan recor of account. The complete relations are shown in Table 8.

17 Bank Assets & Liabilities Flows Assets Liabilities SAM Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Income Repayment of ebt Relening of reserves -R L.F L -R L.F L -R L.F L +L R.B R +L R.B R +L R.B R Bank Reserves Time Reserve Account Capital Repayment of ebt R L.F L +R L.F L Relening of reserves -L R.B R -L R.B R SAM Sum 0 Table 8: Repayment an relening The repayment of loans therefore oes not estroy money, but transfers it out of income accounts where it can be use for expeniture to a reserve account. The proposition that money is estroye when loans are repai in part reflects economic conventions that money is the sum of active bank balances. If money is efine that way, then it is inee estroye; but I feel that the ynamics of enogenous money creation are more clearly illuminate if we efine money in the funamental Circuitist sense as a token whose transfer settles all commitments between traing parties. That token can then resie in active accounts (eposits) or inactive accounts (reserves). Repayment of loans alters the balance between active an inactive accounts, an thus alters the amount of money in circulation, but it oes not estroy the token itself. Once there, it is an unemcumbere asset of the banks which can then be re-lent though not spent irectly on commoities or services. This as an important aitional insight to the concept of enogenous money: not only o loans create eposits, but the repayment of loans creates reserves. This results in the moel shown in equation (0.7):

18 F = + L B R F L R R L L ( ) ( 1 ) ( ω β ) ( ) ( ) β ( 1 ) ω F = r F r F s P F + W + B + L B R F D D D L L D D D R R L L B = r F r F r W B D L L D D D D D W = s P F + r W W D D D D D B = + R F L B (0.7) R L L R R The simulation results for this moel are shown in Figure 3 (with a shorter time span to show the initial ynamics). The new parameters R L an L R were given the values of 2 an 3 respectively. Figure 3: Moel with repayment an relening The equilibrium values are shown in Equation (0.8):

19 LR L L ( ω rd ) ( β rl ) F L L E R (( 1 s) P + ω r ) ( β ) 60 D rd F DE ( ) L r L rd BD = L = 2.55 E R LR + RL β rd W 5.95 DE L ( 1 s) P ( β r ) L B L 40 RE R (( 1 s) P + ω rd ) ( β rd ) RL L (0.8) It is obvious that money is not estroye, but turne into reserves that are then available for relening. However, there is a reuction in money in circulation at any one time, equivalent to the proportion of ebt that has been repai. Given the parameters use in this simulation, the amount of circulating money is reuce from 100 to 60 units. It is thus not money that is estroye by the repayment of ebt, but eposits in income accounts. This in turn reuces the amount available for the financing of prouction, reucing all incomes incluing that of banks. The equilibrium levels of income are now: Growth ΠE 103 = IE 3 W E (0.9) At this stage, the moel accors with Keynes s verbal analysis of the revolving fun of finance without growth. The final problem is how to moel enogenous money in a growing economy, when ecisions to invest are (e.g.) increasing an the extra finance involve will constitute an aitional eman for money. (Keynes 1937b: 248). Accounting for growth integrates Moore s Horizontalism into the Circuitist framework (Moore 1988). As Moore argues, firms negotiate lines of creit with banks that enable them to expan the available money, subject to the same sum being ae to their outstaning ebt. New money is thus create by an aition of an ientical sum to the firms eposit an loan accounts Using F I (for Firms Investment ) to signify the rate, an relating this to the level of firms eposit accounts, 6 this introuces a new term F I.F D into the columns for F L an F D in the final table. I have inclue the creation an simultaneous transfer of this new money in the banks reserve account simply to inicate that the enogenous creation of money by firms epens upon the legal right they have negotiate with banks to expan their borrowings. 7

20 Bank Assets & Liabilities Flows Assets Liabilities SAM Firm Loan (F L ) Firm (F D ) Banker (B D ) Worker (W D ) Income Investment by firms +F I.F D +F I.F D +F I.F D Bank Reserves Time Reserves Capital Investment by firms +F I.F D -F I.F D 0 SAM Sum +F I.F D Table 9: Enogenous creation of new money There is no offsetting transfer between income an capital accounts in this case, so that the term F I.F D causes a net increase in the money stock: it is an enogenous source of growth. As a result, rather than having a zero sum, the complete SAM has a positive sum, equal to the amount of new money F I.F D being create each year. The overall moel, as shown in Equation (0.10), is therefore issipative in the language of moern ynamic analysis rather than conservative, which has important implications for the feasible behaviour of any complete moel built on this skeleton. F = + L B R F + F F L R R L L I D ( ) ( 1 ) ( ω β ) ( ) ( ) β ( 1 ) ω F = r F r F s P F + W + B + L B R F + F F D D D L L D D D R R L L I D B = r F r F r W B D L L D D D D D W = s P F + r W W D D D D D B = + R F L B (0.10) R L L R R Though the amount of money an ebt in this final moel grow exponentially over time, the same relations hol between ebt an income eposits, while the overall money stock inclues both the sum of eposit accounts an the amount in banks reserves. At the en of the simulation perio (30 years), the enogenous money stock has grown from 100 to , of which is in circulation between firm, bank an worker income accounts, an of which is in the banks reserve account.

21 Figure 4: Moel with growth From parameters to behaviours Like a biological skeleton, this moel is esigne to have muscles attache, in that its fixe parameters can be replace by nonlinear behavioral relations that mimic those of real economies. Two that eserve special mention are R L an F I,, representing respectively the rate of relening by banks an the rate of new money creation riven by firms. The latter provies the Horizontalist aspect of this skeletal moel, an in a general moel woul be a nonlinear function of firms expectations of profits (see Keen 1995). The former reflects the Structuralist emphasis on the active role of banks in the creit system. In a financial crisis, this woul ten towars zero, while uring a perio of euphoric expectations the rate of relening woul accelerate. This illustrates another avantage of ynamic moelling over the conventional iagrammatic an static methos that Post Keynesian an Circuitist economists have in the past applie. Diagrammatic methos are necessarily two imensional, while static methos make it ifficult, if not impossible, to examine causal relations even when they are correctly specifie, which is rarely if ever the case. On the other han, this properly specifie ynamic moel enables the integration of the Horizontalist an Structuralist approaches (which coul be further embellishe by making the sprea between r L an r D a variable).

22 Conclusion Keynes was correct that a revolving fun of finance can initiate an inefinite stream of prouction, an that this fun is a necessary prelue to prouction itself in a monetary economy. The Circuitist formalisation of the concept of creit money plays an essential role in converting Keynes s vision from a verbal to a ynamic moel, but at the same time, some prevalent Circuitist concepts must be abanone in favour of Keynes s accurate insights from Both Keynes an Circuitists gain from this moel. Keynes is shown, once again, to have correctly ientifie the ynamics of a monetary prouction economy, even though he i lacke the assistance of mathematical logic to clarify his argument. Circuitists gain an effective expression of their moel, an lose only erroneous conclusions that shackle their capacity to achieve their real goal, of specifying the behaviour of enogenous money in a monetary prouction economy. References Anresen, Tron, (2006), A critique of a Post Keynesian moel of hoaring, an an alternative moel, Journal of Economic Behavior & Organization, 60: Chapman, Brian an Keen, Steve, (2006). Hic Rhous, Hic Salta! Profit in a Dynamic Moel of the Monetary Circuit, Storia Del Pensiero Economico: Bellofiore, Riccaro., Davanzati, G. F. an Realfonzo, R, (2000), Marx insie the Circuit: Discipline Device, Wage Bargaining an Unemployment in a Sequential Monetary Economy, Review of Political Economy, 12: Dow, Sheila (1997), Enogenous money, in Harcourt G.C. & Riach P.A., (es.), A Secon Eition of the General Theory, Routlege, Lonon. Fontana, Guiseppe., Post Keynesians an Circuitists on money an uncertainty: an attempt at generality, Journal of Post Keynesian Economics, 23: Fontana, Guiseppe, & Realfonzo, R., (es.), (2005), The Monetary Theory of Prouction, Palgrave, New York. Graziani, Augusto, (1989). The Theory of the Monetary Circuit, Thames Papers in Political Economy, Spring,:1-26. Reprinte in Musella, M. & Panico, C., (es.), (1995), The Money Supply in the Economic Process, Ewar Elgar, Alershot. Graziani, Augusto, (2003). The Monetary Theory of Prouction, Cambrige University Press, Cambrige. Keen, Steve, (1995). Finance an economic breakown: moelling Minsky s Financial Instability Hypothesis, Journal of Post Keynesian Economics, 17: Keynes, J.M., (1937a), The general theory of employment, Quarterly Journal of Economics, 51: Keynes, J.M., (1937b), Alternative theories of the rate of interest, Economic Journal, 47: pp

23 Keynes, J.M., (1937c), The ex-ante theory of the rate of interest, Economic Journal, 47: pp Moore, B. (1988), Horizontalists an Verticalists: The Macroeconomics of Creit- Money, Cambrige, Cambrige: Cambrige University Press. Rochon, Louis-Philippe, (2005), The existence of monetary profits within the monetary circuit, in Fontana & Realfonzo (2005), pp Similar conclusions are reache in numerous other Circuitist papers from Graziani 1989 on. Rochon puts the problem well: The existence of monetary profits at the macroeconomic level has always been a conunrum for theoreticians of the monetary circuit not only are firms unable to create profits, they also cannot raise sufficient funs to cover the payment of interest. In other wors, how can M become M`? (Rochon 2005: 125). 2 The Central Bank properly enters the Circuitist moel when the banking sector is expane, so that a seller can eposit the procees of a sale in a ifferent bank to that of the buyer. This necessitates a clearing house between banks, which is the primary role of a Central Bank in the Circuitist moel. In this paper, for the sake of simplicity, I omit inter-bank ynamics. 3 Later I apply Graziani s position that the eman for bank creit coming from proucers epens only on the wage rate an on the number of workers that firms inten to hire (29) to calculate the size of the initial loan L as a function of the equilibrium wage bill 4 Again, in a more complete moel, each of these stages of the process woul have their own equation with its own ynamics; here, for reasons of simplicity an exposition, they are all collapse into the values of s an P. 5 It coul equally be relate to the level of F D. 6 It coul as easily be relate to the level of outstaning loans, an woul oubtless have a more complex causal link in a full ynamic moel. 7 In a full moel, this coul be given a rationing ceiling; however I believe that a better way to inicate banks structuralist control over lening is to replace R L with a variable epenent upon financial conitions.