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were trained in the Marshallian concepts of the short and long run. It also has an appeal of apparent simplicity, as Fontana put it: "A single-period theory of money is to be used as a simple device to separate out the effect of constant expectations from the effects of disappointment and changes in the state of expectations.” (Fontana 2004: 83) However, there is a trap in this beguiling simplicity, as Fontana acknowledged. If “horizontalists” treat each single period as being in equilibrium, all disequilibrium change has to occur between periods—and effectively, out of time. With equilibrium analysis explaining the situation during each period, it appears that successive periods can only be linked via comparative statics. On the other hand, “continuation analysis” seems to beset “structuralists” with overwhelming complexity, since expectations—and everything else—are changing continuously. Often this has resulted, as Fontana observed, in “the practical need for structuralists to often rely on comparative statics exercises rather than full-blown dynamic experiments” (Fontana 2004: 381). Whichever way Circuitists turn, comparative statics seems inescapable. The solution, we argue, is to abandon the distinction itself, and instead to seek to combine in one analysis the horizontalist desire for analytic rigor, and the structuralist emphasis on processes of change. We achieve the latter by modeling the Circuit in continuous time using differential equations, and the former by starting with the simplest possible level of analysis, deliberately omitting consideration of behavioral issues, expectations (fulfilled or dashed), uncertainty, etc. We anticipate criticism that, by omitting these issues, our analysis is nonKeynesian. We concur that a full-blown Circuitist model must include expectations and uncertainty. However, until such time as Circuitists can explain the existence of profits in a capitalist economy, Circuitist analysis is not merely non-Keynesian, it is not even an analysis of capitalism itself. Once the basic analysis explains what we perceive in the real world—the long-term perpetuation of monetary production—then we can move on to the signature issues of Post Keynesian analysis. Modeling the Circuit in continuous time We consider a pure credit economy with capitalists, bankers and workers, but no central bank.1 The circuit begins with bankers extending loans to capitalists that enable them to hire workers, buy intermediate goods, produce and sell output.2 Loans necessarily include the obligations to pay interest and repay principal. While loan contracts can take many forms, we model an intermediate form that is also the aggregate outcome of many different loan contracts of different terms in a multi-agent economy. Given an initial loan level of KD(0), by the time T capitalists will attempt to 1 However, the framework we construct can serve as a basis for introducing fiat money at a later stage. 2We use plurals throughout because our model aggregates the outcome of multiple agents, without at this stage considering dynamics between agents of the same type.
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reduce the debt outstanding to the proportion X of its original level, where X<1.This gives us the basic relation: = KTK X () ()0 DD (1) We take the rate of interest on debt rd p.a. as fixed, and likewise the rate of interest on positive account balances of rc, where cd rr < . We assume that capitalists attempt to meet their principal and interest repayment obligations by paying a fixed proportion R p.a. of the outstanding debt. Part of R reflects repayment of the principal only;3 we label this RP. Part reflects repayment of the interest on the debt, and is identical to the amount added to debt by banks under the loan contract. We spell these out here for the sake of clarity, even though the two terms cancel each other out. Recording debt as a positive number, so that interest accruals add to it and repayments subtract from it, the complete equation for the debt account is thus: d =−+ dt KrKrRK DdDdPD () (2) A second account is also needed: a “credit” (more correctly, working capital) account KC, into which the endogenously created money is paid by the banks. When this account has a positive balance, the banks are obliged to pay interest at the rate rc, This second account is the source from which capitalists meet, as best they can, their loan repayment obligations. Its equation of motion is thus: d =−+ dt KrKrRK CCCdPD () (3) As with the debt account, interest receipts accrue to KC and principal and interest repayments subtract from it—and are instantly also deducted from the debt account.4 Finally, accounts are needed to record the banks’ transactions. Here we note an important observation from Graziani: in order to prevent seigniorage, banks cannot spend the money they endogenously create, but only the profit on the spread between loans and deposits. We therefore also provide two accounts for banks: a principal account BP, into which principal repayments flow, and an income account BY for banks’ lending activities. Thus PD RK flows into the principal account: d = dt BRK PPD and the net difference between dD 3 Solving for R, we get rK⋅ and CC ln X Rr T d (4) rK⋅ flows into the income account: =− where X<1. The dr component represents the repayment of interest on debt; the − ln X T component is the repayment of principal (this is positive because X<1) 4 This is the one sense in which “simultaneity” is allowed in this model: when, like a couple kissing, one act is the mirror image of the other.
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit =⋅−⋅ dt BrKrK YdDcC (5) Equations (2) to (5) complete the model at this stage, and encapsulate the dilemma on which all previous attempts to explain profit in the monetary circuit have foundered: it is obvious that, at the putative end of this cycle, capitalists will make a loss. Figure 1 illustrates this with an initial loan D0 of $1 million, a repayment target X of 10%, a target time T of 5 years, debit interest rate rd of 5% and a credit rate rc of 3%. The graphic shows the execution of this model in the mathematical simulation program Mathcad.5 5 This model could be implemented in any of several other packages—including Mathematica, Maple, Matlab, Scientific Workplace—but we find Mathcad to have by far the most intuitive interface. 4 of 20
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit 3/19/2006 5 of 20 X10%:=T5:=rd5%:=rc3%:=D0106:=RPlnX()−T:=y10:=points1000:=GiventKDt()ddrdKDt()⋅rdRP+
()KDt()⋅−KD0()D0tKCt()ddrcKCt()⋅rdRP+()KDt()⋅⎡⎣⎤⎦−KC0()D0tBPt()ddRPKDt()⋅BP0()0tBYt()ddrdKDt()⋅rcKCt()⋅−
BY0()0KDKCBPBY⎛⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎠OdesolveKDKCBPBY⎛⎜⎜⎜⎜⎜⎝⎞⎟⎟
⎟⎟⎟⎠t,y,points,⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦:=τ0ypoints,y..:=024681005.1051.1061.1055.10405.1041.105Capitalist DebtBankers PrincipalKC-KD Account (RHS)BY account (RHS)Capitalist DebtBankers PrincipalKC-KD Account (RHS)BY account (RHS)Transaction Account BalancesYearsKDτ()BPτ()KCτ()KDτ()−BYτ()τKCy()4.463−104×=BPy()9.9105×=KCy()KDy()−5.463−104×=BYy()5.463104×= Figure 1: Mathcad implementation of basic circuit without production or exchange Even at this simple level, our model enables us to reject an accepted Circuitist proposition, that endogenously created credit money is destroyed when debt is repaid. In his seminal paper Graziani’s states that “As soon as firms repay their debt to the banks, the money initially created is destroyed” (Graziani 1989: 5). This belief is echoed in many subsequent Circuitist works, as Rochon documented (Rochon 2005: 126, 127, 128). It is implicit in the “Kaldor-Trevithick reflux principle” (Lavoie 1999—though it is possible to re-interpret this concept in a manner consistent with our results), and accepted widely in Post Keynesian analysis (see for example Lavoie 1992, p. 130, cited in Rochon 2005 p. 130).
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit Money is not destroyed when debt is repaid, even when no income is generated from the borrowed money. Instead, the debt is paid down to (almost) zero, while the money that was simultaneously created with it flows into the bankers’ principal account as an unencumbered asset. Only the failure to repay debt fully can destroy money, because then the flow back to BP is less than the principal repayment required by the debt contract. The total amount of money is conserved in this simple instance of a single injection of endogenous money, and equals (at this stage) CP KB+.6 In a more complex model, with new credit creation, this amount would rise over time—and fall during a crisis, when insolvency and bankruptcy destroyed more money than was newly created. Nonetheless, ten years after accepting our hypothetical $1 million loan, the capitalists in our model are still $5,463 in the red, and bankers are an equivalent amount ahead. The advantages of being a banker are obvious: but why would anyone want to be a capitalist? Because capitalists use the working capital KC to finance production, sell commodities, make a profit, and repay their debts. Production is therefore, not amazingly, an essential aspect of the monetary theory of production. It is this real insight of Marx’s that has become obscured in the initial attempts to come to grips with Graziani’s monetary vision. Without a surplus generated in production, there can be no profit. A prelude: time lags To finance production, an outflow must occur from the capitalist working capital account. Here we introduce the systems engineering concept of a time lag, which is a measure of the rate at which a substance flows out of a vessel—in this case, money out of the working capital account KC. The faster this flow is, the more rapidly money finances production, which in turn generates income for capitalists and workers. While this concept is deliberately mechanistic in this simple model, a time lag can also be interpreted as the aggregate outcome of many different agents with many differing time responses (Andresen, 1998, 1999). In a more complex model, the lags would be a function of behavioral variables—expectations of profit, propensities to consume, etc. At this point, we use constant time lags, since the only question afoot is whether it is feasible for capitalists in the aggregate to make a profit. Whether they do so in practice at a given time, or in a more complete dynamic model, is another matter altogether. A time-lag differs from the discrete time-delay that has been a mainstay of economic reasoning, in which a variable Y(t) is argued to be a function of other variables at times t-1, t-2, etc. While most economic activities are discrete—wages are paid once a fortnight, cars come off the production line one at a time, consumers buy units of commodities at discrete times, etc.—the aggregate of many such discrete events at 6 The Kaldor-Trevithick reflux principle can be made consistent with this by treating the balance in BP as money “not in circulation”, even though it is clearly not destroyed. 6 of 20
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uncorrelated times is better approximated by a continuous time function with a time lag than a discrete time function with a time delay. For technical reasons, the time lag is expressed as a fraction of the time unit of the model—in this case, years—and shown as an inverse in the system equations. We label the time lag for the outflow KCτ, so that the outflow from the account is 1CKCKτ.7 The essence of the circuit: financing production & profit The outflow hires workers and buys intermediate goods from other capitalists to enable the production of commodities, which are then sold to capitalists, workers and bankers. In this simple one-commodity model, all intermediate goods purchases resolve themselves into wages and profits for workers and capitalists. Thus, given production and the sale of output, the outflow 1CKCKτ generates income flows that resolve exclusively into either profits or wages. The ratio of one to the other is, in Marx’s notation, the ratio of s to v, or the rate of surplus value.8 The source of profit within the monetary circuit is thus the generation of a surplus during production, the same as it was within Marx’s abstraction of a real circuit. Given that these represent fractions of a flow that sum to 1 in our model, we express this ratio as 1ssvs=−, so that 1rsvsrsv=+ where rsv is Marx’s rate of surplus value. 1CKCsKτ− is the flow of wages. CKCsKτ is, however, not quite the flow of profits. It is instead the outflow of financial capital needed to generate the flow of profits back. Purchase of inputs, production, and sale, must all first occur, and all these processes take time. We introduce the system state F (for “factory”) to represent this process, and use τF for the related time lag between expenditure on production and income from sale. We treat production implicitly in this simple model. Our explicit model—which we are currently extending—has the inflow CKCsKτ purchasing inputs Q at price P, the production process generating output ()'1QQθ=+ with a production time lag Fτ, which is then added to stocks Θ, from which sales occur at a rate determined by the transaction time lags Fτ, Wτ and Bτ. This, however, raises issues about the time 7 This is a first order time lag. We eschew more complex ones in this simple model, however higher order lags result from the interplay between the related first order differential equations. 8 Given the invalidity of the labor theory of value (Keen 2003a, 2003b, 2001), in a multi-sectoral setting, the Marxian concept of the rate of surplus value has no meaning. However in this one commodity model, it is a valid abstraction relating capitalist to worker income from production.
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dynamics of P, the consideration of which we wish to leave for a later paper.9 Our new implicit-production equation is thus: 1dCdtKCFsFKFττ=− (6) We also add the terms 1CKCKτ− and 1FFτ to the working capital account to represent, respectively, the outflows of money to finance production, and the returning lagged inflow of monetary profits. We introduce an account for workers wages WY with an inflow term of 1CKCsKτ−, and include the fact that workers accounts accrue interest cYrW; this in turn requires a matching outflow from the bankers’ income account BY. To complete the modeling of financial transactions,10 we must introduce expenditure by bankers and workers with time lags that reflect how rapidly each class must draw on its transaction account balances to fund consumption. Bankers’ and workers’ consumption spending is thus proportional to their account balances, with the ratios Bτ and Wτ respectively. There is thus an outflow from workers’ account of 1YWWτ and bankers’ account of 1YBBτ, with matching inflows into the capitalists’ account. The complete model is (with the new inflows and outflows highlighted in matching brackets): 9 Since the model currently lacks an explicit concept of capital, Sraffa prices cannot be used. A simple Kaleckian markup price would be feasible, but this overrules the income distribution dynamics. We have experimented successfully with an inventory-stock pricing equation, but generally feel these issues are best left for a longer, specialized paper. 10 We emphasize that transactions and income are different concepts. The flow of the amount 1YBYBτ from bankers’ accounts to capitalists’ is a transactional flow; the portion of that which exceeds the cost of production is a flow of income to capitalists. All capitalist income flows are incorporated in 1FFτ
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit 3/19/2006 9 of 20 ()11-11-1111FFdDPDdtdCCCdPDdtddtdYCKCCKCCKCYWYcYcdtdPPDdtdYdDcCYBYdtYWBKsKrWrKRKKrFFBBKrRKFWBRKBrWWWKrKsKτττττττττ⎧⎫⎨⎬⎩⎭⎧⎫⎨⎬⎩⎭⎧⎡⎤
⎢⎥⎢⎥⎡⎤⎢⎥⎣⎦⎡=−=−+−++++⎢⎥⎣⎦⎢⎥⎣⎤⎢⎥⎣==−==⋅−⋅+−⎫⎨⎬⎩⎭⎦⎦⎡⎤⎢⎥⎢⎥ (7) Figure 2 shows the results of a simulation of this model over a 20 year time period, with the additional parameter values of 14KCFττ==,2Bτ=, 126Wτ= and 200%rsv= (corresponding to an s value of 0.667). The top graph shows the account dynamics over the full twenty years; the bottom graph highlights the second and third order dynamics that occur in the first three years of the simulation. In contrast to the previous incomplete model, capitalist indebtedness tapers to zero—as do all income accounts. Capitalists have been able to borrow money, produce output, sell it, repay debt, and make a profit.
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit 1.106 5.105 4.104 2.104 0 Capitalist Debt Bankers Principal KC+F-KD (RHS) Capitalist Debt Bankers Principal KC+F-KD (RHS) 0 BY (RHS) WY (RHS) BY (RHS) WY (RHS) 2.104 4.104 02468101214161820 1.106 5.105 4.104 02 Capitalist Debt Capitalist Debt Bankers Principal Bankers Principal KC+F - KD (RHS) KC+F - KD (RHS) 0 0 0.5 1 1.5 2 Figure 2: Transaction account dynamics without relending BY (RHS) WY (RHS) BY (RHS) WY (RHS) 2.5 3 .104 2.104 4.104 Figure 3 shows the associated income flows, and the aggregate income levels generated by the model. These are, respectively:
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit y Net Profits: y Wages: ∫ ∫ 0 11 ⎛⎞ ⎜⎟ τ F FrKdt −⋅ ⋅ dD ⎝⎠ 0 τ s Kdt C KC Bank Income: ∫ y 0 ⋅ rKrKrWdt ⋅−⋅− ⋅ () dDcCcY (8) The first two are the Circuitist versions of Kalecki’s classic statement that “capitalists get what they spend, workers spend what they get”.11 The third adds the component that neither Keynes nor Kalecki properly incorporated, bank profits from finance—“bankers interest what they lend”. In this debt-finance only model, ∫ 1 τ F −⋅ dD FrK is the M+ of Marx’s monetary circuit; the M is solely the servicing costs of their debt because, in the absence of equity finance, capitalists advance no money of their own. In the incomplete model, bankers were the clear winners and capitalists the losers. In this complete model, however, “everybody wins”, though capitalists more so than workers (given the assumed rate of surplus value), and bankers least of all. 11 Workers’ and capitalists’ incomes include interest on their credit balances, so that aggregate income sums to wages plus profits plus interest on outstanding debt. The term y in the integration limit is the number of years in the simulation—in this case, 20. 11 of 20
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit 2.106 1.5 .106 1.106 5.105 0 4.104 3.104 2.104 1.104 Flow of profit Flow of profit Flow of wages Flow of wages 1.5 .106 Aggregate profit (RHS) Aggregate profit (RHS) Aggregate wages (RHS) Aggregate wages (RHS) 1.106 5.105 0 012345678910 1.105 8.104 6.104 4.104 Flow Bank Income Aggregate Bank Income (RHS) Flow Bank Income Aggregate Bank Income (RHS) 0 2.104 0 012345678910 Figure 3: Income dynamics without relending The magnitude and dynamics of profit and income distribution This model indicates other determinants of profit considered by Marx, but neglected until now in Circuitist thinking: the rate of turnover of financial capital, and the speed of the process of production. KC τ financial capital; F determines how quickly capitalists employ their τ determines how quickly production and sale turns inputs into outputs and then profits. The faster both these processes are, the more income that is generated in production per unit of time—and the more quickly capitalists repay their debts to bankers. A fall in either of these time lags thus increases capitalist and worker incomes and reduces bankers’, as shown in Figure 4. For a sufficiently small time lag—under 1/6th of a year in these simulations—the profits earned in this model can exceed the size of the original loan. In general, profits far exceed the interest payments necessitated by the loan, even with a production lag of one year. Clearly, as Minsky once observed in another context, “it pays to lever”. 12 of 20
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit 3/19/2006 13 of 20
Figure 4: Income distribution vs time lags in production The time pattern of relative income flows also bears noting. As Figure 5 shows, given our base simulation with 14KCFττ==, capitalist income starts well below both worker and banker income. However, by the end of the simulation, aggregate profits are precisely twice aggregate wages (equivalent to the rate of surplus value of 200%), while aggregate profits exceed aggregate bank income by a factor of more than 15. 0246810121416182000.511.5205101520
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The non-destruction of money One final point deserves emphasis here: the conservation of money in this simple model without re-lending, and, in capitalism in general, the non-destruction of money except via bankruptcy. The top graph in Figure 6 plots the sum of all income accounts plus bankers’ principal: this is identically equal to the original injection of endogenous money. Aggregate account balances + KC τ() F τ() ... ... + + + WY τ() BY τ() BP τ() ... ... 1.106 9.99999999999.105 1.106 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ + KC τ() F τ() ... ... + + + WY τ() BY τ() BP τ() ⎞ ... ⎟ ⎟ ⎟ ⎟ ... ⎟ ⎠ − KD τ() 5.105 0 5 10 τ 15 Aggregate bank balances minus capitalist debt 20 0 0 5 10 τ 15 Aggregate capitalist debt and bankers' principal 1.106 9.99999999999.105 20 0 5 Figure 6: the non-destruction of money 10 15 20 The middle graph shows that what is destroyed by debt repayment is simply debt. As the impulse from the original injection of endogenous money dies out, all the endogenous money accumulates in the bankers’ principal account, while capitalist debt is paid down to zero.
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The final graph establishes another identity: the sum of bankers’ principal and capitalist debt represents the net assets of bankers, which is identical to the initial creation of endogenous money. Perpetuating the circuit: re-lending of bankers’ principal The model as specified above decides two issues that have remained in contention amongst Circuitists for some time: money is not destroyed by debt repayment; and a profit can be earned on borrowed money. However, it cannot yet address a third area of debate: whether economic activity can be sustained without new injections of money. Contrary to Fontana (2000), Andresen (2006) answers this question in the affirmative. We consider this issue by allowing for re-lending of bankers’ principal BP. Again, we model this with a simple time lag τBP., where in this simulation τ = This is added as new debt to the capitalists’ debit account, and new working capital to the credit account. Our complete model of financial flows is thus (with the new elements highlighted by matching brackets): BP d dt d dt d dt d dt d dt d KRK =− + 1 ⎧⎫ DPD τ B ⎨⎬ P BP ⎩⎭ () 1111 KrKrRK K FW B ⎧ ⎨ 1 =−+−++++ CCCdPD C Y Y KC ττττ F s 1 =− FKF C KC ττ 1s F 1 =+− WKrWW YCcYY KC ττ W BRK 1 =− PPD W B τ ⎩ ⎧⎫ τ B ⎨⎬ P BP ⎩⎭ BrKrKrW d t 1 =⋅−⋅+ − B YdDcCcY Y τ B B BP ⎫ P ⎬ ⎭ 4 (9) As Figures 6 and 7 show, our modeling concurs with Andresen’s: this model economy can function at a sustained level with only a single injection of endogenous money. Economic activity continues because, rather than all the money accumulating in the bankers’ principal account, a proportion of it continues to be lent, renewing the supply of circulating money, and hence production and the generation of income.
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Figure 7: Sustained economic activity with relending of bank principal 2.5 3 .104 2.104 4.104 6.104 Figure 8 confirms that the circulation of this fixed amount of money generates a continuous stream of income for all three classes in the model:
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Figure 8: Sustained income flows with re-lending Flow of profit Flow of wages Flow of profit Flow of wages Aggregate profit (RHS) Aggregate profit (RHS) Aggregate wages (RHS) Aggregate wages (RHS) 6.106 4.106 2.106 0 012345678910 4.105 3.105 2.105 Flow Bank Income Flow Bank Income Aggregate Bank Income (RHS) Aggregate Bank Income (RHS) 1.105 0 012345678910
Re-lending of principal only slightly alters the time pattern of aggregate income flows.12 As Figure 9 shows, the capitalist: worker income ratio does not quite reach the rate of surplus value. The Profit:Bankers’ income ratio, on the other hand, now tapers to 15.608—only slightly more than the 15.549 ratio that applied without re-lending. 12 Aggregate income for a class at time t is the integral of the income from zero years to t.
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Figure 9: Ratio of aggregate incomes over time with re-lending Profit:Wages Profit:Wages Profit:Bank (RHS) Profit:Bank (RHS) 0 5 10 Years 15 From Circuitist skeleton to the body economic 20 15 10 5 0 20 Profit: Bank Income Ratio This is a deliberately skeletal model, designed only to show that the monetary circuit is internally consistent, and that it can explain both the endogeneity of credit money, and the phenomenon of monetary profit. In a full Circuitist model, new injections of money would be occurring all the time; flows between accounts would be determined by behavioral relations rather than fixed parameters; production would be multi-sectoral; prices and the distribution of income would be changing continuously; profits would rise and fall, and uncertainty about the future would lead to booms, slumps, bubbles, depressions, exceeded and dashed expectations, bankruptcy, and all the panoply of everyday actual capitalism. We hope that, in providing this skeleton, we have enabled Circuitist thinking to transcend some early conundrums. We invite other Circuitists to join us in putting flesh on this skeleton. References Andresen, Trond, (1998), “The macroeconomy as a network of money-flow transfer functions”, Modeling, Identification, and Control, 19, p. 207-223. Andresen, Trond, (1999), “The Dynamics of Long-range Financial Accumulation and Crisis”, Nonlinear Dynamics, Psychology, and Life Sciences, 3, pp. 161-96. Andresen, Trond, (2006), “A critique of a Post Keynesian model of hoarding, and an alternative model”, Journal of Economic Behavior & Organization (forthcoming). Bellofiore, Riccardo., Davanzati, G. F. and Realfonzo, R, (2000), “Marx inside the Circuit: Discipline Device, Wage Bargaining and Unemployment in a Sequential Monetary Economy”, Review of Political Economy, 12, pp. 403-17.
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit Fontana, Guiseppe., 2000. “Post Keynesians and Circuitists on money and uncertainty: an attempt at generality”, Journal Of Post Keynesian Economics, 23, pp. 2748. Fontana, Giuseppe, (2003), Post Keynesian Approaches to endogenous money: a time framework explanation, Review of Political Economy, 15, pp. 291-314 Fontana, Guiseppe, (2004), “Hicks on monetary theory and history: money as endogenous money”, Cambridge Journal of Economics, 28, pp. 73-88. Fontana, Giuseppe and Venturino, Ezio, (2003), Endogenous money: an analytical approach, Scottish Journal of Political Economy, 50, pp. 398-416 Fontana, Guiseppe, & Realfonzo, R., (eds.), (2005), The Monetary Theory of Production, Palgrave, New York. Graziani, Augusto, (1989). “The Theory of the Monetary Circuit”, Thames Papers in Political Economy, Spring,:1-26. Reprinted in Musella, M. & Panico, C., (eds.), (1995), The Money Supply in the Economic Process, Edward Elgar,Aldershot. Keen, Steve, (1993a). "Use-value, exchange-value, and the demise of Marx's labor theory of value", Journal of the History of Economic Thought, 15, pp. 107-121. Keen, Steve, (1993b). "The misinterpretation of Marx's theory of value", Journal of the History of Economic Thought, 15, pp. 282-300. Keen, Steve, (2001). "Minsky's thesis: Keynesian or Marxian?" in Bellofiori, R., & Ferri, P., (eds.), Financial Keynesianism and Market Instability, Edward Elgar, Aldershot. Lavoie, Marc (1992), Foundations of Post Keynesian Economic Analysis, Edward Elgar, Aldershot. Lavoie, Marc, (1996), “Horizontalism, Structuralism, liquidity preference and the principle of increasing risk”, Scottish Journal of Political Economy, 43, pp. 275-300. Lavoie, Marc, (1999), “The credit-led supply of deposits and the demand for money: Kaldor’s reflux mechanism as previously endorsed by Joan Robinson”, Cambridge Journal of Economics, 23, pp. 103-113. Marx, Karl, (1951 [1865]), “Wages, price and profit” in Marx-Engels Selected Works , Volume I, Marx-Engels-Lenin Institute (ed.), Foreign Languages Publishing House, Moscow. Marx, Karl, (1954 [1867]), Capital Vol. I, Progress Publishers, Moscow. Messori, Marcello & Zazzaro, A., (2005) “Single-period analysis: financial markets, firms’ failures and closure of the monetary circuit”, in Fontana & Realfonzo (2005), pp. 111-123. Rochon, Louis-Philippe, (2005), “The existence of monetary profits within the monetary circuit”, in Fontana & Realfonzo (2005), pp. 125-138.
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Keen & Chapman 2005 Profit in a dynamic model of the Circuit i We thank Trond Andresen, of the Norwegian University of Technology, for numerous illuminating discussions and practical suggestions in the development of this model.
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