Solving the Paradox of Monetary Profits

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    The paper below was submitted to the journal at the invitation of the editors for a special edition on “Managing Financial Instability in Capitalist Economies“. It took some time to get through the refereeing process, but the paper is finally available online (I was critical of some of the feedback I received—there are in my opinion some teething problems still to be surmounted in balancing the range of people that can comment on papers in this journal against the need to have critically informed readers making the ultimate decision. However the final paper was also much improved by the interactions with referees and the editors).

    Click here for a PDF version of this paper ; you can also read it as a webpage below. I’ve changed the theme for my blog recently to get around formatting hassles, since the previous theme inserted a page break every time I used italic font!. There were still some formatting hassles–I had to substitute for some Greek characters with the English spelling of the Greek letter for example–but it is better than with the old theme.

    This post below deserves the moniker “wonkish”, but I hope that it is still generally readable.


    Bruun and Heyn-Johnsen (2009) state the paradox that economics has failed to provide a satisfactory explanation of how monetary profits are generated, even though the generation of a physical surplus in production is an essential component of non-neoclassical economics. They emphasise that our ability to explain phenomena like the “Great Recession” will be limited while ever we are unable to explain this fundamental aspect of capitalism.

    In fact this paradox can be solved very simply, using insights from Circuit Theory Graziani (1990). Graziani’s brilliant initial proposition was that a credit economy must be using a non-commodity as money, since the alternative of “an economy using as money a commodity coming out of a regular process of production, cannot be distinguished from a barter economy” Graziani (1995: 518). From the fact that an intrinsically valueless token is nonetheless accepted as full payment in the exchange of goods, Graziani derived the conclusion that:

    any monetary payment must therefore be a triangular transaction, involving at least three agents, the payer, the payee, and the bank… Since in a monetary economy money payments go necessarily through a third agent, the third agent being one that specialises in the activity of producing means of payment (in modern times a bank), banks and firms must be considered as two distinct kinds of agents (Graziani 1995: 518–519).

    Unfortunately, attempts by Graziani and subsequent Circuitist authors to develop a viable mathematical model of the creation of monetary profits in a pure credit economy have to date been a failure—a situation well expressed in Rochon’s lament “How does M become M+?” (Rochon 2005: 125). This failure was not due to any weakness in the underlying vision of a pure credit economy, but to confusions of stocks with flows emanating largely from inappropriate mathematical approaches use by these authors. A simple dynamic monetary model that uses the bank account as its fundamental unit explains how capitalists can and do make a profit. In brief, “M becomes M+” via the price mechanism, which converts the sale of the physical surplus generated in production into money.

    The topic has become clouded by many other issues—from the basis for the value of money itself to the impact of debt repayment on the money stock. So that I can focus solely on this issue of how monetary profits are generated, I deliberately abstract from these important but—in this context—tangential issues, as outlined below.

    There are disputes in Post Keynesian monetary theory over the logical basis for the existence and value of money—notably between Chartalists who assert that taxation is the basis of money’s value, and some Circuitists—including Graziani (1989)—who assert that its acceptance in completing obligations between buyer and seller in an exchange is sufficient. The mathematical conundrum about whether capitalists can make a monetary profit when the source of their initial capital is borrowed money exists independently of this philosophical debate. The consensus to date has been that it is mathematically impossible for capitalists in the aggregate to make profits (see for example Bellofiore et al. 2000). I abstract from these philosophical and ex origo debates in order to focus simply on the mathematical issue, to show that this consensus is false.

    This dispute, and the current consensus conclusion, also exist within the confines of models of a pure credit economy—that is, models that treat money as a non-commodity issued by a private banking system, and abstract from the existence of both the State itself, and State or fiat money. The mathematical issue is therefore best treated in a model of a pure credit economy, even if a complete model of the existing monetary system must include both fiat and credit money.

    Finally, there is a difference between modern Post Keynesian theorists and Keynes over what happens to money that is used to repay debt. The convention in Circuit literature is that money used to repay debt is destroyed:

    To the extent that bank debts are repaid, an equal amount of money is destroyed (Graziani 2003: 29–30).

    Money is created as banks lend-mainly to business-and money is destroyed as borrowers fulfill their payment commitments to banks. Money is created in response to businessmen’s and bankers’ views about prospective profits, and money is destroyed as profits are realized Minsky (1982: xxi).

    Keynes, on the other hand, spoke of a “revolving fund of credit” which was continuously replenished by the repayment of debt, which implies that money used to repay debt may be temporarily taken out of circulation, but is not destroyed:

    If investment is proceeding at a steady rate, the finance (or the commitments to finance) required can be supplied from a revolving fund of a more or less constant amount, one entrepreneur having his finance replenished for the purpose of a projected investment as another exhausts his on paying for his completed investment (Keynes 1937: 247).

    I side with Keynes on this issue, but to avoid complications resulting from this difference of interpretation, I first consider the historically relevant example of a private bank using paper notes that it itself creates—see Figure 1 for an example of such a note issued during the “Free Banking” period in the USA (Dwyer 1996).

    A paper note model is also consistent with Graziani’s original paper on the monetary circuit, where he observed that “A true monetary economy must therefore be using a token money, which is nowadays a paper currency” (Graziani 1989: 3). These banks did not destroy their notes when debts were repaid, but treated their specie as a “revolving fund”, with notes stored until they could be recirculated in new loans:

    Free banks were rarely able to keep all of their allowable note issues in circulation at all times. Ratios of idle notes to total legal circulation in New York ranged from a low of 4 percent in 1852 to a high of 21.6 percent during the panic of 1857. The proportion of idle notes dipped below 10 percent in only three years and hovered around 15 percent throughout the 1850s (Bodenhorn and Haupert 1996: 688).

    Though the historical stability of this period is disputed,
    a private banking system of this type is not intrinsically unstable, and as I show below, capitalists can make a profit in such a system, even if their ventures are 100% debt-financed.

    Figure 1: Bank of Florence (Nebraska) Dollar Note (Smithsonian Institution 2010)

    The Basic Model: A Set Quantity of Notes

    Consider a private bank which, having fulfilled the legal requirements for Free Banking (see Bodenhorn 2008: 183–184), creates a stock N of dollar notes like those in Figure 1. These notes are initially held by the new bank in its vault. The bank then issues loans to firms, which enables the firm to hire workers, who then produce output which is sold to workers, capitalists and bankers.

    A minimum of 5 classes of accounts are needed to model this system:

    1. The bank vault (BV), into which the newly-minted notes are first placed
    2. Firm deposit accounts (FD), into which actual transfers of loaned dollars are made
    3. Workers deposit accounts (WD), into which wages are paid by firms
    4. A bank transactions account (BT), into and out of which interest payments are made
    5. Firm loan accounts (FL), where ledger entries that record the quantity of notes that have been lent to firms

    The first four of these are physical repositories of notes. The fifth is not a repository for notes, but a ledger recording the legal claim that the bank has upon those to whom it has lent. Operations on it therefore do not involve monetary transfers, but record the impact of those transfers on the indebtedness of borrowers.

    The basic transactions that occur in this model are detailed in Table 1. Seven of these steps involve the physical transfer of money:

    1. Lending of money from the bank vault to the firms’ deposit accounts (row 1)
      1. Payment of interest by firms to the bank’s transactions account (row 4)
      2. Payment of interest by the bank to firms’ deposit accounts (row 6)
      3. Payment of wages (row 7)
      4. Payment of interest on workers’ account balances (row 8)
      5. Payment for consumption of the output of firms by bank and workers (row 9)
    2. Repayment of loans by firms (row 10)

    Four steps are ledger entries only, involving the recording of a money transfer related to the level of debt:

    1. Recording the loans to firms (row 2)
    2. Compounding the debt at the rate of interest on loans (row 3)
    3. Recording the payment of interest on loans (row 5)
    4. Recording the repayment of loans (row 11)

    Table 1: Basic Financial Transactions in a Free Banking Economy

    Row Transaction Type Bank vault (BV) Bank transaction (BT) Firm loan (FL) Firm deposit (FD) Worker deposit (WD)
    1 Lend money Money transfer



    2 Record loan Ledger entry


    3 Compound debt Ledger entry


    4 Pay interest Money transfer



    5 Record payment Ledger entry


    6 Deposit interest Money transfer



    7 Wages Money transfer



    8 Deposit interest Money transfer



    9 Consumption Money transfer




    10 Repay loan Money transfer



    11 Record repayment Ledger entry


    Sum of flows






    The financial flows in each column of Table 1 can be summed to describe the dynamics of the bank accounts in this model:

    To model this system, we need to provide values for the operations a to i. Table 2 specifies these, with each operation being related to the current level of the relevant account—lending from the vault, for example, is assumed to occur at a constant rate “beta”V related to the current amount of money in the vault at time t, BV(t).

    Table 2: Financial Operations

    Flow Description
    a Loans to firms at the rate bV times the balance in the vault at time t BV(t) bv.BV(t)
    b The rate of interest on loans rL times the level of loans at time t FL(t) rL.FL(t)
    c Payment of interest on loans rL.FL(t)
    d Payment of interest on firm deposits FD(t) at the rate rD rD.FD(t)
    e Payment of wages by firms at the rate fD times firm deposits at time t FD(t) fD.FD(t)
    f Payment of interest on deposits at the rate rD rD.WD(t)
    g Payment for goods by banks at the rate bT times the level of the bank transaction account at time t BT(t) bT.BT(t)
    h Payment for goods by workers at the rate wD times the level of the bank transaction account at time t WD(t) wD.WD(t)
    i Repayment of loans at the rate “phi”L
    times the outstanding loan balance at time t FL(t)

    The full dynamic system is given by Equation :

    As is easily shown, with realistic parameter values (see Table 3; the values are explained later in the text prior to Table 5, and Table 5 itself) this describes a self-sustaining system in which all accounts settle down to equilibrium values, and in which capitalists earn a monetary profit.

    Table 3: Parameter Values

    Parameter Value Description
    bV ¾ p.a. Rate of outflow of notes from the vault BV
    rL 5% p.a. Rate of interest on loans
    rD 2% p.a. Rate of interest on deposits
    fD 2 p.a. Rate of outflow of notes from FD to pay wages
    bT 1 p.a. Rate of outflow of notes from BT to pay for bankers consumption
    wD 26 p.a. Rate of outflow of notes from WD to pay for workers consumption
    fL 1/7 p.a. Rate of repayment of loans

    Figure 2: Bank Account Balances over Time

    Figure 2 shows the dynamics of this system with an initial stock of N=100 million dollar notes.

    The equilibrium values of the accounts can be solved for symbolically in this constant money stock model:

    From Account Balances to Incomes

    The equilibrium yearly wages of workers (and gross interest earnings by bankers) can be calculated from Equation , and they in part explain why, in contrast to the conventional belief amongst Circuitist writers, capitalists can borrow money, pay interest, and still make a profit. Though only $100 million worth of notes were created, the circulation of those notes generates workers’ wages of $151 million per annum (given the parameter values used in this simulation), 1.5 times the size of the value of the notes in the economy (see Figure 3):

    This indicates the source of the Circuitist conundrums: the stock of money has been confused with the flow of economic activity that money can finance over time. A stock—the initial amount of notes created in this model—has been confused

    Figure 3: Wages and Gross Interest

    with a flow—the economic turnover in notes per year. In fact, for a wide range of values for the parameter ?D, the flows initiated by the money borrowed by the firms over a year exceed the size of the loan itself.

    This is possible because the stock of money can circulate several times in one year—something that Marx accurately enunciated over a century ago in Volume II of Capital (though his numerical example is extremely large):

    “Let the period of turnover be 5 weeks, the working period 4 weeks… In a year of 50 weeks … Capital I of £2,000, constantly employed in the working period, is therefore turned over 12½ times. 12½ times 2,000 makes £25,000” (Marx and Engels 1885, Chapter 16: The Turnover of Variable Capital).

    Aggregate wages and aggregate profits therefore depend in part upon the turnover period between the outlay of money to finance production and the sale of that production. This turnover period can be substantially shorter than a year, in which case fD will be substantially larger than 1, as I explain below.

    The Making of Monetary Profits

    A second fundamental insight from Marx lets us explain what fD is, and simultaneously derive an expression for profits: the annual wages bill reflects both the turnover period, and the way in which the surplus value generated in production is apportioned between capitalists and workers. The value of fD therefore reflects two factors: the share of surplus (in Sraffa’s sense) that accrues to workers; and the turnover period measured in years—the time between M and M+. Labelling the share going to capitalists as s and the share to workers as (1–s), and labelling the turnover period as tS and expressing it as a fraction of a year, I can perform the substitution shown in below:

    Money wages are therefore:

    Since national income resolves itself into wages and profits (interest income is a transfer between classes, and sums to zero across all classes), we have also identified gross profit:

    Using a value of s= 40%—which corresponds to historical norm of 60% of pre-interest income going to workers (see Figure 4)—this implies a value for tS of 0.3.

    This means that the turnover period in Marx’s terminology is roughly 16 weeks. This is much longer than in Marx’s numerical illustration above, but still sufficient to give capitalists profits that are substantially greater than the servicing costs of debt. Figure 5 shows the annual incomes for each class in society over time; all are positive and the equilibrium levels (once account levels stabilise) are $151 million, $98 million and $2.5 million for workers, capitalists and bankers respectively out of a national income of $252 million (see Equation ).

    Figure 4: Wages Percentage of US GDP

    Figure 5: Class Incomes after Interest Payments

    The value of tauS also determines the velocity of money: the ratio of nominal GDP to the proportion of the money stock in circulation (the equivalent of M3–M0 in monetary statistics, since in this pure credit model there is no fiat money), which is 3 given the parameters used in this simulation. This is within the highly volatile range suggested by historical data (see Figure 6).

    Table 4 summarises the equilibrium values for account balances, gross and net incomes in this hypothetical pure credit economy.

    Figure 6: US GDP to Money Supply Ratios

    Table 4: Equilibrium Account Balances, Gross and Net Incomes

    Account balances Class incomes Net incomes
    Bank vault 16 N/A N/A
    Firm loans 84 N/A N/A
    Firms 75.6081 100.811 (profits) 98.123
    Workers 5.8205 151.216 (wages) 151.333
    Bankers 2.5714 4.2 (debt servicing) 2.571
    Totals 84 (in Deposits) 252.027+4.2 252.027

    We can also derive a symbolic expression for the equilibrium level of profits


    This allows us to specify the general conditions under which equilibrium monetary profits will exceed zero, given the existence of a physical surplus from production. They are far from onerous: the rate at which the bank transaction account turns over each year has to exceed the rate of interest on loans and the rate at which the workers’ deposit account turns over has to exceed the rate of interest on deposits . Reasonable values for these parameters easily meet these conditions, as detailed below.

    Other Parameters and Time Lags

    The parameters rL and rD are nominal interest rates, and their values are roughly in line with historical norms at times of low-inflation; that leaves the parameters bV, fL, fD and bT to account for.

    The values for “phi”V and fL respectively specify how rapidly the balance in the vault is turned over, and how rapidly loans are repaid, and were chosen so that the equilibrium value of BV would be roughly the value noted by Bodenhorn and Haupert (1996: 688) of 15% of available notes:

    The parameters “omega”D and “beta”T signify how rapidly workers and bankers respectively spend their bank balances on the output produced by firms: workers are assumed to turnover their accounts 26 times a year—which corresponds to workers living from fortnightly paycheque to paycheque, with only modest savings. Bankers are assumed to turnover their account just once a year, reflecting their much higher per capita incomes.

    In the remainder of the paper, all parameters are expressed using the systems engineering concept of a time constant, which gives the fundamental frequency of a process. In every case, the time constant is the inverse of the parameter used thus far; for instance, the value of 26 for wD corresponds to workers’ consumption having a fundamental frequency of 1/26th of a year, or two weeks.

    Table 5: Time Constants in the Model

    Parameter and value Time constant and value Meaning
    bV = ¾ tV = 4/3 years Banks lend their reserve holdings of notes every 15 months
    fL= 1/7 tL= 7 years Firms repay their loans every 7 years
    wD = 26 tW= 1/26 years Workers spend their savings every 2 weeks
    bT = 1 tB= 1 year Bankers spend their savings every 1 year
    tP= 1 year Time constant in price setting (introduced in Equation )
    t M= 15 years Banks double the money supply every 15 years (introduced in Table 7 on page 24)

    Production, Prices and Monetary Profits

    Consider a simple production system in which output is proportional to the labour input L with constant labour productivity a:

    Labour employed in turn equals the monetary flow of wages divided by the nominal wage rate W:

    Prices then link this physical output subsystem to the financial model above. In equilibrium, it must be the case that the physical flow of goods produced equals the monetary demand for them divided by the price level. We can therefore derive that in equilibrium, the price level will be a markup on the monetary wage, where the markup reflects the rate of surplus as defined in this paper.

    To answer Rochon’s vital question, M becomes M+ (that is, monetary profits are realised) via a price-system markup on the physical surplus produced in the factory system. This markup can be derived simply by considering demand and supply factors in equilibrium. The flow of demand is the sum of wages and profits (since interest payments are a transfer and do not contribute to the value of output—despite Wall Street’s bleatings to the contrary). The monetary value of demand is thus:

    The physical units demanded equals this monetary demand divided by the price level:

    In equilibrium this physical demand will equal the physical output of the economy:

    Solving for the equilibrium price Pe yields:

    The markup is thus the inverse of workers’ share of the surplus generated in production. Circuit theory therefore provides a monetary expression of Marx’s theory of surplus value, as it was always intended to do.

    With these physical and price variables added to the system, we are now able to confirm that profit as derived from the financial flows table corresponds to profit as the difference between the monetary value of output and the wage bill (in this simple single-sectoral model).

    Table 6: Parameters and Variables for Physical Production Subsystem

    Variable, parameter or initial condition Definition Value
    a Labour productivity a = Q/L 2
    W Nominal wage 1
    Pe Equilibrium price 0.833
    P0 Initial price 1
    Le Equilibrium employment 151.216
    Qe Equilibrium output 302.432

    Using the values given in Table 6, it is easily confirmed that the equilibrium level of profits derived from the financial flows corresponds to the level derived from the physical production system:

    The price relation given above applies also only in equilibrium. Out of equilibrium, it is reasonable to postulate a first-order convergence to this level, where the time constant ?P reflects the time it takes firms to revise prices. This implies the following dynamic pricing equation:

    A simulation also confirms that the monetary flows (demand) and the monetary value of physical flows (supply) converge over time (Figure 7).

    This solves the “paradox” of monetary profits: it was not a paradox at all, but a confusion of stocks with flows in previous attempts to understand the monetary circuit of production.

    Figure 7: Supply, Demand and Price Convergence

    Analysing the “Great Recession”

    We can now use this framework to consider one aspect of the current financial crisis: if a “credit crunch” occurs, what is the best way for government to address it?—by giving fiat money to the banks to lend, or by giving it to the debtors to spend?

    Our current crisis is, of course, more than merely a “credit crunch”—a temporary breakdown in the process of circulation of credit. It is also arguably a secular turning point in debt akin to that of the Great Depression (Keen 2009), as Figure 8 illustrates. While the model developed here cannot assess this claim, it can assess the differential impact of a sudden injection of fiat money to rescue an economy that has experienced a sudden drop in the rate of circulation and creation of private credit. This is an important point, since although the scale of government response to the crisis was enormous across all affected nations, the nature of that response did vary: notably, the USA focused its attention on boosting bank reserves in the belief—as expressed by President Obama—that the money multiplier made refinancing the banks far more effective than rescuing the borrowers:

    And although there are a lot of Americans who understandably think that government money would be better spent going directly to families and businesses instead of banks – “where’s our bailout?,” they ask – the truth is that a dollar of capital in a bank can actually result in eight or ten dollars of loans to families and businesses, a multiplier effect that can ultimately lead to a faster pace of economic growth (Obama 2009: 3. Emphasis added).

    Figure 8: Private Debt to GDP Ratios, USA & Australia

    The Australian policy response to the crisis, on the other hand, was pithily summed up in the advice given by its Treasury: “go early, go hard, go households” (Gruen 2008). Though many other factors differentiate these two countries—notably Australia’s position as a commodity producing supplier to China—the outcomes on unemployment imply that the Australian measures more successful than the American “money multiplier” approach (see Figure 9).

    The next section applies this endogenous money model to consider a differential response to a credit crunch in a growing economy: an injection of funds is made into either the Banks’ Vault accounts—simulating the USA’s policy response—or into the Workers’ Deposit accounts—simulating the Australian response.

    Figure 9: Unemployment Rates USA and Australia

    Endogenous Money Creation and Economic Growth

    To model a credit crunch in a growing economy, while otherwise maintaining the structure of the Free Banking/pure credit money model above, I move beyond the limitations of a pure paper money system to allow for endogenous money creation as described in Moore (1979):

    “In the real world banks extend credit, creating deposits in the process, and look for the reserves later” (Holmes 1969, Moore 1979: 53); see also more recently Disyatat (2010: 7 “loans drive deposits rather than the other way around”).

    In the model, new credit to sustain a growing economy is created by a simultaneous increase in the loan and deposit accounts for the borrower. The financial flows in this system are given in Table 7. The two changes to Free Banking model are the addition of row 12 (and its ledger recording in row 13), with the qualitatively new operation of Money Creation being added to the previous operation of Money Transfer, and a “Deus Ex Machina” injection of fiat money into either Bank Vault or Worker Deposit accounts one year after a credit crunch.

    Again, simply to illustrate that the system is viable, a constant growth parameter “tau” M has the banks doubling the stock of loans every 15 years (see Table 3):

    A credit crunch is simulated by varying the three crucial financial flow parameters tauV, tauL, and tauM at an arbitrary time in the following simulation (at t=25 years): tauV and tauM are doubled and tauL is halved, representing banks halving their rates of circulation and creation of new money and firms trying to repay their loans twice as quickly (see Table 8). The government fiat-money rescue is modelled as a one-year long injection of a total of $100 million one year after the credit crunch.

    Several extensions to the physical side of the model are required to model economic growth. In the absence of Ponzi speculation (which is the topic of a later

    Table 7: Endogenous Money Creation

    Row Transaction Type Bank vault (BV) Bank trans-action (BT) Firm loan (FL) Firm deposit (FD) Worker deposit (WD)
    1 Lend money Money transfer



    2 Record loan Ledger entry


    3 Compound debt Ledger entry


    4 Pay interest Money transfer



    5 Record payment Ledger entry


    6 Deposit interest Money transfer



    7 Wages Money transfer



    8 Deposit interest Money transfer



    9 Consumption Money transfer




    10 Repay loan Money transfer



    11 Record repayment Ledger entry


    12 New money Money creation


    13 Record loan Ledger entry


    14 Government policy Exogenous injection into


    BE or WD



    Sum of flows






    ey supply is only warranted if economic growth is occurring, which in turn requires a growing population and/ or labour productivity. These variables introduce the issue of the employment rate, and this in turn raises the possibility of variable money wages in response to the rate of unemployment—a Phillips curve. These additional variables are specified in Equation :

    Table 8: Financial Flow Parameters before and after a Credit Crunch

    Pre-credit crunch Post-credit crunch Impact of credit crunch
    tV = 4/3 years tV = 8/3 years Banks lend their reserve holdings of notes every 15 months
    tL= 7 years tL= 3.5 years Firms repay their loans every 3.5 years
    t M= 15 years t M= 30 years Banks double the money supply every 30 years
    k=$100 million Injected either into bank vault BE or worker deposit WD at year 26, one year after the credit crunch

    The parameter values and functional form for this physical growth extension are shown in Table 9.

    Figure 10 shows the impact of the credit crunch upon bank accounts: loans and deposits fall while the proportion of the money supply that is lying idle in bank reserves rises dramatically.

    The US empirical data to date has displayed a similar pattern, though with a much sharper increase in bank reserves as shown in Figure 11.

    A very similar pattern to the empirical data is evident in the model when the US policy of increasing bank reserves is simulated (Figure 12).

    The simulation of Australian household-oriented policies generates a very different dynamic: reserves still rise dramatically during the credit crunch, but their increase is not further augmented by the policy intervention. Instead, firm and worker deposits rise substantially (see Figure 13), whereas they fall in the bank-oriented rescue.

    This higher level of money in circulation in the household-oriented policy intervention is the cause of the dramatic difference in the outcomes of the two policy interventions: the household-oriented approach has a far more immediate and substantial impact upon employment (Figure 14). Contrary to the expectations of President Obama and his mainstream economic advisers, there is far more “bang for your buck” out of a household rescue than out of a bank rescue.

    Table 9: Parameters and Function for Growth Model

    Variable or parameter Description Value
    alpha Rate of growth of labor productivity 1% p.a.
    beta Rate of growth of population 2% p.a.
    Pop Population Initial value = 160
    lambda Employment rate Initial value = 94.5%

    Phillips curve:

    Figure 10: Bank Accounts before and after a Credit Crunch

    Figure 11: Drop in Business Loans and Dramatic Rise in Bank Reserves during Great Recession

    Figure 12: Simulating US Bank-oriented Policy towards a Credit Crunch

    Figure 13: Simulating Australian Household-oriented Policy towards a Credit Crunch

    Figure 14: Comparing Bank-oriented and Household-oriented Policies


    The paradox of monetary profits is solved simply by avoiding the problem so wittily expressed by Kalecki, that economics is “the science of confusing stocks with flows” cited in Godley and Lavoie (2007). With that confusion removed by working in a framework that explicitly records the flows between bank accounts and the production and consumption they drive, it is obvious that Circuit Theory achieves what it set out to do: to provide a strictly monetary foundation for the Marx–Schumpeter–Keynes–Minsky tradition in economics. As an explicitly monetary model, it also provides an excellent foundation for explaining the processes that led to the “Great Recession”, and for testing possible policy responses to it.


    This work results from a collaborative research effort between the United Nations Environment Program (UNEP) and CSIRO Sustainable Ecosystems to establish a regional report on Resource Efficiency: Economics and Outlook for Asia?Pacific. I thank 4 anonymous referees, an editor and Trond Andresen (Norwegian University of Technology) for comments that greatly improved the final paper.


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    Keynes, J. M. (1937). Alternative theories of the rate of interest, Economic Journal, 47: 241–252.

    Marx, K. and Engels, F. (1885). Capital II, Moscow: Progress Publishers.

    Minsky, H. P. (1982). Can “It” Happen Again? Essays on Instability and Finance, Armonk, N.Y.: M.E. Sharpe.

    Moore, B. J. (1979). The Endogenous Money Stock, Journal of Post Keynesian Economics, 2(1): 49–70.

    Obama, B. (2009). Obama’s Remarks on the Economy, New York Times, New York.

    Rochon, L.-P. (2005). The Existence of Monetary Profits within the Monetary Circuit’, in G. Fontana and R. Realfonzo (eds), Monetary Theory of Production: Tradition and Perspectives, Basingstoke: Palgrave Macmillan.

    Smithsonian Institution (2010). National Numismatic Collection (NNC), National Museum of American History, Washington, D.C.

    About Steve Keen

    I am Professor of Economics and Head of Economics, History and Politics at Kingston University London, and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous private debts accumulated globally, and our very low rate of inflation.
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    68 Responses to Solving the Paradox of Monetary Profits

    1. Tom Shaw says:

      Steve, sorry I should have addressed my earlier comment to you (August 4, 2011 at 12:33 am – except for the first paragraph).

      Torrey, I don’t subscribe to the distinctions you’re making regarding objective v subjective, absolute v relative, real v all in the mind, natural v artificial. It all depends on the level of abstraction that you’re working at. I think Steve taps into a much better framework when he talks about the fallacy of strong reductionism (slides 17-18 at that link).

      I also recommend Leonard Susskind’s thoughts on what is “fundamental” (from 1:11:10, but especially from 1:19:10).

    2. kys says:

      Tom Shaw,

      Sorry for my late repsponse.

      By definition,

      1. w_D is the rate of outflow of notes from Worker Deposit W_D to pay for workers’ consumption.

      2. b_T is the rate of outflow of notes from Bank Transaction B_T to pay for bankers’ consumption.

      For simulation purposes, 26 p.a. & 1 p.a. are assigned to w_D & b_T respectively, both of which are realistic. I therefore do not see any “internal contradiction” like you do.

      In equilibrium, g = b_T * B_T = bankers’ consumption = bankers’ net income = Bank Transaction Account, which means Steve’s reply is accurate.

      As to your assumption that g = $x,

      1. The assumption does not hold when x > c-d-f because bankers can not plunder the vault.

      2. When x < c-d-f, bankers save money. Where do they put the money? do you need a new entry "Banker Deposit" that gives bankers interests? do bankers seek to lend out their savings to firms at higher interest rates? Do they simply consume more when savings reach certain levels? Do these considerations help in solving the paradox of monetary profits?

      I look forward to a meaningful discussion.

    3. Tom Shaw says:

      Hi Kys, Steve’s reply is accurate in that he recognised that this would indeed produce the outcome I noted :)

      The contradiction is simple: w_D and b_T are said to be different because of different levels of savings/income. This implies that the consumption coefficient of a person (as reflected in w_D and b_T) is a decreasing function of their savings/income. And yet b_T is said to be a constant for all values of a banker’s savings/income. Contradiction, Q.E.D.

      Even ignoring the internal contradiction, there is no empirical justification for saying that b_T is a constant value. I’ve given a real-world example of someone whose consumption has remained relatively stable once it reached a certain point. It’s certainly a much more realistic proposition than assuming consumption is linearly related to the account balance. The truth is probably somewhere in the middle (maybe g is proportional to ln(B_T), who knows) but that would still be enough to alter the qualitative outcome.

      Regarding your other points, you’re just confirming the divergent nature of the outcome. In your scenario 1, the banker goes broke and the system breaks down. In your scenario 2, instead of leaving the money in B_T, the banker earns interest on it, captures the money supply even faster and the system breaks down.

    4. kys says:

      Since you like to turn “sectoral” into “individual”, I guess you must be able to re-model the whole thing. Please do not forget us when you release your magnum opus.

      I just wonder if the system breakdown actually means a computer breakdown or a nervous breakdown…

    5. Tom Shaw says:

      Hi Kys, I thought you were after a reasonable discussion..

      It’s Steve’s model which turns “sectoral” into “individual” by positing a single private bank – I’m just pointing out the obvious flaw in the model. I’ve never claimed to be able to model the economy. In fact a couple of comments ago I gave my opinion that economic reality may well be too complex to model from the bottom-up, thus my preference for top-down analysis.

    6. kys says:

      But what do you mean by top-down and Bottom-up? I can’t tell the difference.

    7. Tom Shaw says:

      Hi Kys, this is discussed a bit in this presentation including an interesting conversation around 23:45. There’s also an article on Wikipedia.

      The bottom-up approach is to start from smaller, simpler components and build upwards. For example, you could theoretically take your knowledge of physics, and based on this derive the rules of chemistry. Of course this is difficult because even though the components are simple, the interactions may create emergent behaviour. Small flaws in your assumptions can create qualitatively different outcomes. Only recently with super-powerful computers and extremely accurate physical understanding can chemical properties be modeled from the bottom-up.

      The top-down approach is to start from a birds-eye view of the whole system and derive rules from what you see. In practice this is how chemistry was really developed. Friedman’s “F-Twist” actually makes sense if this is explicitly your approach. The problem with the top-down approach is that it’s difficult to extend your knowledge to new situations.

      The tragedy of modern economics is that the flaws of each approach have not been respected. The bottom-up approach failed because, as Steve likes to point out, the all-important assumptions underlying keep being forgotten or ignored (e.g. SMD conditions or expected utility). The top-down approach failed because not enough attention was paid to history (e.g. the great depression) to get a big enough set of empirical data to analyse. By ignoring these flaws, economists clearly became way too confident in their models, which is why so many were surprised by the GFC.

    8. kys says:


      This discussion is really meaningful but I’ve got to run now.

      I will talk to you soon in the next debate.

    9. torreybyles says:

      Thanks Tom. I appreciate your comments and will look into the links that you provide. I do like Steve’s fallacy of strong reduction, btw.

    10. RJ says:

      I’m not sure from the above if Steve understands double entry book keeping or not?

      Or how double entry book keeping relates to the P+L account and balance sheet

      Commercial banks, central bank, the treasury and companies etc MUST post a journal entry for every transaction. It is from these journal entries that the P+L account and balance sheet is produced

      Failure to understand this results in many economists forming incorrect conclusions (as I beleive Steve has in this report. Although I’m open to being convinced otherwise).

      Example from figure Figure 1

      The journal entries are for the BoF

      Action 1 Print notes BoF JE

      Debit Notes asset BoF dollars (bank asset)
      Credit Printed money offset Liability
      This liability reflects a liability the bank has to the holders of these $ notes

      Action 2 BoF issues notes to a customer

      BoF account
      Debit Customer loan (bank asset / customer debt liability)
      Credit Customer cheque account (bank liability / customer financial asset)

      Customer accounts
      Debit Bank balance at the BoF
      Credit Liability Bank loan BoF

      Action 3 Customer withdraws bank notes

      BoF account
      Debit Customer cheque account (reduce bank liability account)
      Credit Notes BoF dollars (reduce holding on notes asset)

      Customer accounts
      Debit Notes BoF dollars
      Credit Liability Bank balance at the BoF (reduce bank balance)
      In effect the credit held at the BoF has been converted to a BoF supported $ dollar notes

      And the dollar notes are supported by debt and nothing but debt.

      What if the BoF had gold holdings. For me debt still supports the dollar notes but gold is used as a safety cover (insurance) in case some debt can not be paid back.

      BoF JE
      Debit Gold on hand
      Credit Shareholders funds

      When the full journals are done as above it shows clearly that this statement

      “Keynes, on the other hand, spoke of a “revolving fund of credit” which was continuously replenished by the repayment of debt, which implies that money used to repay debt may be temporarily taken out of circulation, but is not destroyed:”

      is incorrect

      When money is taken out of circulation to repay debt

      The banks journal entry is

      Debit BoF notes
      Credit Customer deposit account

      And then

      Debit Customer deposit account (MONEY IS DESTROYED)
      Credit Customer loan (bank asset reduced / customer debt liability reduced)

      So this statement below is correct

      “Money is created as banks lend-mainly to business-and money is destroyed as borrowers fulfill their payment commitments to banks.”

      The problem occurs because Keynes considered notes held in a bank safe as money. It is not.

      If a bank printed a 100 trillion note and left it locked in a bank safe. It would have no impact on the money supply at all

      Only when it is released does it impact on the money supply. This is why Notes and coins (currency) in bank vaults do NOT form part of M1 M2 M3 or MZM

    11. RJ says:


      Action 2 above is

      BoF loans money to a customer

      This article on money is worth reading

      “Money, then, is credit and nothing but credit. A’s money is B’s debt to him, and when B pays his debt, A’s money disappears. This is the whole theory of money.”

      Credit came first and notes and coins later.

      Notes and coins are nothing more than a token to allow the easy transfer of credit. Notes and coins are exchanged for bank credit (deposits). These tokens can then be exchanged for goods services or assets. The new holder can then bank these notes and coins in exchange for bank credit

      The journal entries above clearly shows this.

    12. RJ says:

      “Keynes, on the other hand, spoke of a “revolving fund of credit” which was continuously replenished by the repayment of debt, which implies that money used to repay debt may be temporarily taken out of circulation, but is not destroyed:”


      “Which implies”. Does it imply this though.

      If Keynes just called bank held notes and coins a “revolving fund of credit”. Yes debt repayment does replenish bank held notes and coins. But it does not imply credit is not destroyed. It just means notes and coins are replenished in the bank nothing more. Credit is destroyed as the journal entries above show

    13. Steve Keen says:

      Hi RJ,

      I think the technically correct definition you gave earlier:

      “This is why Notes and coins (currency) in bank vaults do NOT form part of M1 M2 M3 or MZM” is not inconsistent with Keynes as you’re read him here:

      ” Yes debt repayment does replenish bank held notes and coins. But it does not imply credit is not destroyed. It just means notes and coins are replenished in the bank nothing more. Credit is destroyed as the journal entries above show”

      If one defines credit (or money) as “money in circulation as defined by M1 M2 M3 or MZM” then yes credit/money is destroyed by debt repayment. However the notes and coins are not destroyed, as you note. They can re-enter circulation later when money is created once more by additional debt.

      To handle this in a dynamic model of the money creation and circulation process, I am effectively working with a broader definition of money that includes these “not in circulation” notes and coins (and other liquid assets). This may be the source of the conflict between me and other Post Keynesians on this–certainly that’s what Warren Mosler argued in a verbal debate some years ago. I argue for my approach and my wider definition when modelling a dynamic process, since to do otherwise implies there is a “sink” (in dynamic systems terminology) through which the notes and coins literally are destroyed.

    14. Pingback: The Debtwatch Manifesto | Steve Keen's Debtwatch

    15. Keynes (Article above) : “If investment is proceeding at a steady rate…”
      … “then the Profits of the Business will decline to zero” – Me : … so using the CFS the Current Financial System, we may have no physical need to increase “Investment” – we might have all the machines we need but the CFS forces an increase to keep the show on the road as it where. So at base the Financial system does not reflect reality and it would be a good idea to design one that does

    16. Steve has failed to establish that there is a “Paradox of Monetary Profits”
      in the 1st place. A company knows if it has made a profit or loss by looking
      at its accounts – not its bank statement and the equation for profits across he whole economy is :
      Retained Profits of Business = Fixed Assets Of Business + Government Debt + Household Debt + Foreigner’s Debt
      This can be demonstrated using numbers for the UK National Accounts :

      The step by step, Debits and Credits, of how it moves from one situation
      to another through the banking system you can see in the spreadsheet model financial_scenarios.xls in :

      – There is no Paradox to solve

    17. EconCCX says:

      Greetings All

      Steve, we’ve met. I was one of the lucky geeks who caught your presentation in NYC last fall around the impending release of the revised Debunking. We had a lively group conversation on the way to and at dinner: MMT vs. circuit theory; the exorbitant privilege; your planned work with Hudson. The increasing and misplaced confidence by borrower and lender (Minsky) vs control fraud and principal/agent conflict (Black). At presentation Q&A, I flogged Soddy; you politely responded that you hoped to get to him some day. Thanks, belatedly, for that great talk, and to Robert (commenter Robert K?) for hosting.

      I’m quite late to the discussion, but hope you’ll still entertain a few questions about the Monetary Profits Paradox.

      First is a bookkeeping question about a very simple transaction. But I think it provides us a window on more complex ones:

      A firm maintains a bank checking account with a $10 monthly fee. Suppose its balance is $1000 before the fee, and $990 after. Which do you believe most accurately describes the outcome of the transaction:

      A) The firm’s balance is reduced by $10; the banks funds are increased by $10. Whether the increment is booked as reserves or profits or additional loanable funds, some account at the bank shows that journal entry, and a $10 gain. Money in the amount of $10 has been transferred from firm to bank, and from aggregate firm holdings to aggregate bank holdings.

      B) The firm’s balance is reduced by $10. That $10 vanishes completely. It’s on nobody’s account; it simply ceases to exist. That debit to the firm’s account has diminished the universe’s total stock of money. -OR-

      C) Some other outcome as yet undescribed.

      Prof. Keen: if you’re able to address this question, perhaps you could also tell us whether you believe Graziani would agree with your reply. Fellow commenters: I hope you’ll kindly take a stab at this as well. I have some terms or premises wrong, no doubt; so I look forward to seeing how others book and characterize this transaction.


    18. Bhaskara II says:

      Double entry journal entries describing the transaction from the point of view of each entity would be:

      Firm entity:
      Dr. Fee Expense // Cr. House of Bank (asset account)* $10

      Bank entity:
      Dr. House of Firm (liability deposit account) // Cr. Bank’s Revenue or Equity $10

      * house of is an old term that could mean company, bank, family, etc. Example “House of Morgan”.

      The firm’s balance is reduced by $10; the banks equity or claim on funds are increased by $10. The increment is booked as the banks’ profits. And the increment of the firms expense or reduction in firms’ equity. Money in the amount of $10 has been transferred from firms’ equity to banks’ equity.

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