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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    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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    • The sec­ond half of the equa­tion was in the “Are we it yet?” model Fred. On all your other points, read the paper: I dis­agree with you, and I’ve writ­ten up why in that and numer­ous other papers.

    • Steve,

      It seems to me that since the bank vault account bulges when the banks induce a credit crunch, that this gain is due to the pur­chas­ing power gain of the incom­ing loan repay­ments.

      What I am think­ing is that the bank “destroys” the debt oblig­a­tion money but is left with a profit for the bank vault.

      Is the bank vault level some­how con­nected to the price level?

    • Brian Macker

      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”

      Bril­liant? It’s just plain wrong. One can dis­tin­guish and econ­omy using a com­mod­ity (of any kind suit­able which includes ones pro­duced by reg­u­lar processes of pro­duc­tion) money from barter. In a barter econ­omy no com­mod­ity is suit­able for use as money, or no such com­mod­ity (or set of com­modi­ties) has been set­tle on by the mar­ket. Com­modi­ties suit­able for use as money have cer­tain prop­er­ties that have been out­lined by the Aus­tri­ans, so I will not repeat here.

      BTW, you can have a credit econ­omy with a com­mod­ity money, and even with­out frac­tional reserve bank­ing. You just need con­tract law and peo­ple will­ing to bor­row and lend on the basis of inter­est.

      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:

      There is no such thing as intrin­sic value. Value is sub­jec­tive. Sup­pos­edly “val­ue­less tokens” can have value in trade. Credit based money has value in pay­ing off the cred­i­tor. For exam­ple, early Amer­i­can schemes at credit money had value because the gov­ern­ment accepted them in pay­ment of taxes. The same is true of all fiat cur­ren­cies in exis­tence today.

      This whole line of think­ing smells of foun­da­tion­al­ist think­ing. There are no foun­da­tions to prices. One can­not fol­low the stream back to the source. Mises’ bril­liant con­clu­sion is that it prices are sub­jec­tive and rel­a­tive, and that goods have no “intrin­sic value”. As Roth­bard pointed out prices evolve from prior states of affair via past and cur­rent sub­jec­tive val­u­a­tions of the par­tic­i­pants, and as revealed by trade.

    • Brian Macker

      any mon­e­tary pay­ment must there­fore be a tri­an­gu­lar trans­ac­tion, involv­ing at least three agents, the payer, the payee, and the bank”

      This is wrong too. A non-barter econ­omy based on a com­mod­ity money like gold has no bankers, and no need for a third party. 

      Humans spe­cial­ize in pro­duc­tion. In a barter econ­omy some­one who pro­duces eggs and wants beef has to find either: Some­one who pro­duces beef who wants eggs, or some other pro­ducer that pro­duces some­thing which a beef pro­ducer wants, or the same three lev­els deep, or four, .… 

      It’s not likely that the beef pro­ducer will want the eggs in a pro­por­tion­ate quan­tity to the amount of beef desired, nor with the same tim­ing. Com­mod­ity money solves these prob­lems by being a com­mon unit of exchange and a store of value. The store of value prop­erty of money (the fact that it doesn’t rot, and doesn’t grow on trees) allows a bridg­ing of the issues related to the tim­ing of trans­ac­tions. Other prop­er­ties of money such as divis­i­bil­ity, mal­leabil­ity, ease of assay, etc. allow it to be used as a unit of exchange, which solves the prob­lem of the mis­match in quan­ti­ties in the trades. 

      When the mar­ket has set­tled on a com­mod­ity money the per­son who wants eggs can sell them for money, and then go buy the beef with that money. No banker involved.

      Graziani is lost before he even starts.

    • Brian Macker


      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?”

      No you can’t use your frame­work for decid­ing because it is not a proper sim­u­la­tion of the real world. There is no cap­i­tal (real goods) in your model and no prices for exam­ple. Your last sen­tence is a false dichotomy. Another option is to do noth­ing which you exclude from con­sid­er­a­tion as “best”. Your model has no means of cap­tur­ing how price cor­rec­tions will solve the issue. It is empir­cally at odds with the 1920 depres­sion and recov­ery where the solu­tion was to do nei­ther of your two options.

      Your final graph on employ­ment lev­els works in the sim­u­la­tion but you have to remem­ber what you are sim­u­lat­ing, a sys­tem with­out real cap­i­tal or prices, one where it is assumed that all com­pa­nies make a profit, that is sta­tic where prices do NOT serve the pur­pose of com­mu­ni­cat­ing infor­ma­tion. Your model could just as well describe the oper­a­tion of a com­mand econ­omy run by Stalin where he decides which firms can bor­row.

      In short it your con­clu­sion about “what is best” is a non sequitur. The math is use­less with­out proper rea­son­ing.

      In your model econ­omy, exactly where do the cap­i­tal­ists get the real funds to pay their work­ers until their projects have com­pleted? Print­ing credit cur­rency does not gen­er­ate the real sav­ings (the food, sup­plies, etc) required for con­vert­ing into real cap­i­tal (eg. indus­trial machin­ery) needed to gen­er­ate prof­its. The work­ers need to feed and cloth them­selves while they are build­ing that loom, or cul­ti­va­tor.

    • Brian Macker

      Could it be that the Aus­tralian econ­omy is behav­ing dif­fer­ently because inject­ing new money with the banks is not a good way to keep inflat­ing the bub­ble com­pared to hand­ing it out to the bor­row­ers? I also think there are other major dif­fer­ences between the US and Aus­tralia that that explain the dif­fer­ences in behav­ior like being a com­modi­ties exporter to a devel­op­ing coun­try that is itself still in the boom phase of a bub­ble (includ­ing hous­ing bub­ble), and also one that is still ben­e­fit­ing from restruc­tur­ing of the world econ­omy due to the open­ing of freer trade.

    • Brian Macker

      I see print­ing up money to hand to peo­ple who bet badly on the hous­ing mar­ket as nearly as bad as print­ing it up to hand to the peo­ple who lent them the money. 

      You are sub­si­diz­ing a bad trans­ac­tion, and as Hazlett wisely taught you need to pay atten­tion not just to the near term but the long term. Over the long term the extra money increases price lev­els (yes it does as is empir­i­cally proven by coun­tries on fiat vs. non-fiat cur­ren­cies which is the proper way to com­pare), which ends up hurt­ing the poor, those on fixed incomes, and savers. 

      It has to harm some­one because you are print­ing up war­rants against goods with­out increas­ing the quan­tity of goods. It’s only a mat­ter of fig­ur­ing out who is harmed. That is sim­ple because it is the peo­ple who are cur­rently hold­ing fiat notes (the war­rants).

      When I have the direct sim­ple proof to the solu­tion of the muti­lated chess­board then why should I believe an oppos­ing solu­tion that involves com­pli­cated math based on improper assump­tions about the scope of the prob­lem?

      Also, even if you feel the bor­row­ers are blame­less, you can­not con­trol the sub­si­diza­tion of the trans­ac­tion to the point where none of the ben­e­fit goes to the bankers. Giv­ing the money to the bor­row­ers to pay the lenders means that the lenders make out on a bad loan when the mar­ket should have pun­ished them too.

      If you do feel the bor­row­ers are blame­less and incom­pe­tent then from a moral stand­point, if you are con­sis­tent, you must also believe that no bor­rower ever deserves the prof­its they gain from a rise in value of that which they bor­rowed against. Thus to truly cor­rect the sys­tem in a fair fash­ion you’d need to undo all the trans­ac­tions. Which is ridicu­lous.

      Why should only those who were the very most irre­spon­si­ble (as proven by the fact that they fail­ing to meet pay­ments, or lent to dead­beats) be the ones to be bailed out? Per­haps we should do the oppo­site. We should hand out free money in directly oppo­site pro­por­tion to how much your pay­ments on loans are. Seems more fair to say, we need to inject X bil­lion into the sys­tem in order to bring fiat cur­rency lev­els into line with bank lever­age, divide by the pop­u­la­tion and a) hand out the same amount of free cash to every­one includ­ing those who never bor­rowed a cent. or b) hand out the money in inverse pro­por­tion to how much total debt peo­ple are in. 

      I’m not sug­gest­ing that because that would still harm savers, and the poor in the long run, but it makes more sense. 

      Our economies are based on a tem­po­ral pyra­mid scheme called frac­tional reserve bank­ing. Some of us, the non-fools, rec­og­nized that fact and arranged our lives so we would not get stuck with the bag. Now that you other fools finally catch on (not really you just are notic­ing the bag is empty but have no idea why) you now want to throw all the rules out the win­dow and print money to bail out your pre­ferred char­ity cases at the expense of the wise. 

      The pyra­mid scheme is crash­ing. The prob­lem is that the fan­tasy prof­its and retire­ments were never a real­ity. There are real losses that the gov­ern­ment low­er­ing of inter­est rates caused, and the issue now is who to stick hold­ing the bag. For some rea­son every­one who was in on the pyra­mid scheme thinks the losses should fall on those who never par­tic­i­pated. They cer­tainly aren’t try­ing to shift the losses between them­selves. The banks know they can’t shift it onto the bank­rupt bor­row­ers, and the bank­rupt bor­row­ers can’t shift it onto the banks (who live off their pay­ments). There­fore they dig into the pock­ets of those who were respon­si­ble (or at least more so).

      I see the Key­ne­sians and the Mon­e­tarists act­ing as ratio­nal­iz­ers to screw the respon­si­ble to the major ben­e­fit of bankers (and lesser so the irre­spon­si­ble bor­row­ers), whereas I see you Steve as ratio­nal­iz­ing the screw­ing of the respon­si­ble to bail out the irre­spon­si­ble bor­row­ers.

      Yep, I have a mort­gage, and a house, and sure my net worth will go down on paper if we do not bail one way or the other, but I won’t fool myself into think­ing it is right to screw some for­eigner (or net saver) to main­tain my net worth. Print­ing more money will do just that. It will screw the for­eign­ers hold­ing the cash.

      I bor­rowed specif­i­cally because I knew where the polit­i­cal pres­sure would be. Had I been even more fru­gal I would have been even more screwed by my respon­si­ble behav­ior. I won’t how­ever pre­tend that there is an eco­nomic need to make my bets on the idiocy of the rest of the coun­try pay off. 

      The world has lived through many a frac­tional reserve con­trac­tion where no bailouts were done, no spend­ing projects, and things cor­rected via price changes, and much faster than things are going now. The econ­omy needs to read­just and bailouts to either bankers or bor­row­ers just delays that process. The delay­ing is what hurts because peo­ple con­sume their sav­ings wait­ing for things to turn round.

    • Harry

      I can see I’m way late for this dis­cus­sion; is any­body still inter­ested?

      TITINT, were you happy with those expla­na­tions? I con­fess I have the same prob­lem: where is the profit? Most def­i­n­i­tions of “profit” would have the firm’s deposit account increas­ing over time. Profit as a flow, with no increase in net worth? It’s not very intu­itive. (Inci­den­tally, which flow?)

      Of course it’s a no-brainer that in a closed sys­tem with con­stant money, no player can accu­mu­late money indef­i­nitely — once he has all the money, it’s the end of the game, i.e. no steady state.

      So I think it hinges on the def­i­n­i­tion of “profit” — does any­body have one which is under­stand­able and is com­pat­i­ble with Steve’s con­clu­sions?

    • Hi Harry,

      The basic model I built was of an econ­omy with no growth and a con­stant money stock–just to show that it was nonethe­less sus­tain­able and gen­er­ated pos­i­tive incomes for all classes over time. The world we live in is one of growth with expand­ing money stock. In that sit­u­a­tion, every­one is “saving”–it is the first deriv­a­tive of the rel­e­vant bank account and in fact is mod­eled directly in my tab­u­lar finan­cial sys­tem.

    • Harry

      Hi Steve,

      Thanks for the response. I real­ize that the model is basic, and not really intended to rep­re­sent the real world. 

      But I have been won­der­ing about “money sup­ply” — hence an ear­lier ques­tion about when money is destroyed. In the absence of large bank fail­ures which might wipe out deposit accounts, and in the pres­ence any­way of wide­spread deposit insur­ance, I won­der whether money is not ever being destroyed, and money stock is only ever increas­ing. And if so what the end result is likely to be, espe­cially as debt lev­els are grad­u­ally reduced.

    • I won­der that myself Harry, and it will take a bit of delv­ing into actual bank pro­ce­dures in the case of bank­ruptcy to work it out. The key issues include how banks appor­tion for losses when those losses have to be financed out of their own equity (ie prior to the bank itself going bank­rupt when state guar­an­tees of deposits take over and effec­tively con­vert bank deposits from credit-backed money to fiat money).

    • Hi Steve,
      I appre­ci­ate your paper a lot, and see it as the com­ple­tion of your ear­lier draft arti­cle, Keyne’s revolv­ing fund of finance and trans­ac­tions in the cir­cuit.

      I won­der what you have to say about the impli­ca­tions of your model and bank credit money regard­ing geog­ra­phy?

      It seems to me that your find­ings cor­rob­o­rate the via­bil­ity of regional credit cur­ren­cies — cur­ren­cies used to sup­port, say, some por­tion but not all of a region’s trans­ac­tion and invest­ment needs. The credit-cur­rency could be bank cre­ated as in your model, or busi­ness cre­ated, as in using trade credit as a means for financ­ing. Fur­ther­more, such regional, credit-cur­ren­cies may in effect use a sin­gle national cur­rency as its “base” or “back­ing.”

      The Swiss Wir domes­tic cur­rency is a case in point. It uses trade credit among busi­nesses (denom­i­nated in Swiss Francs) as the basis for trans­ac­tion­able cur­rency.

      Your use of “free bank­ing notes” at the begin­ning of the arti­cle points to this pos­si­bil­ity, it seems to me (or is this only a coin­ci­dence?).


    • Hi Tor­rey,

      It’s a coin­ci­dence, but a mean­ing­ful one. A regional cur­rency would be viable if not abused in the man­ner that many 19th cen­tury free bank­ing cur­ren­cies were–fraud, Ponzi Schemes, and seignor­age, as well as (in some instances) not expand­ing fast enough to sup­port grow­ing com­merce.

    • Aran­fan


      As regards avoid­ing the abuses of the banks in the free bank­ing era, might a dif­fer­ent inter­nal orga­ni­za­tional form help? A credit union has demo­c­ra­tic over­sight of the “bank” by the peo­ple with accounts. It seems to me that the rank-and-file would mil­i­tate against the abuses you out­line that would result in pain to them. (assum­ing a one per­son, one vote credit union with fairly short elec­tion cycles as com­pared to polit­i­cal elec­tion cycles).

    • vir­gule

      Read­ing the above com­ments, I find it absolutely fas­ci­nat­ing that grown-up, very learned men, hav­ing stud­ied this sub­ject to death, still can’t quite have a straight sim­ple agree­ment about the in/outs of our finan­cial system(s).

      As an engi­neer, I’m very tempted to con­clude that the problem/questions are not phrased prop­erly (by the eco­nomic com­mu­nity, not just Steve), and/or the finan­cial rules not clear/mutually exclu­sive, hence the never-end­ing vari­ety of possible/plausible view points. 

      Per­haps every­one (in eco­nom­ics) should take a few steps back for a bet­ter view?

    • Indeed Vir­gule! That’s why I wrote Debunk­ing Eco­nom­ics. The whole dis­ci­pline has gone utterly awry and we need to start again–and engi­neer­ing would be a far bet­ter start­ing point than eco­nomic the­ory.

    • Tom Shaw

      Hi Vir­gule, great point. I think the issue is that the whole dis­ci­pline of actu­ally mod­el­ling the econ­omy is very imma­ture. Friedman’s “F-Twist” has been used to excuse all kinds of unre­al­is­tic assump­tions, so it’s refresh­ing that Steve actu­ally puts the effort in to jus­tify the assump­tions here.

      That said, this is obvi­ously a toy model. Hav­ing just read it for the first time, I’m sur­prised that no-one has pointed out the key inter­nal con­tra­dic­tion: the assump­tion of dif­fer­ent, yet con­stant val­ues for w_D and b_T. The dif­fer­ence is jus­ti­fied by the dif­fer­ences in income and sav­ings between work­ers and bankers. How­ever, by the same logic, a richer banker should have a lower b_T than a poorer banker, i.e. b_T should decrease as a func­tion of B_T.

      If this were incor­po­rated into the model, B_T would likely grow to con­sume the entire sys­tem; you would lose the con­ver­gence that this paper says resolves the “para­dox” of mon­e­tary prof­its.

    • No you wouldn’t Tom. Of course it’s a toy model, but it’s robust to a wide range of para­me­ter val­ues. Allow­ing for dis­per­sion as you sug­gest would make it more real­is­tic, but wouldn’t alter the over­all out­comes.

    • Tom Shaw

      I agree that’s it’s robust to a wide range of para­me­ter val­ues. I’ve played with QED and tried dif­fer­ent con­stant val­ues. How­ever, that’s not what I’m talk­ing about; I’m talk­ing about chang­ing b_T from a con­stant to a func­tion of B_T.

      For exam­ple, say the banker is War­ren Buf­fett. Despite a con­stantly grow­ing for­tune, his con­sump­tion remains steady at g = $X (that is, b_T = X/B_T). Solv­ing the equa­tion for equi­lib­rium of B_T (i.e. 0 = dB_T/dt = c-d-f-X), we get X = c-d-f. This is the ONLY equi­lib­rium point. If X is greater than c-d-f, Buf­fett will have to plun­der the vault or cur­tail his spend­ing. If X is less than c-d-f, B_T will grow to con­sume the sys­tem.

      Now that’s an extreme exam­ple, but it’s much more real­is­tic than con­stant b_T. In fact you’ve admit­ted as much by hav­ing dif­fer­ent w_D and b_T.

    • kys

      If g=$x, which is a con­stant, not a vari­able rel­a­tive to time, then dx/dt = 0.

      Thus dB_T(t)/dt = c-d-f

      Your assump­tion makes the model sim­pler but does not change the out­come.

    • Yes, but I wouldn’t make b_T a func­tion of B_Y alone but B_T divided by out­put.

      Your idea makes b_T->infinity as time->infinity, which of course pro­duces the out­come you note. But it also means that War­ren Buf­fett (or being more accu­rate, who­ever runs Gold­man Sacks) being sat­is­fied with a mere $1 bil­lion dol­lars income for­ever, even if GDP rises.

    • Tom Shaw

      Kys, the unsta­ble equi­lib­rium I referred to is at dB_T/dt = 0. Yes, dX/dt = 0, but it’s not rel­e­vant and not in any equa­tions.

      I’m not claim­ing to know the pre­cise nature of b_T. I’m just show­ing that it’s def­i­nitely not a con­stant and that a choice of func­tion based on real­ity can affect the end result quite dra­mat­i­cally.

      I’m also not talk­ing about con­stant income — I’m talk­ing about con­stant con­sump­tion. The whole point of the sit­u­a­tion I iden­ti­fied is that past a tip­ping point, the banker’s income keeps grow­ing even as his con­sump­tion remains rel­a­tively con­stant.

      I don’t under­stand your point about GDP. Real or nom­i­nal?

    • Hi Vir­gule, Steve and Tom,

      Tak­ing an “engi­neer­ing approach” to eco­nom­ics is pre­cisely the WRONG thing to do. This is how eco­nom­ics has got­ten itself into such a mess (for exam­ple, the Arrow Debreu approach, the con­cept of “equi­lib­rium” — totally engi­neer­ing). Eco­nom­ics is not a pos­i­tive sci­ence, it is an inter­pre­tive sci­ence. See Georgescu-Roe­gen, Her­man Daly, or such philoso­phers as Jur­gen Haber­mas, John Searle and of course Marx. The phe­nom­ena of eco­nom­ics, such as “money,” is overde­ter­mined, dialec­ti­cal. Is a credit card money, a source of credit? Is money a medium of exchange or a store of value? Is that asset’s price its exchange value or use value? Eco­nom­ics is a social sci­ence and as such its method­ol­ogy is hermeneu­tic and inter­pre­tive, not positive/objective.

    • Tom Shaw

      Hi Tor­rey, I actu­ally agree with you. Real progress in eco­nom­ics will be mostly through empir­i­cal obser­va­tion and inter­pre­ta­tion — oth­er­wise it’s just peo­ple argu­ing about the pre­cise details of fan­tasy worlds.

      Steve’s work is use­ful because he stands for some­thing: that if mod­els are built bot­tom-up, they should have real­is­tic assump­tions. That’s a key par­a­digm shift, and it opens the mod­els up to crit­i­cism. The next step may well be: real­ity is too com­plex to include all of the rel­e­vant assump­tions, so we should aban­don bot­tom-up model build­ing.

      So yes, I believe the top-down approach is more likely to suc­ceed: learn­ing the his­tory of eco­nomic real­ity rather than the his­tory of eco­nomic thought.

    • Hi Tom,
      Don’t get me wrong: (quan­ti­ta­tive) mod­els have a place in eco­nom­ics. (And, I like Steve’s model of endoge­nous money alot! And I do a lot of mod­el­ing myself as an applied econ­o­mist.) But from a wider per­spec­tive, the phe­nom­ena of eco­nom­ics — e.g. money, prop­erty, and mar­kets, among oth­ers — are con­structed by social con­sen­sus, col­lec­tive inten­tion­al­ity and are “observer rel­a­tive” (to use Searle’s terms). They are epis­te­mo­log­i­cally objec­tive but onto­log­i­cally sub­jec­tive. They are real, but they only exist in peo­ples’ minds. They do not exist inde­pen­dently of the atti­tudes of peo­ple. They are not nat­u­rally occur­ring objects of nature. With­out this recog­ni­tion, par­tic­u­larly macro­eco­nom­ics will be doomed to con­tin­u­ous ide­o­log­i­cal bat­tles.