Solving the Paradox of Monetary Profits

Flattr this!

The Eco­nom­ics E‑Journal

    The Eco­nom­ics E‑Journal is a rel­a­tive­ly new jour­nal that imple­ments sev­er­al new approach­es to aca­d­e­m­ic pub­lish­ing:

    • It is open access and free. Most aca­d­e­m­ic jour­nals are restrict­ed to sub­scribers or those with access to aca­d­e­m­ic libraries that sub­scribe, which excludes the gen­er­al pub­lic from access to intel­lec­tu­al endeav­our.
    • Any­one paper sub­mit­ted to the jour­nal is per­ma­nent­ly avail­able. Nor­mal­ly only papers that have been ref­er­eed and accept­ed for pub­li­ca­tion can be accessed.
    • Any­one can com­ment on a paper, and com­ments and the num­ber of down­loads goes some way to influ­enc­ing whether a paper is pub­lished in the jour­nal prop­er.

    Papers are still ref­er­eed as in a stan­dard jour­nal, and those that are accept­ed by the ref­er­ees are pub­lished in the jour­nal sec­tion of the web­page.

    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.


    Bhaduri, A. (1969). On the Sig­nif­i­cance of Recent Con­tro­ver­sies on Cap­i­tal The­o­ry: A Marx­i­an View. The Eco­nom­ic Jour­nal, 79(315): 532–539.

    Bellofiore, R., Davan­za­ti, G. F. and Real­fon­zo, R. (2000). Marx Inside the Cir­cuit: Dis­ci­pline Device, Wage Bar­gain­ing and Unem­ploy­ment in a Sequen­tial Mon­e­tary Econ­o­my. Review of Polit­i­cal Econ­o­my, 12(4): 403–417.

    Boden­horn, H. (2008). Free Bank­ing and Bank Entry in Nine­teenth-Cen­tu­ry New York. Finan­cial His­to­ry Review, 15(2): 175–201.

    Boden­horn, H. and Hau­pert, M. (1996). The Note Issue Para­dox in the Free Bank­ing Era. Jour­nal of Eco­nom­ic His­to­ry, 56(3): 687–693.

    Char­lotte Bru­un and Carsten Heyn-Johnsen (2009). The Para­dox of Mon­e­tary Prof­its: An Obsta­cle to Under­stand­ing Finan­cial and Eco­nom­ic Cri­sis? Eco­nom­ics Dis­cus­sion Papers, No 2009–52.–52.

    Disy­atat, P. (2010). The bank lend­ing chan­nel revis­it­ed, BIS Work­ing Papers, 297, Bank of Inter­na­tion­al Set­tle­ments, Basel.

    Dwyer, G. P., Jr. (1996). Wild­cat Bank­ing, Bank­ing Pan­ics, and Free Bank­ing in the Unit­ed States’, Fed­er­al Reserve Bank of Atlanta Eco­nom­ic Review, 81(3–6): 1–20.

    God­ley, W. and Lavoie, M. (2007). Mon­e­tary Eco­nom­ics: An Inte­grat­ed Approach to Cred­it, Mon­ey, Income, Pro­duc­tion and Wealth, Hound­mills, U.K. and New York: Pal­grave Macmil­lan.

    Graziani, A. (1989). The The­o­ry of the Mon­e­tary Cir­cuit, Thames Papers in Polit­i­cal Econ­o­my, Spring: 1–26.

    Graziani, A. (1990). The The­o­ry of the Mon­e­tary Cir­cuit, Economies et Soci­etes, 24(6): 7–36.

    Graziani, A. (1995). The The­o­ry of the Mon­e­tary Cir­cuit, in M. Musel­la and C. Pan­i­co (eds), The Mon­ey Sup­ply in the Eco­nom­ic Process: A Post Key­ne­sian Per­spec­tive, 60, Elgar Ref­er­ence Col­lec­tion. Alder­shot, UK: Inter­na­tion­al Library of Crit­i­cal Writ­ings in Eco­nom­ics. http://www.e‑

    Graziani, A. (2003). The Mon­e­tary The­o­ry of Pro­duc­tion, Cam­bridge, UK: Cam­bridge Uni­ver­si­ty Press.

    Gru­en, N. (2008). Go Ear­ly, Go Hard, Go House­holds, vol. 2010, Hen­ry Thorn­ton, Mel­bourne.

    Holmes, A. R. (1969). Oper­a­tional Con­traints on the Sta­bi­liza­tion of Mon­ey Sup­ply Growth, paper pre­sent­ed to Con­trol­ling Mon­e­tary Aggre­gates, Nan­tuck­et Island, 1969.

    Keen, S. (2001) Debunk­ing Eco­nom­ics: The Naked Emper­or of the Social Sci­ences, Annan­dale Syd­ney & Lon­don UK: Plu­to Press Aus­tralia & Zed Books UK.

    Keen, S. (2009) Bail­ing out the Titan­ic with a Thim­ble, Eco­nom­ic Analy­sis & Pol­i­cy, 39(1): 3–24.

    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.

    Bookmark the permalink.

    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.