A dynamic monetary multi-sectoral model of production

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I will be speak­ing at the Inter­na­tion­al Sci­en­tif­ic Sym­po­sium for Devel­op­ment devot­ed to the 110th anniver­sary of Simon Kuznets in Kyev, The Ukraine, next week. Simon Kuznets, one of the few recip­i­ents of the faux Nobel Prize in Eco­nom­ics whose work I respect, was one of the pio­neers of empir­i­cal research in eco­nom­ics, a stu­dent of busi­ness cycles, and a crit­ic of sta­t­ic eco­nom­ic method­ol­o­gy.

My paper for this con­fer­ence is repro­duced below. It def­i­nite­ly deserves the label “wonkish”–in fact it’s cer­tain­ly the most wonk­ish thing I’ve ever post­ed here.

A dynam­ic mon­e­tary mul­ti-sec­toral mod­el of pro­duc­tion

Steve Keen, Uni­ver­si­ty of West­ern Syd­ney
Click here for the paper in PDF

Though Keynes enti­tled his mag­num opus The gen­er­al the­o­ry of employ­ment, inter­est and mon­ey (Keynes 1936), he acknowl­edged that mon­ey did not fea­ture heav­i­ly in his tech­ni­cal analy­sis, and that he saw a sub­stan­tial con­ti­nu­ity between mon­e­tary analy­sis and the Mar­shal­lian mod­el of sup­ply and demand:

whilst it is found that mon­ey enters into the eco­nom­ic scheme in an essen­tial and pecu­liar man­ner, tech­ni­cal mon­e­tary detail falls into the back­ground. A mon­e­tary econ­o­my, we shall find, is essen­tial­ly one in which chang­ing views about the future are capa­ble of influ­enc­ing the quan­ti­ty of employ­ment and not mere­ly its direc­tion. But our method of ana­lyz­ing the eco­nom­ic behav­ior of the present under the influ­ence of chang­ing ideas about the future is one which depends on the inter­ac­tion of sup­ply and demand, and is in this way linked up with our fun­da­men­tal the­o­ry of val­ue. We are thus led to a more gen­er­al the­o­ry, which includes the clas­si­cal the­o­ry with which we are famil­iar, as a spe­cial case. (Keynes 1936, p. xxii)

After Keynes, macro­eco­nom­ics frag­ment­ed around the impor­tance of both uncertainty—implicit in the state­ment above that “chang­ing views about the future are capa­ble of influ­enc­ing the quan­ti­ty of employ­ment”, but strong­ly explic­it else­where (Keynes 1936; Keynes 1937)—and mon­ey. Both con­cepts dis­ap­peared from main­stream macro­eco­nom­ic analy­sis, to be replaced ini­tial­ly by IS-LM analysis—in which an exoge­nous­ly deter­mined mon­ey played a minor role, but uncer­tain­ty dis­ap­peared (Hicks 1937; Min­sky 1975; Hicks 1981)—and ulti­mate­ly by Real Busi­ness Cycle mod­el­ing (Kyd­land and Prescott 1982), in which “ratio­nal expec­ta­tions” neutered uncer­tain­ty com­plete­ly (Lucas 1972), and mon­ey was entire­ly absent.

On the periph­ery of the pro­fes­sion, a rump of self-described “Post Key­ne­sians” clung to the posi­tion that both mon­ey and uncer­tain­ty were essen­tial aspects of macro­eco­nom­ics. Going far fur­ther than Keynes him­self, this rump incor­po­rat­ed Schum­peter’s argu­ments on the essen­tial role of endoge­nous­ly cre­at­ed mon­ey in financ­ing growth (Schum­peter 1927; Schum­peter 1934; Moore 1979) and Fish­er’s debt-defla­tion per­spec­tive (Fish­er 1933) to devel­op the “Finan­cial Insta­bil­i­ty Hypoth­e­sis” (Min­sky 1975; Min­sky 1977; Min­sky 1982; Min­sky 1993), while it also reject­ed Mar­shal­lian analysis—following on this issue Sraf­fa (Sraf­fa 1926; Robert­son, Sraf­fa et al. 1930) rather than Keynes. Oth­ers added insights from the­o­ret­i­cal devel­op­ments like com­plex­i­ty the­o­ry, which post-dat­ed Keynes, to argue that the macro-econ­o­my was inher­ent­ly cycli­cal (Good­win 1967; Good­win 1986; Good­win 1990).

This rump was ignored by the main­stream, which over time expunged not only uncer­tain­ty and mon­ey but even Keynes him­self from macro­eco­nom­ics (despite the fact that the dom­i­nant seg­ment of the main­stream described its work as “New Key­ne­sian”). Main­stream macro­eco­nom­ics became applied neo­clas­si­cal micro­eco­nom­ics, as Oliv­er Blan­chard, found­ing edi­tor of the jour­nal AER: Macro, out­lined in his sur­vey of macro­eco­nom­ics in 2009.

The most vis­i­ble out­comes of this new approach are the dynam­ic sto­chas­tic gen­er­al equi­lib­ri­um (DSGE) mod­els. They are mod­els derived from micro foundations—that is, util­i­ty max­i­miza­tion by con­sumers-work­ers; val­ue max­i­miza­tion by firms; ratio­nal expec­ta­tions; and a full spec­i­fi­ca­tion of imper­fec­tions, from nom­i­nal rigidi­ties to some of the imper­fec­tions dis­cussed above—and typ­i­cal­ly esti­mat­ed by Bayesian meth­ods. (Blan­chard 2009, p. 223)

As the end of the first decade of the 21st cen­tu­ry approached, the main­stream was tri­umphal. At the pol­i­cy lev­el, it took the cred­it for the decline in eco­nom­ic volatil­i­ty since the ear­ly 1980s:

As it turned out, the low-infla­tion era of the past two decades has seen not only sig­nif­i­cant improve­ments in eco­nom­ic growth and pro­duc­tiv­i­ty but also a marked reduc­tion in eco­nom­ic volatil­i­ty, both in the Unit­ed States and abroad, a phe­nom­e­non that has been dubbed “the Great Mod­er­a­tion.” Reces­sions have become less fre­quent and milder, and quar­ter-to-quar­ter volatil­i­ty in out­put and employ­ment has declined sig­nif­i­cant­ly as well. The sources of the Great Mod­er­a­tion remain some­what con­tro­ver­sial, but as I have argued else­where, there is evi­dence for the view that improved con­trol of infla­tion has con­tributed in impor­tant mea­sure to this wel­come change in the econ­o­my. (Bernanke 2004; empha­sis added)

At the lev­el of pure the­o­ry, a sim­i­lar con­tent­ment pre­vailed. Though he acknowl­edged one notable dis­senter (Solow 2008), Blan­chard’s sur­vey was unequiv­o­cal:

The state of macro is good. (Blan­chard 2009, p. 210)

Few more poor­ly timed state­ments have ever been made by promi­nent econ­o­mists. This paper was first pub­lished online as a work­ing paper in August 2008 (Blan­chard 2008)—one year after the event that is now regard­ed as the begin­ning of the finan­cial cri­sis (New York Times 2007) and 8 months after the NBER’s date for the com­mence­ment of the Great Reces­sion (NBER 2011). Its pub­li­ca­tion as a jour­nal paper in May 2009 pre­ced­ed the NBER’s date for the end of this reces­sion by one month (a deci­sion that I expect will prove pre­ma­ture).

Blan­chard was forced into recant­i­ng his opti­mism less than a year lat­er (Blan­chard, Del­l’Ar­ic­cia et al. 2010). But while he crit­i­cized macro­eco­nom­ic pol­i­cy pri­or to the cri­sis, he remained a believ­er in neo­clas­si­cal the­o­ry itself:

Iden­ti­fy­ing the flaws of exist­ing pol­i­cy is (rel­a­tive­ly) easy. Defin­ing a new macro­eco­nom­ic pol­i­cy frame­work is much hard­er… It is impor­tant to start by stat­ing the obvi­ous, name­ly, that the baby should not be thrown out with the bath­wa­ter. Most of the ele­ments of the pre-cri­sis con­sen­sus, includ­ing the major con­clu­sions from macro­eco­nom­ic the­o­ry, still hold. Among them, the ulti­mate tar­gets remain out­put and infla­tion sta­bil­i­ty. The nat­ur­al rate hypoth­e­sis holds, at least to a good enough approx­i­ma­tion, and pol­i­cy­mak­ers should not design pol­i­cy on the assump­tion that there is a long-term trade-off between infla­tion and unem­ploy­ment. Sta­ble infla­tion must remain one of the major goals of mon­e­tary pol­i­cy. Fis­cal sus­tain­abil­i­ty is of the essence, not only for the long term but also in affect­ing expec­ta­tions in the short term. (Blan­chard, Del­l’Ar­ic­cia et al. 2010, p. 207; empha­sis added)

Blan­chard’s unwill­ing­ness to coun­te­nance the pos­si­bil­i­ty that the Great Reces­sion may be a Kuhn­ian crit­i­cal anom­aly for neo­clas­si­cal macro­eco­nom­ics (Beze­mer 2011) is rep­re­sen­ta­tive of this school of thought:

Indeed, the extreme sever­i­ty of this great reces­sion makes it tempt­ing to argue that new the­o­ries are required to ful­ly explain it… But … it would be pre­ma­ture to aban­don more famil­iar mod­els just yet. (Ire­land 2011, p. 1; empha­sis added)

As a rep­re­sen­ta­tive of the Post Key­ne­sian and com­plex­i­ty the­o­ry rump, and one of the hand­ful of econ­o­mists to fore­see the Great Reces­sion (Keen 1995; Keen 2000; Keen 2006; Keen 2007; Keen 2007; Beze­mer 2009; Beze­mer 2011), I could not dis­agree more with Blan­chard and his col­leagues. Though neo­clas­si­cal econ­o­mists believe they are being method­olog­i­cal­ly sound in apply­ing micro­eco­nom­ic con­cepts to mod­el the macro-econ­o­my, deep research long ago estab­lished that this is a fal­la­cy. The Son­nen­schein-Man­tel-Debreu con­di­tions alone estab­lish that even the micro­eco­nom­ics of demand in a sin­gle mar­ket can­not be derived by extrap­o­la­tion from the behav­ior of a sin­gle util­i­ty-max­i­miz­ing agent, let alone the macro­eco­nom­ics of the whole econ­o­my. As Solow him­self not­ed in the paper cit­ed in Blan­chard (2009, p. 210):

Sup­pose you want­ed to defend the use of the Ram­sey mod­el as the basis for a descrip­tive macro­eco­nom­ics. What could you say? …

You could claim that … there is no oth­er tractable way to meet the claims of eco­nom­ic the­o­ry. I think this claim is a delu­sion. We know from the Son­nen­schein-Man­tel-Debreu the­o­rems that the only uni­ver­sal empir­i­cal aggrega­tive impli­ca­tions of gen­er­al equi­lib­ri­um the­o­ry are that excess demand func­tions should be con­tin­u­ous and homo­ge­neous of degree zero in prices, and should sat­is­fy Wal­ras’ Law. Any­one is free to impose fur­ther restric­tions on a macro mod­el, but they have to be jus­ti­fied for their own sweet sake, not as being required by the prin­ci­ples of eco­nom­ic the­o­ry. Many vari­eties of macro mod­els can be con­struct­ed that sat­is­fy those basic require­ments with­out impos­ing any­thing as extreme and prej­u­di­cial as a rep­re­sen­ta­tive agent in a favor­able envi­ron­ment. (Solow 2008, p. 244; empha­sis added; see also Solow 2001 and 2003)

I cov­er the myr­i­ad flaws in neo­clas­si­cal macro­eco­nom­ics in much more detail in Keen 2011b; suf­fice it to say here that, far from it being unwise to “throw the baby out with the bath­wa­ter”, neo­clas­si­cal macro­eco­nom­ics should nev­er have been con­ceived in the first place. The Great Reces­sion will hope­ful­ly prove to be the Bib­li­cal eco­nom­ic flood need­ed to final­ly sink this super­fi­cial­ly appeal­ing but fun­da­men­tal­ly flawed vision of how the macro-econ­o­my func­tions.


How do I fault thee? Let me count the ways


The flaws of neo­clas­si­cal macro­eco­nom­ics are almost too numer­ous to enu­mer­ate, but the key weak­ness­es are:

  1. Treat­ing a com­plex mon­e­tary mar­ket econ­o­my as a barter sys­tem;
  2. Assum­ing that the macro-econ­o­my is either in equi­lib­ri­um (par­tial or gen­er­al, per­fect or imper­fect), or that it will return to equi­lib­ri­um rapid­ly if dis­turbed;
  3. Mod­el­ing the entire econ­o­my using “applied micro­eco­nom­ics” and ignor­ing social class, when the Son­nen­schein-Man­tel-Debreu con­di­tions (Son­nen­schein 1972; Son­nen­schein 1973; Kir­man 1989; Shafer and Son­nen­schein 1993) estab­lish that, as Kir­man put it:

    we may well be forced to the­o­rise in terms of groups who have col­lec­tive­ly coher­ent behav­iour. Thus demand and expen­di­ture func­tions if they are to be set against real­i­ty must be defined at some rea­son­ably high lev­el of aggre­ga­tion. The idea that we should start at the lev­el of the iso­lat­ed indi­vid­ual is one which we may well have to aban­don” (Kir­man 1992, p. 138);

  4. Oblit­er­at­ing uncer­tain­ty from macro­eco­nom­ic the­o­ry with the absurd propo­si­tion that a ratio­nal indi­vid­ual is some­one who can accu­rate­ly fore­see the future—which is what “ratio­nal expec­ta­tions” real­ly means;
  5. Per­sist­ing with a sim­plis­tic “mon­ey mul­ti­pli­er” mod­el of mon­ey cre­ation when the empir­i­cal evi­dence against this mod­el is over­whelm­ing (Holmes 1969; Moore 1979; Moore 1988; Kyd­land and Prescott 1990); and
  6. Ignor­ing the piv­otal roles of cred­it and debt in the macro-econ­o­my.

All these flaws are absent from the non-neo­clas­si­cal rump—especially in the work of Min­sky. But what the rump lacks, in com­par­i­son to the neo­clas­si­cal main­stream, is a coher­ent math­e­mat­i­cal expres­sion of its mod­el that is wide­ly accept­ed with­in that school. In this paper I con­tribute to the devel­op­ment of such a mod­el (though I appre­ci­ate that my mod­el is a long way from being accept­ed by my peers) using a mod­el­ing framework—which I call Mon­e­tary Cir­cuit The­o­ry (MCT)—that, in con­trast to the neo­clas­si­cal litany of sins above:

  1. Treats the econ­o­my as inher­ent­ly mon­e­tary;
  2. Makes no assump­tions about the nature of equi­lib­ri­um and mod­els the econ­o­my dynam­i­cal­ly;
  3. Mod­els behav­ior at the lev­el of social class­es rather than iso­lat­ed agents;
  4. Pre­sumes ratio­nal but not prophet­ic behav­ior: peo­ple in social class­es act in what they per­ceive as their best inter­ests giv­en infor­ma­tion avail­able, but do not attempt to fore­cast the future state of the econ­o­my (and they can­not do so in any case, because of the well-known fea­tures of com­plex sys­tems);
  5. Mod­els the endoge­nous cre­ation of mon­ey by the bank­ing sec­tor in a pure cred­it econ­o­my (lat­er exten­sions will incor­po­rate fiat mon­ey cre­ation by gov­ern­ments); and
  6. Gives cred­it and debt the piv­otal roles in eco­nom­ic the­o­ry that the Great Reces­sion has shown they have in the real world.


A framework for monetary macroeconomics


At one lev­el, MCT is decep­tive­ly sim­ple: all demand in the macro­econ­o­my is treat­ed as orig­i­nat­ing in bank accounts, where, in accor­dance with the empir­i­cal lit­er­a­ture (Holmes 1969; Moore 1979, 1988; Kyd­land and Prescott 1990), the bank­ing sys­tem has the capac­i­ty to endoge­nous­ly cre­ate new cred­it-based mon­ey. The devel­op­ment of the frame­work is described else­where (see Keen 2006b, 2008, 2009); here I will sim­ply illus­trate MCT with the finan­cial flows used in the mod­el of the 19th cen­tu­ry “free bank­ing” sys­tem in Keen (2010). The core of MCT is a tab­u­lar lay­out of the finan­cial rela­tions between the eco­nom­ic enti­ties in the mod­el, where each col­umn rep­re­sents an aggre­gate bank account, and each row rep­re­sents oper­a­tions on and between those accounts.

Table 1: Sam­ple Finan­cial Flows God­ley Table





Account Name

Bank Vault

Firm Loan

Firm Deposit

Work­er Deposit

Bank Equi­ty







Ini­tial con­di­tions






Lend Mon­ey



Record Loan


Com­pound Debt


Ser­vice Debt



Record Pay­ment


Deposit Inter­est






Deposit Inter­est







Repay Loan



Record Repay­ment




Using a sym­bol­ic alge­bra pro­gram, the place­hold­ers A to H are then replaced by suit­able func­tions:

The pro­gram then auto­mat­i­cal­ly derives a set of dif­fer­en­tial equa­tions for this sys­tem, which can be ana­lyzed sym­bol­i­cal­ly or sim­u­lat­ed numer­i­cal­ly:

This cov­ers the finan­cial side of the econ­o­my. The real econ­o­my is cou­pled to this via a price mech­a­nism (and links between the wages flow—which deter­mines employment—and invest­ment, which is not shown in the sim­ple mod­el in Table 1, but which deter­mines the cap­i­tal stock in a larg­er mod­el).

The price mech­a­nism is derived ana­lyt­i­cal­ly in Keen 2010 (pp. 17–18), and cor­re­sponds to the exten­sive empir­i­cal lit­er­a­ture into how firms actu­al­ly set prices—which has noth­ing to do with mar­gin­al cost and mar­gin­al rev­enue (see Lee 1998, Blind­er et al. 1998, and Keen & Stan­dish 2006 and 2010) but instead rep­re­sents a markup on the wage costs of pro­duc­tion


The real econ­o­my itself is mod­eled using Good­win’s growth cycle (Good­win 1967; see also Blatt 1983, pp. 204–216), but expressed in absolute val­ues (Employ­ment, Wages, etc.) rather than ratios (rate of employ­ment, wages share of out­put) as in Good­win’s orig­i­nal mod­el.


Applying the framework: a “corn economy” with a financial crisis


The sam­ple God­ley Table shown in Table 1 has to be extend­ed to allow for invest­ment, which as Schum­peter argued is the sound basis on which the cred­it sys­tem endoge­nous­ly cre­ates new debt-based mon­ey (Schum­peter 1934, pp. 95–101).

Table 2: God­ley Table for Corn Econ­o­my Mod­el





Account Name

Bank Vault

Firm Loan

Firm Deposit

Work­er Deposit

Bank Equi­ty







Lend from Vault



Record Loan


Com­pound Debt


Ser­vice Debt



Record Pay­ment


Debt-financed Invest­ment


Record Invest­ment Loan





Deposit Inter­est








Repay Loan



Record Repay­ment



This God­ley Table results in the fol­low­ing gener­ic sys­tem of finan­cial flows:

The sub­sti­tu­tions for this table are show in Equa­tion ; the rates of lend­ing, invest­ment and loan repay­ment (respec­tive­ly A, D and J in Table 2) are now func­tions of the rate of prof­it, and wage pay­ments (E) are now wages times employ­ment.

The basic causal cycle in the Good­win mod­el (to which the finan­cial flows above are attached) is quite sim­ple. Cau­sa­tion flows from left to right in equa­tions to :

  • The lev­el of the phys­i­cal cap­i­tal stock deter­mines the lev­el of phys­i­cal out­put per year:

  • Out­put per year deter­mines employ­ment :

  • The rate of employ­ment deter­mines the rate of change of the mon­ey wage—thus link­ing the phys­i­cal sec­tor to the mon­e­tary sec­tor; in keep­ing with Phillip­s’s orig­i­nal inten­tions (and in con­trast to most macro­eco­nom­ic mod­els), the wage change func­tion includes a reac­tion to the rate of change of employ­ment and the lev­el of infla­tion, as well as a non­lin­ear reac­tion to the lev­el of employ­ment:

  • The mon­ey wage deter­mines the rate of change of the price lev­el :

  • The mon­e­tary val­ue of out­put minus wages deter­mines prof­it:

  • The rate of prof­it deter­mines invest­ment (and hence the amount of new cred­it mon­ey need­ed should desired invest­ment exceed prof­it) and invest­ment minus depre­ci­a­tion deter­mines the rate of eco­nom­ic growth :

  • The inte­gral of invest­ment deter­mines the cap­i­tal stock:

  • The rate of change of the employ­ment rate is the rate of growth minus the rates of growth of labor pro­duc­tiv­i­ty and pop­u­la­tion:

  • Equa­tions for growth in labor pro­duc­tiv­i­ty and pop­u­la­tion com­plete the mod­el:


The rates of lend­ing (A), debt-financed invest­ment (D) and loan repay­ment (J) are mod­eled as non­lin­ear func­tions of the rate of prof­it, while the Phillips Curve is also a non­lin­ear func­tion of the lev­el of employ­ment. The basic func­tion used in all cas­es is a gen­er­al­ized expo­nen­tial func­tion where the argu­ments to the func­tion are an (xc,yc) coor­di­nate pair, the func­tion’s slope at that point s, and its min­i­mum m:

The com­plete mod­el is described by a set of ten dif­fer­en­tial equa­tions:

Giv­en suit­able ini­tial con­di­tions and para­me­ter val­ues, this high­ly non­lin­ear mon­e­tary mod­el can gen­er­ate the styl­ized facts of the last 20 years of macro­eco­nom­ic data: an appar­ent “Great Mod­er­a­tion” in employ­ment and inflation—which was actu­al­ly dri­ven by an expo­nen­tial growth in pri­vate debt—followed by a “Great Reces­sion” in which unem­ploy­ment explodes, infla­tion turns to defla­tion, and the debt level—absent of bank­rupt­cy and gov­ern­ment intervention—goes pure­ly expo­nen­tial as unpaid inter­est is com­pound­ed.

Fig­ure 1: US Data 1980–2008

As a com­plex sys­tems mod­el, the behav­ior of this sys­tem depends upon its ini­tial con­di­tions as well as upon its inher­ent dynam­ics. In Keen 2011 I used a set of ini­tial con­di­tions that result­ed in both a Great Mod­er­a­tion and a Great Recession—with no change to the under­ly­ing para­me­ters of the system—to indi­cate that this mod­el fits Min­sky’s cri­te­ria for a suc­cess­ful mod­el of cap­i­tal­ism:

Can “It”—a Great Depression—happen again? And if “It” can hap­pen, why did­n’t “It” occur in the years since World War II? These are ques­tions that nat­u­ral­ly fol­low from both the his­tor­i­cal record and the com­par­a­tive suc­cess of the past thir­ty-five years. To answer these ques­tions it is nec­es­sary to have an eco­nom­ic the­o­ry which makes great depres­sions one of the pos­si­ble states in which our type of cap­i­tal­ist econ­o­my can find itself.(Min­sky 1982 , p. 5; empha­sis added)

Fig­ure 2: Sim­u­la­tion Results with uncal­i­brat­ed con­stant para­me­ter val­ues

This mod­el cap­tures the macro­eco­nom­ic expe­ri­ence of the last 2 decades far more effec­tive­ly than any neo­clas­si­cal mod­el. How­ev­er, the Holy Grail of eco­nom­ics has always been to mod­el the com­plex dynam­ic process by which com­modi­ties are pro­duced using oth­er com­modi­ties and labor. In the next sec­tion I show that a struc­tured exten­sion of this corn econ­o­my model—with finan­cial flows deter­min­ing demand, and pro­duc­tion mod­eled using Good­win’s growth cycle—can gen­er­ate a coher­ent dynam­ic mon­e­tary mul­ti­sec­toral mod­el of pro­duc­tion.


A dynamic monetary multisectoral model of production


First a strong caveat: this mod­el is very ten­ta­tive, and many refine­ments need to be made. How­ev­er even in its ten­ta­tive state, it shows that a mon­e­tary, dynam­ic mul­ti­sec­toral mod­el of pro­duc­tion can be con­struct­ed.

The mod­el repro­duces the struc­ture of the pre­ced­ing corn econ­o­my mod­el, extend­ed to mul­ti­ple com­modi­ties in both pro­duc­tion (with each sec­tor need­ing to pur­chase inputs from oth­er sec­tors pro­por­tion­al to its desired out­put lev­el), and con­sump­tion. I also address one of the weak­ness­es of input-out­put analysis—that pur­chas­es with­in a sec­tor are not explic­it­ly shown—by the sim­ple expe­di­ent of split­ting each sec­tor in two. There are 4 sec­tors in this sim­ple “proof of con­cept” mod­el (notion­al­ly Cap­i­tal Goods, Con­sumer Goods, Agri­cul­ture and Ener­gy).

The God­ley Table for this sys­tem has 19 sys­tem states— Bank Reserve, Bank Equi­ty and Work­er Deposit accounts as in the sin­gle sec­toral mod­el, plus two Deposit and two Loan accounts per sector—and 16 finan­cial operations—debt com­pound­ing, debt repay­ing, mon­ey relend­ing and wages pay­ment as in the sin­gle sec­toral mod­el, plus one inter­sec­toral pur­chase for pro­duc­tion and one for con­sump­tion per sec­tor. A styl­ized rep­re­sen­ta­tion of these flows is giv­en in Table 3 (the inter­sec­toral flows are only par­tial­ly indi­cat­ed).

Table 3: Styl­ized rep­re­sen­ta­tion of mul­ti­ec­toral God­ley Table

Assets Lia­bil­i­ties Equi­ty
Account Bank Reserve Sec­tor 1 Loan Sec­tor 2 Loan Sec­tor 1 Deposit Sec­tor 2 Deposit Work­er Deposit Bank Equi­ty
Sym­bol BR(t) FL1(t) FL1(t) FD1(t) FD2(t) WD(t) BE(t)
Com­pound Debt A1 A2
Deposit Inter­est B1 B2
Wages -C1 -C2 C1+C2
Work­er Inter­est -D -D
Invest­ment K E -E
Inter­sec­toral C -F F
Inter­sec­toral A -G G
Inter­sec­toral E -H H
Con­sump­tion K I -I
Con­sump­tion C -J J
Con­sump­tion A -K K
Con­sump­tion E -L L
Pay Inter­est -M M
Repay Loans N -N
Recy­cle Reserves -O O O
New Mon­ey P P



An extract from the actu­al God­ley Table for this sys­tem (as imple­ment­ed in Math­cad) is shown in Fig­ure 3.


Fig­ure 3: 7 of the 19 columns in the mul­ti­sec­toral God­ley Table

The rate of prof­it is now net of inter­sec­toral pur­chas­es for each sec­tor, and of course there is a dif­fer­ent rate of prof­it in each sec­tor. Inter­sec­toral pur­chas­es of inputs dif­fer for each sec­tor, and are pro­por­tion­al to the labor input need­ed to pro­duce the required out­put in each sector—signified by where the first sub­script rep­re­sents the sec­tor pur­chas­ing the inputs and the sec­ond the sec­tor from which the inputs are pur­chased. Equa­tion shows the rate of prof­it for­mu­lae for the cap­i­tal goods and con­sumer good sec­tors:


As with the sin­gle sec­toral mod­el, behav­ior in five cru­cial areas is mod­eled as a non­lin­ear response to a rel­e­vant vari­able:

  • The rate of change of mon­ey wages as a func­tion of the rate of employ­ment;
  • The time con­stant in invest­ment deci­sions as a func­tion of the rate of prof­it;
  • The time con­stant in loan repay­ment as a func­tion of the rate of prof­it;
  • The time con­stant in mon­ey relend­ing as a func­tion of the rate of prof­it;
  • The time con­stant in new mon­ey cre­ation as a func­tion of the rate of prof­it;

Table 4: Para­me­ters for Behav­ioral Func­tions


With the pur­chas­es of inter­me­di­ate inputs tak­en care of in the mon­e­tary demand com­po­nent of the mod­el, pro­duc­tion in each sec­tor is mod­eled as lagged response to installed cap­i­tal, and employ­ment is a lagged response to out­put. The func­tions for the con­sumer goods sec­tor, which are rep­re­sen­ta­tive of those for the oth­er sec­tors, are shown in Equa­tion :

The full mod­el is a sys­tem of dif­fer­en­tial equa­tions, where n is the num­ber of sec­tors, and the first set of terms spec­i­fies the equa­tions in the finan­cial sect­sor, the sec­ond the equa­tions in pro­duc­tion, and the final equa­tion is for pop­u­la­tion growth. In this sam­ple 4‑sector mod­el, this results in a sys­tem of 40 non­lin­ear ODEs.




The rate of prof­it var­ied between sec­tors, and, once the sys­tem had set­tled into its lim­it cycle, ranged from 0.4% p.a. and 8.7%.

Fig­ure 4

The aggre­gate real rate of eco­nom­ic growth var­ied between minus 1 and plus 5 per­cent p.a., and growth fol­lowed a saw­tooth pat­tern:

Fig­ure 5

This shape cor­re­sponds with the styl­ized nature of the busi­ness cycle, as Blatt observed:

In the real world, upswings are slow; down­swings go with an almighty rush. In the words of Gal­braith:

The usu­al image of the busi­ness cycle was of a wave­like move­ment, and the waves of the sea were the accept­ed metaphor… The real­i­ty in the nine­teenth and ear­ly twen­ti­eth cen­turies was, in fact, much clos­er to the teeth of a rip­saw which go up on a grad­ual plane on one side and drop pre­cip­i­tate­ly on the oth­er…” (Blatt 1983, pp. 203–204, cit­ing Gal­braith 1975, p. 104)

The growth rate and the debt to out­put lev­el moved togeth­er, and the debt ratio cycled between 50 and 110 per­cent of GDP.

Fig­ure 6

The dis­tri­b­u­tion of income was real­is­tic, though the dynam­ics were rather more volatile than in actu­al data:

Fig­ure 7

The rate of infla­tion was unre­al­is­tic, with a min­i­mum of 8 per­cent p.a. and a max­i­mum of 45 per­cent.

Fig­ure 8

These last two empir­i­cal weak­ness­es prob­a­bly reflect the spec­i­fi­ca­tion for the Phillips curve, and the ten­den­cy of the mod­el to oper­ate in over-full employ­ment (defined as a ratio of 1 in this sim­ple mod­el) giv­en the para­me­ters used for cap­i­tal­ist and banker behav­ior.

Fig­ure 9

Final­ly, finan­cial dynam­ics were an essen­tial part of this mod­el: mon­ey is far from neu­tral in this mod­el (and in the real world). Peri­ods of falling eco­nom­ic growth coin­cid­ed with an increase in bank reserves, and a decline in the lev­el of loans.

Fig­ure 10




Though this pre­lim­i­nary mod­el has many short­com­ings, the fact that it works at all shows that it is pos­si­ble to mod­el the dynam­ic process by which prices and out­puts are set in a mul­ti­sec­toral econ­o­my. The fail­ure of the neo­clas­si­cal school to achieve this objective—which it has had since the time of Walras—may relate to the abstrac­tions it made with the inten­tion of mak­ing this process eas­i­er to mod­el. These devices—everything from Wal­ras’s taton­nement, to ignor­ing the role of money—may in fact be why they failed. The real world is com­plex and the real econ­o­my is mon­e­tary, and com­plex mon­e­tary mod­els are need­ed to do it jus­tice.

Giv­en the com­plex­i­ty of this mod­el and the sen­si­tiv­i­ty of com­plex sys­tems to ini­tial con­di­tions, it is rather remark­able that an obvi­ous lim­it cycle devel­oped out of an arbi­trary set of para­me­ter val­ues and ini­tial conditions—with most (but by no means all) vari­ables in the sys­tem keep­ing with­in real­is­tic bounds. A con­jec­ture is that this lim­it cycle is a man­i­fes­ta­tion of the well-known insta­bil­i­ty of an input-out­put matrix (Jor­gen­son 1960; Jor­gen­son 1960; Jor­gen­son 1961; Jor­gen­son 1961; Hahn 1963; Blatt 1983; Fleiss­ner 1990; Heester­man 1990; John­son 1993), com­bined with non­lin­ear rela­tions that reverse the insta­bil­i­ty prop­er­ties of the sys­tem as it diverges from its equi­lib­ri­um. This con­jec­ture was first made by Blatt in a dis­cus­sion of both the his­tor­i­cal evi­dence of the busi­ness cycle and the dual insta­bil­i­ty of the equi­lib­ri­um growth path:

At this stage of the argu­ment, we feel free to offer a con­jec­ture: The repeat­ed devel­op­ment of an unsta­ble state of the econ­o­my is asso­ci­at­ed with, and indeed is an unavoid­able con­se­quence of, the local insta­bil­i­ty of the state of bal­anced growth. (Blatt 1983, p. 161)

The pres­ence of mon­e­tary buffers—in the guise of deposit accounts—surely also plays a role in the sys­tem’s capac­i­ty, despite its insta­bil­i­ty, to stay with­in real­is­tic bounds, in con­trast to most (if not all) oth­er dynam­ic mul­ti­sec­toral mod­els.

I doubt that Kuznets would have been sur­prised by the fail­ure of equi­lib­ri­um-ori­ent­ed attempts to build dynam­ic mul­ti­sec­toral mod­els of eco­nom­ic growth, since he argued long ago that dynam­ics had to be dif­fer­ent to sta­t­ics, and in par­tic­u­lar that the fetish with equi­lib­ri­um had to be aban­doned:

Accord­ing to the econ­o­mists of the past and to most of their mod­ern fol­low­ers, sta­t­ic eco­nom­ics is a direct step­ping stone to the dynam­ic sys­tem, and may be con­vert­ed into the lat­ter by the intro­duc­tion of the gen­er­al ele­ment of change… Accord­ing to oth­er econ­o­mists, the body of eco­nom­ic the­o­ry must be car­di­nal­ly rebuilt, if dynam­ic prob­lems are to be dis­cussed effi­cient­ly…

… as long as sta­t­ic eco­nom­ics will remain a strict­ly uni­fied sys­tem based upon the con­cept of equi­lib­ri­um, and con­tin­ue to reduce the social phe­nom­e­non to units of rigid­ly defined indi­vid­ual behav­ior, its ana­lyt­ic part will remain of lit­tle use to any sys­tem of dynam­ic eco­nom­ics… the sta­t­ic scheme in its entire­ty, in the essence of its approach, is nei­ther a basis, nor a step­ping stone towards a prop­er dis­cus­sion of dynam­ic prob­lems. Kuznets, S. (1930, pp. 422–428, 435–436; empha­sis added)

Yet the sta­t­ic approach—masquerading as dynam­ics via word games such as using the moniker “Dynam­ic Sto­chas­tic Gen­er­al Equi­lib­ri­um” to describe bas­tardized Ram­say-Solow equi­lib­ri­um growth models—still dom­i­nate eco­nom­ics, even after the con­tin­u­ing dis­as­ter of the cri­sis of 2007. Part of the rea­son for this per­sis­tence, I believe, is the seduc­tive sim­plic­i­ty of the “Mar­shal­lian Cross” that forms the basis of edu­ca­tion in eco­nom­ics: it con­forms to Hen­ry Menchen’s apho­rism that “Expla­na­tions exist; they have exist­ed for all time; there is always a well-known solu­tion to every human problem—neat, plau­si­ble, and wrong”. For eco­nom­ics to escape the trap of sta­t­ic equi­lib­ri­um think­ing, we need an alter­na­tive foun­da­tion method­ol­o­gy that is neat, plau­si­ble, and—at least to a first approximation—right.

I offer this mod­el and the tools used to con­struct it as a first step towards such a neat, plau­si­ble and gen­er­al­ly cor­rect approach to macro­eco­nom­ics. A col­league has imple­ment­ed the God­ley Table method for build­ing a dynam­ic mod­el of finan­cial flows in a pro­to­type dynam­ic mod­el­ing pro­gram QED, which is freely down­load­able from my blog. A Math­e­mat­i­ca imple­men­ta­tion is being devel­oped as part of a project with the CSIRO, and it will also be freely avail­able from my blog when it is com­plet­ed. The ulti­mate objec­tive is to devel­op a stand­alone dynam­ic mon­e­tary macro­eco­nom­ic mod­el­ing tool that is more suit­ed to finan­cial flows than exist­ing sys­tems dynam­ics pro­grams like Simulink (http://www.mathworks.com/products/simulink/), Ven­sim (http://www.vensim.com/) and Vis­sim (http://www.vissim.com/).

The glob­al econ­o­my was blind­ly led into our cur­rent finan­cial cri­sis by an eco­nom­ics pro­fes­sion that had delud­ed itself into the belief that such phe­nom­e­na can­not occur. Hope­ful­ly, dur­ing this cri­sis, mon­e­tary macro­eco­nom­ic dynam­ics will final­ly sup­plant the sta­t­ic method against which Kuznets inveighed so elo­quent­ly at the start of cap­i­tal­is­m’s pre­vi­ous great finan­cial cri­sis.




Bernanke, B. S. (2004). Pan­el dis­cus­sion: What Have We Learned Since Octo­ber 1979? Con­fer­ence on Reflec­tions on Mon­e­tary Pol­i­cy 25 Years after Octo­ber 1979, St. Louis, Mis­souri, Fed­er­al Reserve Bank of St. Louis.

Beze­mer, D. J. (2009). “No One Saw This Com­ing”: Under­stand­ing Finan­cial Cri­sis Through Account­ing Mod­els. Gronin­gen, The Nether­lands, Fac­ul­ty of Eco­nom­ics Uni­ver­si­ty of Gronin­gen.

Beze­mer, D. J. (2011). “The Cred­it Cri­sis and Reces­sion as a Par­a­digm Test.” Jour­nal of Eco­nom­ic Issues
45: 1–18.

Blatt, J. M. (1983). Dynam­ic eco­nom­ic sys­tems: a post-Key­ne­sian approach. Armonk, N.Y, M.E. Sharpe.

Blind­er, A. S. (1998). Ask­ing about prices: a new approach to under­stand­ing price stick­i­ness. New York, Rus­sell Sage Foun­da­tion.

Blan­chard, O. J. (2008). “The State of Macro.” Nation­al Bureau of Eco­nom­ic Research Work­ing Paper Series
No. 14259.

Blan­chard, O. (2009). “The State of Macro.” Annu­al Review of Eco­nom­ics
1(1): 209–228.

Blan­chard, O., G. Del­l’Ar­ic­cia, et al. (2010). “Rethink­ing Macro­eco­nom­ic Pol­i­cy.” Jour­nal of Mon­ey, Cred­it, and Bank­ing
42: 199–215.

Fish­er, I. (1933). “The Debt-Defla­tion The­o­ry of Great Depres­sions.” Econo­met­ri­ca
1(4): 337–357.

Fleiss­ner, P. (1990). “Dynam­ic Leon­tief Mod­els on the Test Bed.” Struc­tur­al Change and Eco­nom­ic Dynam­ics
1(2): 321–357.

Gal­braith, J. K. (1975). Mon­ey: whence it came, where it went. Boston, Houghton Mif­flin.

God­ley, W. and M. Lavoie (2007). “Fis­cal Pol­i­cy in a Stock-Flow Con­sis­tent (SFC) Mod­el.” Jour­nal of Post Key­ne­sian Eco­nom­ics 30(1): 79–100.

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

Good­win, R. M. (1967). A growth cycle. Social­ism, Cap­i­tal­ism and Eco­nom­ic Growth. C. H. Fein­stein. Cam­bridge, Cam­bridge Uni­ver­si­ty Press: 54–58.

Good­win, R. M. (1986). “Swing­ing along the Turn­pike with von Neu­mann and Sraf­fa.” Cam­bridge Jour­nal of Eco­nom­ics
10(3): 203–210.

Good­win, R. M. (1990). Chaot­ic eco­nom­ic dynam­ics. Oxford, Oxford Uni­ver­si­ty Press.

Hahn, F. H. (1963). “On the Dis­e­qui­lib­ri­um Behav­iour of a Mul­ti-Sec­toral Growth Mod­el.” The Eco­nom­ic Jour­nal
73(291): 442–457.

Heester­man, A. R. G. (1990). “The Insta­bil­i­ty of the Dynam­ic Input-Out­put Mod­el.” Eco­nom­ic Sys­tems Research
2(4): 351–355.

Hicks, J. R. (1937). “Mr. Keynes and the “Clas­sics”; A Sug­gest­ed Inter­pre­ta­tion.” Econo­met­ri­ca
5(2): 147–159.

Hicks, J. (1981). “IS-LM: An Expla­na­tion.” Jour­nal of Post Key­ne­sian Eco­nom­ics
3(2): 139–154.

Holmes, A. R. (1969). Oper­a­tional Con­straints on the Sta­bi­liza­tion of Mon­ey Sup­ply Growth. Con­trol­ling Mon­e­tary Aggre­gates. F. E. Mor­ris. Nan­tuck­et Island, The Fed­er­al Reserve Bank of Boston: 65–77.

Ire­land, P. N. (2011). “A New Key­ne­sian Per­spec­tive on the Great Reces­sion.” Jour­nal of Mon­ey, Cred­it, and Bank­ing
43(1): 31–54.

John­son, T. G. (1993). The Dynam­ics of Input-Out­put Intro­duc­tion. Micro­com­put­er-based input-out­put mod­el­ing: Appli­ca­tions to eco­nom­ic devel­op­ment. D. M. Otto and T. G. John­son, Boul­der and Oxford:

West­view Press: 216–228.

Jor­gen­son, D. W. (1960). “A Dual Sta­bil­i­ty The­o­rem.” Econo­met­ri­ca
28(4): 892–899.

Jor­gen­son, D. W. (1960). “Growth and Fluc­tu­a­tions: A Causal Inter­pre­ta­tion.” THE QUARTERLY JOURNAL OF ECONOMICS
74(3): 416–436.

Jor­gen­son, D. W. (1961). “Sta­bil­i­ty of a Dynam­ic Input-Out­put Sys­tem.” The Review of Eco­nom­ic Stud­ies
28(2): 105–116.

Jor­gen­son, D. W. (1961). “The Struc­ture of Mul­ti-Sec­tor Dynam­ic Mod­els.” Inter­na­tion­al Eco­nom­ic Review
2(3): 276–293.

Keen, S. (1995). “Finance and Eco­nom­ic Break­down: Mod­el­ing Min­sky’s ‘Finan­cial Insta­bil­i­ty Hypoth­e­sis.’ ” Jour­nal of Post Key­ne­sian Eco­nom­ics
17(4): 607–635.

Keen, S. (2000). “The Non­lin­ear Eco­nom­ics of Debt Defla­tion”. In Com­merce, com­plex­i­ty, and evo­lu­tion: Top­ics in eco­nom­ics, finance, mar­ket­ing, and man­age­ment: Pro­ceed­ings of the Twelfth Inter­na­tion­al Sym­po­sium in Eco­nom­ic The­o­ry and Econo­met­rics. W. A. Bar­nett. New York, Cam­bridge Uni­ver­si­ty Press: 83–110.

Keen, S. (2006). Steve Keen’s Month­ly Debt Report Novem­ber 2006 “The Reces­sion We Can’t Avoid?”. Steve Keen’s Debt­watch. Syd­ney. 1: 21.

Keen, S. (2006b). The Need and Some Meth­ods for Dynam­ic Mod­el­ling in Post Key­ne­sian Eco­nom­ics. Com­plex­i­ty, Endoge­nous Mon­ey and Macro­eco­nom­ic The­o­ry: Essays in Hon­our of Basil J. Moore. M. Set­ter­field, Chel­tenham, U.K. and Northamp­ton, Mass: Elgar: 36–59.

Keen, S. (2007). Debt­watch. Steve Keen’s Debt­watch. www.debtdeflation.com/blogs.

Keen, S. (2007b). Deep­er in Debt: Aus­trali­a’s addic­tion to bor­rowed mon­ey. Occa­sion­al Papers, Cen­tre for Pol­i­cy Devel­op­ment.

Keen, S. (2008). Key­nes’s ‘revolv­ing fund of finance’ and trans­ac­tions in the cir­cuit. Keynes and Macro­eco­nom­ics after 70 Years. R. Wray and M. Forstater. Chel­tenham, Edward Elgar: 259–278.

Keen, S. (2009). The dynam­ics of the mon­e­tary cir­cuit. The Polit­i­cal Econ­o­my of Mon­e­tary Cir­cuits: Tra­di­tion and Change. S. Rossi and J.-F. Pon­sot. Lon­don, Pal­grave Macmil­lan: 161–187.

Keen, S. (2010). “Solv­ing the Para­dox of Mon­e­tary Prof­its.” Eco­nom­ics: The Open-Access, Open Assess­ment E‑Journal 4 (2010–31).

Keen, S. (2011). “A mon­e­tary Min­sky mod­el of the Great Mod­er­a­tion and the Great Reces­sion.” Jour­nal of Eco­nom­ic Behav­ior & Orga­ni­za­tion In Press, Cor­rect­ed Proof.

Keen, S. (2011b). Debunk­ing eco­nom­ics: The naked emper­or dethroned? Lon­don, Zed Books.

Keen, S. and R. Stan­dish (2006). “Prof­it max­i­miza­tion, indus­try struc­ture, and com­pe­ti­tion: A cri­tique of neo­clas­si­cal the­o­ry.” Phys­i­ca A: Sta­tis­ti­cal Mechan­ics and its Appli­ca­tions 370(1): 81–85.

Keen, S. and R. Stan­dish (2010). “Debunk­ing the the­o­ry of the firm—a chronol­o­gy.” Real World Eco­nom­ics Review 54(54): 56–94.

Keynes, J. M. (1936). The gen­er­al the­o­ry of employ­ment, inter­est and mon­ey. Lon­don, Macmil­lan.

Keynes, J. M. (1937). “The Gen­er­al The­o­ry of Employ­ment.” The Quar­ter­ly Jour­nal of Eco­nom­ics
51(2): 209–223.

Kir­man, A. (1989). “The Intrin­sic Lim­its of Mod­ern Eco­nom­ic The­o­ry: The Emper­or Has No Clothes.” Eco­nom­ic Jour­nal
99(395): 126–139.

Kir­man, A. P. (1992). “Whom or What Does the Rep­re­sen­ta­tive Indi­vid­ual Rep­re­sent?” The Jour­nal of Eco­nom­ic Per­spec­tives
6(2): 117–136.

Kuznets, S. (1930). “Sta­t­ic and Dynam­ic Eco­nom­ics.” The Amer­i­can Eco­nom­ic Review 20(3): 426–441.

Kyd­land, F. E. and E. C. Prescott (1982). “Time to Build and Aggre­gate Fluc­tu­a­tions.” Econo­met­ri­ca 50(6): 1345–1370.

Kyd­land, F. E. and E. C. Prescott (1990). “Busi­ness Cycles: Real Facts and a Mon­e­tary Myth.” Fed­er­al Reserve Bank of Min­neapo­lis Quar­ter­ly Review
14(2): 3–18.

Lee, F. S. (1998). Post Key­ne­sian price the­o­ry. Cam­bridge, Cam­bridge Uni­ver­si­ty Press.

Lucas, R. E., Jr. (1972). Econo­met­ric Test­ing of the Nat­ur­al Rate Hypoth­e­sis. The Econo­met­rics of Price Deter­mi­na­tion Con­fer­ence, Octo­ber 30–31 1970. O. Eck­stein. Wash­ing­ton, D.C., Board of Gov­er­nors of the Fed­er­al Reserve Sys­tem and Social Sci­ence Research Coun­cil: 50–59.

Min­sky, H. (1993). “On the Non-neu­tral­i­ty of Mon­ey.” Fed­er­al Reserve Bank of New York Quar­ter­ly Review
18(1): 77–82.

Min­sky, H. P. (1975). John May­nard Keynes. New York, Colum­bia Uni­ver­si­ty Press.

Min­sky, H. P. (1977). “The Finan­cial Insta­bil­i­ty Hypoth­e­sis: An Inter­pre­ta­tion of Keynes and an Alter­na­tive to ‘Stan­dard’ The­o­ry.” Nebras­ka Jour­nal of Eco­nom­ics and Busi­ness
16(1): 5–16.

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.

Moore, B. J. (1988). “The Endoge­nous Mon­ey Sup­ply.” Jour­nal of Post Key­ne­sian Eco­nom­ics
10(3): 372–385.

NBER. (2011). “US Busi­ness Cycle Expan­sions and Con­trac­tions.” from http://www.nber.org/cycles/cyclesmain.html.

New York Times (2007). BNP Paribas sus­pends funds because of sub­prime prob­lems. New York Times. New York, New York Times.

Robert­son, D. H., P. Sraf­fa, et al. (1930). “Increas­ing Returns and the Rep­re­sen­ta­tive Firm.” The Eco­nom­ic Jour­nal
40(157): 79–116.

Schum­peter, J. (1927). “The Expla­na­tion of the Busi­ness Cycle.” Eco­nom­i­ca(21): 286–311.

Schum­peter, J. A. (1934). The the­o­ry of eco­nom­ic devel­op­ment : an inquiry into prof­its, cap­i­tal, cred­it, inter­est and the busi­ness cycle. Cam­bridge, Mass­a­chu­setts, Har­vard Uni­ver­si­ty Press.

Shafer, W. and H. Son­nen­schein (1993). Mar­ket demand and excess demand func­tions. Hand­book of Math­e­mat­i­cal Eco­nom­ics. K. J. Arrow and M. D. Intrili­ga­tor, Else­vi­er. 2: 671–693.

Solow, R. M. (2001). “From Neo­clas­si­cal Growth The­o­ry to New Clas­si­cal Macro­eco­nom­ics.” In Advances in Macro­eco­nom­ic The­o­ry. J. H. Drèze (ed.), New York, Pal­grave.

Solow, R. M. (2003). “Dumb and Dumb­er in Macro­eco­nom­ics”. Festschrift for Joe Stiglitz. Colum­bia Uni­ver­si­ty.

Solow, R. (2008). “The State of Macro­eco­nom­ics.” The Jour­nal of Eco­nom­ic Per­spec­tives
22(1): 243–246.

Son­nen­schein, H. (1972). “Mar­ket Excess Demand Func­tions.” Econo­met­ri­ca
40(3): 549–563.

Son­nen­schein, H. (1973). “Do Wal­ras’ Iden­ti­ty and Con­ti­nu­ity Char­ac­ter­ize the Class of Com­mu­ni­ty Excess Demand Func­tions?” Jour­nal of Eco­nom­ic The­o­ry
6(4): 345–354.

Sraf­fa, P. (1926). “The Laws of Returns under Com­pet­i­tive Con­di­tions.” The Eco­nom­ic Jour­nal
36(144): 535–550.


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 Peter Humphreys of the UWS School of Account­ing (and pre­vi­ous­ly Man­ag­er in the Group Account­ing Research and Pol­i­cy Sec­tion of the Com­mon­wealth Bank of Aus­tralia) for advice on bank­ing prac­tice.

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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.