Ponzi Maths–Part 1

Flattr this!

This is an unplanned post that partly pre-empts what I’ll be writ­ing in the Feb­ru­ary Debt­watch Report, where I will explain in full my the­ory of money cre­ation in a pure credit econ­omy. So this is some­what out of sequence, and will undoubt­edly be badly explained com­pared to what I put together for Feb­ru­ary. 

I will also have to fin­ish this in a later post–probably in the first cou­ple of days of the New Year–because Sydney’s fire­works beckon, and we have to be on board the cruiser we’re watch­ing them from at 7pm.  But what is here is part of a long-promised expla­na­tion of my model of money cre­ation. In a cou­ple of days I’ll pub­lish the punch line, which is a newly devel­oped model of a Ponzi Scheme.

To begin at the begin­ning: in the last year, I have devel­oped a method of build­ing dynamic mod­els of finan­cial processes using a table lay­out that is closely related to the account­ing method­ol­ogy of “dou­ble-entry book-keep­ing”. The table rep­re­sents the flows in and out of bank accounts:

Type Asset (1)  Liability(-1)
Account Loans or Reserves Deposit Accounts
Activ­ity Flow in/out Flow in/out

As I illus­trate below, a dynamic model of a finan­cial sys­tem can eas­ily be derived from this basic schema, since each row rep­re­sents a spe­cific rela­tion­ship between accounts, and the entries in a col­umn rep­re­sent all the action for that account. Sim­ply add up the entries in each col­umn, and you have a sys­tem (of dif­fer­en­tial equa­tions) that rep­re­sents the rel­e­vant model of the finan­cial sys­tem.

I orig­i­nally devel­oped this as a means to com­mu­ni­cate my dynamic mod­el­ling to other econ­o­mists, since the vast major­ity of them have never stud­ied dif­fer­en­tial equations–let alone sys­tems dynam­ics. When I pre­sented a model as a sys­tem of ODEs (“Ordi­nary Dif­fer­en­tial Equa­tions”), they fre­quently failed to grasp the logic–and col­leagues who are sys­tems engi­neers, such as Trond Andresen or Mike Radz­icki, found a sim­i­lar response to their sophis­ti­cated flow­chart mod­els. Econ­o­mists, even non-ortho­dox ones, sim­ply aren’t accus­tomed to think­ing dynam­i­cally, and nor­mally lack any expo­sure to the sophis­ti­cated tools that engi­neers in par­tic­u­lar use rou­tinely today.

This applied in spades when I first pre­sented my model of the endoge­nous cre­ation of money to the bi-annual Post Key­ne­sian Eco­nom­ics Con­fer­ence in Kansas City in 2006. A room packed with about 100 con­fer­ence par­tic­i­pants broke out in a vig­or­ous debate, with many crit­i­cis­ing my analy­sis because “You must have made mis­takes in your dou­ble-entry book-keep­ing.” 

I knew the model was accu­rate, so the thought occurred to me that, if so, it should be pos­si­ble to present the model in dou­ble-entry book-keep­ing for­mat. Sure enough, when I pre­sented exactly the same model to the Soci­ety of Het­ero­dox Econ­o­mists con­fer­ence later that year (with sev­eral peo­ple from the pre­vi­ous con­fer­ence in atten­dance), the reac­tion was far bet­ter.

One per­son even com­mented that he was a bit dis­ap­pointed because my pre­sen­ta­tion was less math­e­mat­i­cal than usual! I then informed him that he’d actu­ally seen a pre­sen­ta­tion involv­ing a six-dimen­sional dynamic sys­tem.

Since then, I have found that this method was not merely a pre­sen­ta­tion tool, but also a very use­ful devel­op­ment tool for build­ing dynamic sys­tems. I’ve built mod­els of non-bank lend­ing, a credit crunch, etc., all of which will turn up in (non-neo­clas­si­cal!) eco­nom­ics jour­nals at some stage, and in my forth­com­ing books.

Since Bernie Madoff’s spec­tac­u­lar col­lapse, I’ve wanted to add an exten­sion to model Ponzi finance, and at 11.30am Syd­ney time on Decem­ber 30th, I’ve cracked the basic math­e­mat­ics of a Ponzi Scheme. I can’t resist post­ing (part of!) this before the New Year, as a “Happy New Year” present to my loyal band of blog­gers.

But first things first: the math­e­mat­ics of an absolutely min­i­mal­ist pure credit econ­omy. In Feb­ru­ary I’ll explain why I believe that the endoge­nous expan­sion of credit money–and not the “money multiplier”–is the key dri­ver still today in the growth of the finan­cial sys­tem (and also why I dif­fer from Aus­tri­ans like Peter Schiff in my analy­sis of the econ­omy, and how it might be reformed to avoid asset bub­bles in future). For now, just take this on board as a thought exper­i­ment: IF there was no Cen­tral Bank, and no Gov­ern­ment, how would money be cre­ated in a pure credit econ­omy?

The answer, in a nut­shell, is “by the bank­ing sys­tem cre­at­ing match­ing deposits when it issues loans”. In this model, loans by the banks cre­ate deposits, which then finance eco­nomic activ­ity. Eco­nomic activ­ity con­sists of firms that own fac­to­ries hir­ing work­ers to work in them to pro­duce goods for sale, using bor­rowed money to finance their wage pay­ments (and their own con­sump­tion and inter-firm pur­chases as well), and banks mak­ing prof­its on the spread between loan and deposit rates of inter­est.

The basic mechan­ics of this sys­tem, which can func­tion indef­i­nitely at a con­stant level of pro­duc­tion with a sin­gle loan injec­tion, are shown in the fol­low­ing table, which has 4 accounts: a Firm Sec­tor Loan, Firm Sec­tor Deposit, Bank Sec­tor Deposit (strictly the Banksector’s  profit and loss account), and Work­ers Deposit.

For now I’ll use a sim­ple cap­i­tal let­ter to indi­cate each flow–in every case this will be replaced by some appro­pri­ate prod­uct (for exam­ple, “A” below will be replaced by the inter­est rate on loans times the cur­rent out­stand­ing loan bal­ance for the firm sec­tor).

The six processes in this model are:

  1. Inter­est accrues on the out­stand­ing loan at the rate +A;
  2. The bank pays the firm inter­est on the bal­ance in its deposit account by a trans­fer B from its deposit account to the firm’s deposit account;
  3. The firm sec­tor trans­fers the sum C from its deposit account to the bank’s deposit account to pay the inter­est on the out­stand­ing debt. The bank is then obliged to record that the out­stand­ing debt has been reduced by that amount–hence the –C entry in the Firm Loan account;
  4. The firm hire work­ers to pro­duce output–a flow D goes from the Firm’s Account to the Work­ers’;
  5. The bank is obliged to pay inter­est to the work­ers on the bal­ance in their accounts; the flow E goes from the bank’s deposit account to the work­ers;
  6. Finally, the bank and the work­ers con­sume some of the out­put of the firm sec­tor and pay for this with trans­fers from their accounts of F and G.







Firm Loan (FL)

Firm Deposit (FD)

Bank Deposit (BD)

Worker Deposit (WD)

Inter­est on Loan





Inter­est on Deposit





Pay Inter­est on Loan





Pay Wages





Inter­est on Deposit     –E +E






This sim­ple sys­tem describes a self-sus­tain­ing econ­omy which could func­tion indef­i­nitely at a con­stant level.  Sim­u­lat­ing this sys­tem with equi­lib­rium val­ues yields a model in which bank accounts remain at a con­stant level and finance a con­stant level of income for all classes over time. The first graph below indi­cates the equi­lib­rium val­ues of bank accounts, and the sec­ond shows the equi­lib­rium annual incomes that result (I don’t want to scare off non-math­e­mat­i­cal read­ers with math­e­mat­i­cal sym­bols right now, so any­one who wants to see what A to G are, please scroll to the bot­tom of this blog entry). 

Notice that incomes are sub­stan­tially greater than the size of the ini­tial loan. A lot of peo­ple who have attempted to build a mon­e­tary model have made the mis­take of believ­ing that the spend­ing the loan can finance is iden­ti­cal to the amount of the loan itself. This ignores the fact that the loan finances a turnover of eco­nomic activity–in effect, it ignores what econ­o­mists call the veloc­ity of cir­cu­la­tion. The inter­est bill is also effec­tively paid out of the “small change” from the prof­its cap­i­tal­ists make–whereas a lot of ana­lysts have pre­sumed that the inter­est couldn’t be paid at all. I’ll go into what was wrong with that per­spec­tive in more detail in the Feb­ru­ary Debt­watch Report; for now take it from me–and from the simulations–that pay­ing inter­est on debt is a breeze for cap­i­tal­ists in a pro­duc­tive econ­omy in which there is no unpro­duc­tive debt.

The impact of unpro­duc­tive debt–money bor­rowed sim­ply to spec­u­late on ris­ing asset prices–is the focus of this post, but unfor­tu­nately time has got away from me and I have to get off the blog and on to the boat.

Thanks to all read­ers, and espe­cially to the blog par­tic­i­pants. Most peo­ple will fin­ish 2008 in a state of absolute bewil­der­ment. Mem­bers of the debt­de­fla­tion blog will only feel that way tonight if they overdo the alco­hol con­sump­tion!

So here’s a toast to you all. Happy New Year, and I look for­ward to cor­re­spond­ing with you all in 2009.

Steve Keen 


Flow Let­ter Sym­bolic Value Expla­na­tion
 A  rL × FL  Loan inter­est rate times out­stand­ing loan
 B  rD × FD  Deposit inter­est rate times deposit bal
 C  rL × FL  Loan inter­est rate times out­stand­ing loa
 (1-s)/tF  Work­ers share of sur­plus divided by time lag in pro­duc­tion
 E  rD × WD   Deposit inter­est rate times deposit bal­ance
 F  BD/tB  Account bal­ance divided by time lag in con­sump­tion
 G WD/tW   Account bal­ance divided by time lag in con­sump­tion



Parameter Values

These are just for illus­tra­tive purposes–they are not derived from any fit with empir­i­cal data–but they are rea­son­able val­ues nonethe­less for this toy mon­e­tary econ­omy model.

Para­me­ter Mean­ing Value
rL Inter­est rate on loans 5%
rD Inter­est rate on deposits 1%
s Cap­i­tal­ists share of sur­plus from pro­duc­tion 33%
tF Delay between financ­ing pro­duc­tion and sell­ing out­put 2 months=1/6th Year
tB Con­sump­tion time lag for bankers 1 year
tW Con­sump­tion time lag for work­ers 2 weeks=1/26th Year

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.
Bookmark the permalink.
  • Effit

    Hi Steve
    Hope you enjoyed your river cruise and the fire­works. The fire­works looked won­der­ful on TV – yes, a ter­ri­ble waste of money, but bring joy to many.

    I’ve read your Ponzi Maths 1 a cou­ple of times…Phew…not sure if some­one like me with Grade 3 Arith­metic and a poor grasp of Eco­nom­ics 101 will ever catch on. I think I get the gist of it, but I may have to read it again and again.

  • tom­myt

    Hi Steve, thanks for your greet­ings. I could not resisit send­ing you in a new ‘brick­bats’ post from …yes Craig James, per­haps he is a nos­tradamus fig­ure, any­way in today’s ‘smh’,finance section,page 27,”…fear of reces­sion wiped 43% from the mar­ket, or 2699points…it closed at 3722­points…” later in the piece Mt Craig is quoted “Mr James was opti­mistic about the mar­ket reach­ing 4700 points by the end of the year.” We shall see, we shall see!

  • Bull­turned­bear

    Good model Steve. I think the steady state model is a good model for Mankind.

    The prob­lem is that one can’t take Mankind out of the model. The psy­chol­ogy of mankind has dic­tated that when peo­ple are feel­ing bull­ish the trend is for growth and risk ris­ing over time. In his­tory this has been the pre­dom­i­nant trend by far. Once that goes too far though peo­ple switch to risk aver­sion and go the other way. Regard­less of Gov­ern­ment inter­ven­tion or “rules”, when Mankind is bull­ish they seem to ignore the “rules” and risk and growth take over. 

    I know you believe this too as I have read what you have writ­ten on Min­sky in the past.

    There­fore, I believe at present that sys­tems and mod­els can some­times be good at pre­dict­ing or explain­ing out­comes but not so good at caus­ing out­comes. I get excited when you talk about solu­tions to the prob­lems. But I get scep­ti­cal when I read the solu­tions pre­sented by your­self and oth­ers.

    Mankind and his­tory seem to keep repeat­ing them­selves.

    An exam­ple of this may be the belief that a gold stan­dard would pre­vent a bub­ble. If Mankind wanted an invest­ment and debt boom, “to get more done”. They would either invent a new way to cre­ate debt within a gold stan­dard. Or they would con­vince the politi­cians to scrap the stan­dard. When Mankind becomes bull­ish, we find a way to run with the bulls. The older the bull mar­ket gets the more crazy it becomes. The bull mar­ket that fin­ished in 2007 was very very old.

  • Bull­turned­bear

    Hi Tom­myt,

    If Craig James was true to him­self and his read­ers. He should have pub­lished his pre­dic­tion for the mar­ket at the end of 2008 that was made in 2007. I checked back. Not that hard to find. A table was pub­lished in the Aus­tralian around the same time a year ago.

    Craig James pre­dicted 7550 for the ASX and 15400 for the DOW. Not bad Craig! Only out by a bit. At the time of Craig’s pred­i­tion the ASX was at 6423. Craig pre­dicted a rise of 1127 (17.5%. This time he is pre­dict­ing a rise of 978 (26.3%). Craig James is the eter­nal bull. I can’t wait to see his pre­dic­tion next year. 

    I think the ASX will be in the mid to low 1000s by the end of next year. When the point of recog­ni­tion takes over in Aus­tralia, I’m keen to see if Craig James changes to being a bear. 

    When Craig and his crew become bear­ish the mar­ket will be approach­ing a major bot­tom. That’s my pre­dic­tion.

  • It’s not a steady-state model Bull­turned­bear; while it describes one (and shows that it is fea­si­ble at least at the level of finance), it’s just a pre­lude to a model includ­ing growth, finan­cial insta­bil­ity, and all the other sig­nif­i­cant para­pher­na­lia of the real econ­omy. I’m still work­ing on Parts 2 and 3–they should turn up in the next cou­ple of days.

  • Excel­lent. It would be great if some­one (not me–I don’t have the time I’m afraid!) put together a table show­ing the key pre­dic­tions of these char­ac­ters ver­sus the out­comes over time.

  • Hoss

    Jim Cramer’s pre­dic­tions for 2008:

    What fol­lows are my top-ten finan­cial pre­dic­tions for 2008—some mor­tal locks, oth­ers long shots, in that order.

    1. Gold­man Sachs makes more money than every other bro­ker­age firm in New York com­bined and fin­ishes the year at $300 a share. Not a prediction—an inevitabil­ity. In fact, it’s only Jan­u­ary, and I think it’s already come true.

    2. Oil goes much higher, maybe as much as $125 a bar­rel. That sends gaso­line to $5 a gal­lon, even at those ter­rific ser­vice sta­tions out­side the Hol­land Tun­nel. Pun­dits keep blam­ing the end­less rise on geopol­i­tics, but in the lat­ter half of 2007, we saw reduced ten­sion in Iraq, Iran, and Venezuela, plus flat-out pro­duc­tion by the Saudis and the Rus­sians, and all that hap­pened is the price went from the $70s to the $90s. We are run­ning out of oil more quickly than peo­ple can imag­ine, and that means great returns for oil com­pa­nies. Just buy the stock of the com­pany you filled up at today or buy a driller (Transocean’s my favorite), then sit back and make money. The odds oil will rise? Two to 1. The $125-per-bar­rel tar­get might be push­ing it, but higher oil is pretty much a sure thing.

    3. The Fed arranges an Ara­bic Heim­lich maneu­ver on Cit­i­group, so the bank­ing giant doesn’t choke on the worst mort­gage port­fo­lio in the coun­try. Rather than face the demise of the biggest U.S. bank, and the panic its fall could trig­ger, Con­gress looks the other way as Arab investors buy 51 per­cent of the som­nam­bu­lant bank. Unfor­tu­nately for Cit­i­group, I’d lay 3 to 1 on this hap­pen­ing. I say “unfor­tu­nately,” but I shouldn’t. It’s unfor­tu­nate that a proud insti­tu­tion basi­cally has to give up its auton­omy, but its stock would go up con­sid­er­ably once it got that cap­i­tal.

    4. Ver­i­zon becomes your cable provider. In one of the most remark­able frog-to-prince trans­for­ma­tions I’ve seen, Ver­i­zon CEO Ivan Sei­den­berg offers an alter­na­tive, Fios, that is bet­ter and cheaper than any­thing Time Warner, Cable­vi­sion, or Com­cast can pro­duce. Throw in Verizon’s grow­ing cell-phone busi­ness and growth accel­er­ates dra­mat­i­cally, mak­ing VZ the best-per­form­ing stock in the Dow Jones aver­ages. Time Warner and Com­cast hit new lows, and the retreat of cable begins. Sorry, cable guys: We’re look­ing at 4 to 1 here.

    5. In the first real deba­cle of the pri­vate-equity era, Cer­berus Cap­i­tal Man­age­ment, the quiet hedge-fund king, fails in its bid to resus­ci­tate Chrysler—not a sur­pris­ing turn, given that it picked Bob “I ruined Home Depot and all I got was $200 mil­lion” Nardelli to run the country’s worst car com­pany. The com­bi­na­tion of Chrysler and the 51 per­cent of GM’s lousy mort­gage busi­ness that it paid top dol­lar for forces for­mer Trea­sury sec­re­tary John Snow to seek a bailout for Cer­berus. Amaz­ingly, given the love of hedge-fund con­tri­bu­tions by both par­ties, Con­gress agrees and writes checks for bil­lions to save Cer­berus’ wealthy investors. Call the Chrysler fail­ure a lock. The bailout? I’d say 5 to 1.

    6. Google con­tin­ues its dom­i­nance and becomes one of the top three com­pa­nies in the U.S. in mar­ket cap­i­tal­iza­tion. It dou­bles its adver­tis­ing share, at the expense of tele­vi­sion and print. It also suc­cess­fully chal­lenges Microsoft for oper­at­ing-sys­tem dom­i­nance. Microsoft calls for a gov­ern­ment inves­ti­ga­tion of Google’s power, but no one cares because Microsoft is just too hated for any­one in Wash­ing­ton to cham­pion. The stock roars to $1,000. I like Google enough to put this one at 7 to 1. If you use an $800 tar­get, make it 5 to 2.

    7. Euro­pean com­pa­nies, eye­ing the weak dol­lar, snap up New York real estate, and offer to buy Mer­rill Lynch and JPMor­gan. John Thain and Jamie Dimon, the com­pa­nies’ respec­tive CEOs, agree to the bids (Thain sold a chunk of stock to a for­eign entity just last week). Col­gate, Clorox, Whirlpool, and Black & Decker get snapped up, too. All six com­pa­nies’ stock prices head north. Lots of mov­ing parts, but let’s put the odds of at least one of these deals hap­pen­ing at 3 to 1. A per­fect Pick Six pays 50 to 1.

    8. Apple com­pletes its dom­i­nance of the music busi­ness, as the music pro­duc­ers decide no longer to pro­duce new CDs. It’s just too expen­sive for them. Warner Music Group files for bank­ruptcy. Apple goes to $300. Okay, these may not be 2008 events, but they will hap­pen, sooner rather than later. This year: 25 to 1. Next year: 5 to 1.

    9. The New York Times, after spend­ing sev­eral hun­dred mil­lion dol­lars buy­ing back its stock while it was in the $30s and $40s, slashes its div­i­dend in half because of a cash short­age. The stock drops to $10. To save the world’s great­est news­pa­per, the com­pany accepts a buy­out offer from Mayor Michael Bloomberg at $20 a share. Don’t be so quick to scoff: The cash is spare change for Bloomberg, who, don’t for­get, already owns a small media com­pany. I’d say the $10 share price is even money. That’s how bad it is at the Times. The Bloomberg buy­out is prob­a­bly a 100-to-1 shot, but may be less if he decides not to run for pres­i­dent and needs some­thing else to do this year.

    10. An Army of the Fore­closed marches on the White House, then launches a siege at the Fed­eral Reserve, before camp­ing out in front of the Wash­ing­ton Mon­u­ment. The army demands relief from evic­tion. Bernanke, rec­og­niz­ing that he did noth­ing to reg­u­late the mort­gage mess in 2006 and then did not cut rates fast enough in ’07, resigns. The siege ends, the new guy slashes rates, and the mar­ket takes off. Here, the odds are 1,000 to 1 (as Marx taught us, peo­ple have a hard time los­ing their chains). But if Bernanke or a future Fed chair does cut rates mean­ing­fully, here’s a sure bet: That’s the time to start buy­ing.

    Can’t wait for the 2009 pre­dic­tions.

  • Zulu

    Good start­ing point Steve, I look for­ward to the rest of your blog. I’ve been read­ing your blogs for over a year now, but this is my first post.

    They tried to teach me Eco­nom­ics at Uni, I under­stood what they were say­ing but I could never see how it would work. Now that I’ve found your web­site (& I’m older and don’t trust every­thing I’m told even by pro­fes­sors etc.) Now I under­stand why! They were wrong! You are one of the few who actu­ally makes sense to me.

    As some­one who’s worked pri­mar­ily as an engi­neer I’m amazed to read that most econ­o­mists can’t under­stand things like dif­fer­en­tial equa­tions & sys­tem dynam­ics!! You can’t pos­si­bly under­stand the finan­cial sys­tem, or sim­i­lar com­plex sys­tems if you do not know how to make a real­is­tic model.

  • Hoss


    You might be inter­ested in this about your col­leagues in Amer­ica.


  • clive

    This is Michael Pascoe’s pre­dic­tions DEC 19 2007
    “The US reces­sion is a bit like reli­gion and global warm­ing – peo­ple don’t really believe”


    And this one on DEC 12 2007

    I must keep a look out for his 2009 pre­dic­tions. I won­der what brand of crys­tal ball he’s using?

  • clive

    Shane Oliver on 2009

    The All Ordi­nar­ies index plunged as much as 53 per cent last year from its high in Novem­ber 2007.

    AMP Cap­i­tal Investors chief econ­o­mist Shane Oliver says the share­mar­ket could remain volatile in the early part of 2009.

    But he believes the mar­ket could rise more than 25 per cent this year.

    It’s also quite con­ceiv­able that we’ll might see more lows in the mar­ket ear­lier in the year but I think as the year pro­gresses the share­mar­ket will start to get on to a sus­tain­able upswing,” he said.

    My view is that global growth and Aus­tralian growth should start to look a bit health­ier through the sec­ond half of the year and going in to 2010.“‘

    With over a bil­lion of peo­ples money locked up for a year, you would be hop­ing 2009 was bet­ter… wouldn’t you?


  • Hello Steve,

    I notice that D (wages) has evolved since your older papers. In the older ones it was a frac­tion of firms deposits here you use the (1-s)/tF for­mu­la­tion.

    For con­sump­tion you use frac­tions of deposits mul­ti­plied by 1/tB and 1/tW respec­tively for bank and work­ers con­sump­tion.

    I am not famil­iar with this for­mu­la­tion for con­sump­tion and wages can you expand a lit­tle bit how one comes to these? is this stan­dard in the lit­er­a­ture? Is there a text­book entry on these and what they rep­re­sent?


  • Hi mar­cf999,

    Thanks for pay­ing that post such close atten­tion!

    Noth­ing I do is stan­dard in the eco­nom­ics lit­er­a­ture, unfortunately–I’m try­ing to influ­ence them to get them to take up a strictly dynamic approach to mod­el­ling, but that will take a very long time. But the for­mu­la­tion is stan­dard in sys­tems engi­neer­ing lit­er­a­ture, where a time lag is rep­re­sented as one over the frac­tion of the time period over which it occurs.

    Thus if the rate of flow of water out of a lake is such that, if there were no flow into it and this rate kept up lin­early, it would empty in 3 months, the time lag is given as 1/4 of a year and the expres­sion would be d/dt Lev­el­OfLake = –1/(1/4) * Lev­el­OfLake.

    This gen­er­ates an expo­nen­tial decay in the level of the lake–not a lin­ear one–which describes most processes of that nature.

    The actual terms are “stan­dard” in a way, but the prac­ti­tion­ers on those areas have for­got­ten them. “s” is the term Marx used for the rate of sur­plus value’ I’ve cheated here a bit by using the same term to describe the share of the sur­plus gen­er­ated in pro­duc­tion that goes to cap­i­tal­ists (so that the share [1-s] goes to work­ers). Marx also spent con­sid­er­able time talk­ing about the pro­duc­tion period of capitalism–the time between fork­ing out the M and get­ting the M+, in his bril­liant expla­na­tion of why Say’s Law doesn’t apply in a cap­i­tal­ist econ­omy.

    This can be expressed as a time lag–which is how I’ve used the tau_F in that paper–between the start of a process (hir­ing work­ers effec­tively) and the end of it (receiv­ing rev­enue from the sale of the com­modi­ties the work­ers pro­duced).

    In equilibrium–and only in equilibrium–this flow to cap­i­tal­ists (s/tau_F) equals P*Q — Wages. At other times it will be greater (if out­put is expand­ing) or less (v.v.). See the paper “Not Keen on Bailouts” on the Research page for a table that illus­trates these dynam­ics in the con­text of a credit crunch (but with­out the Ponzi com­po­nent of that paper).