Conservation laws, financial entropy and the Eurozone crisis

0.41 MB·English

by  Paul Cockshott

Conservation laws, financial entropy and the Eurozone crisis
Paul Cockshott and David Zachariah∗
January 28, 2013
3
Abstract
1 2.1 Profit rate constraints . . . . . . . . 10
0 2.2 Resource constraints . . . . . . . . . 12
2 The report attempts of apply econophysics con- 2.3 Emission constraints . . . . . . . . . 12

n ceptstotheEurozonecrisis. Itstartsbyexamining 2.4 Contradictions of exponential accu-
a the idea of conservation laws as applied to mar- mulation . . . . . . . . . . . . . . . . 13
J
keteconomies. Itformulatesa measureoffinancial

5 entropyand givesnumericalsimulations indicating 3 Contradictions between laws of mar-
2
that this tends to rise. We discuss an analogue ket exchange and capital accumula-

for free energy released during this process. The tion 14
]
N conceptsofrealandsymbolicappropriationarein- 3.1 Value conservation and the signa-
G troduced as a means to analyse debt and taxation. ture of capital . . . . . . . . . . . . . 14
. We then examine the conflict between the con- 3.2 Formation of interest . . . . . . . . . 17
n
servation laws that apply to commodity exchange 3.3 Dynamics of sector balances . . . . . 19
i
f with the exponential growthimplied by capital ac-
-
q cumulation and how these have necessitated a se- 4 The crisis in the Eurozone 19
[ quence of evolutionaryforms for money, and go on 4.1 Greek debt . . . . . . . . . . . . . . 22

to presentasimple stochasticmodelfor the forma- 4.2 The Stability Pact . . . . . . . . . . 22
1
v tion of rates of interest and a model for the time 4.2.1 Household sector . . . . . . . 23
4 evolution of the rate of profit. 4.2.2 Nonfinancial companies . . . 23
7 Finally we apply the conservation law model to 4.2.3 Financial companies . . . . . 24
9 examining the Euro Crisis and the European Sta- 4.2.4 Rest of the world . . . . . . . 24
5
bility pact, arguingthat if the laws we hypothesise 4.3 Conclusion on the Stability Pact . . 24
.
1
actually hold, then the goals of the stability pact
0
are unobtainable.
3 1 Conservation laws in mar-
1
ket exchange
:
v Contents
i
X In the physical sciences conservation laws provide
r 1 Conservationlawsinmarketexchange 1 a basic framework within which theories are cast.
a 1.1 Finance and conservation laws . . . 3 Theyaresofundamentalthatitishardtoconceive
1.2 The phase space of finance. . . . . . 3 ofanymathematicallyexpressedsystemofmechan-
1.3 Tendancy of financial entropy to rise 5 ics that does not rest on such laws.
1.4 Relation to the productive economy 6 Do similar laws exist in economic theory?
1.5 Contradiction between real and for- Inasenseyes,wheretheyaretermed‘accounting
mal appropriation of value . . . . . . 9 identities’ and regarded as something pretty triv-
ial. We want to argue that this view of them as
2 Nonconservation laws of capital accu- something trivial is misplaced, and that they can
mulation 10 actuallytellusalotmoreaboutthenatureofsocial
∗E-mail: [email protected] and relations and their degree of constrainedness than
[email protected] is generally realised.
1
Marx, to an extent greater than is sometimes 1 coat = 20 yards of linen or 1 coat is worth 20
recognised,wantedtoestablishatheoryofthecap- yards of linen.
italist economy informed by the laws of physics.
He then presents what he calls the expanded form
[3, ch. 2] This comes across in several ways: his
of the relation
avowed aim to write a book on the ‘laws of mo-
20 yards of linen = 1 coat
tion’ofcapitalism;hisdistinctionbetweenthecon-
20 yards of linen = 10 lbs of tea, etc.
ceptoflabourandlabourpower;hispresentationof
And goes on from this to state that 1 coat will
valueasthecrystalisationofhumanenergy;andhis
beequalto10lbstea. Whatheisdoinghereisset-
analysis of commodity exchange as an equivalence
tingoutwhatinmodernmathematicalterminology
relation.
is an equivalence relation. For some relational op-
Marx said that in Capital he was investigating
erator+wesaythat+ isanequivalence relationif
the ‘laws of motion’ of capitalism. This might
the relations is commutative, transitive and reflex-
be understood as only a metaphor derived from
ive, that is
physics, but we think that it is worth taking it
seriously. If you think of the time he was writ- • if a+a
ing – the 1860s – one of the key recent discover-
ies of physics was the idea of the conservation of • and if a+b implies b+a
energy. The conservation of energy had been for-
• and if a+b and b+c implies a+c
malised by Helmholtz and Grove in the late 1840s.
This held that although energy might appear in then the relation + is an equivalence relation. In
various forms: heat, motion, gravitational poten- his case + would stand for exchange of commodi-
tial,itwasconservedinitsexchangebetweenthese ties. Now equivalence relations are interesting be-
forms.1 cause systems goverened by conservation laws dis-
Marx’sinitial argumentinCapital, before he de- play them. Thus in a many-body gravitational
rives labour power as the source of surplus value problem with a predefined collection of particle
is similar. Value is neither created nor destroyed masses, the set of possible configurations of parti-
in the exchange process, but can only change its clepositionandvelocitiesispartitionedintoequiv-
form. His argument asserts in effect a law of the alence sets with respect to energy. Within eachset
conservation of value in exchange. all configurations share the same total energy and
Think of the distinction between ‘labour’ and the conservation of energy prevents transitions of
‘labour power’. This is so closely parallels Watt’s configurations between these sets.
distinction between ‘work’ and ‘power’, that it is This is in essence what we understand by a con-
surprising that the similarity is rarely remarked servation law.
on.2 His analysis of commodity exchange is also We infer the existence of energy as a conserved
structured like an analysis of a conservation law quantity by the fact that, in closed systems, we
[20]. He introduces as an example never observe transitions between configurations
with different total energies.
20 yards of linen = 1 coat or 20 yards of linen are
Marx’sdemonstrationthatcommodityexchange
worth 1 coat,
is anequivalence relationis then used to infer that
there is a conserved quantity ‘value’, the sum of
inthis notationhesaysthatthe coatplaysthe role
which is unchanged under the operation of ex-
of the equivalent and that it implies also the con-
changes. Commodity exchange is governed by a
verse relation
conservation law. To borrow much later terminol-
1“WhatLucretiussaysisself-evident;‘nilpossecrearide ogy, exchange is shown to be a zero-sum game.
nihilo,’out ofnothing, nothing canbecreated. Creationof
This may seema trivialobservation,but it leads
valueistransformationoflabour-powerintolabour. Labour-
power itself is energy transferred to a human organism by to an important deduction: that in a conservative
meansofnourishingmatter.” [20,ch.9] system, any surplus of value – profit – must arise
2This need not have been via a direct study of Watt by
from outside of the system and thus that profit
Marx. Watt’sdistinctionbetweenworkdoneandpower: the
must originate from production rather than ex-
abilitytoperformwork,measuredinstandardhorse-powers
hadbecomeacommonplaceofindustrialsociety. change. Marx argued that the conserved quantity
2
incommodityexchangesishumanenergyexpended Research in agent-based modeling has shown
as labour and that this energy provides the exter- thatifyoupartitionthepopulationintobuyersand
nal input that allows a surplus. At the economy’s sellers of labour power and run agent-based simu-
twoends,productionandconsumption,theprocess lations, you a reproduce the combination of Gibbs
isnonconservativebutinbetweenthemliesmarket andpower-lawdistributionsofwealth[32]observed
exchange: a conservative system. in real capitalist economies [9, 24]. Further, when
producerscanspecialiseinandswitchbetweendif-
1.1 Finance and conservation laws ferentcommodity-types,Marx’slawoflabourvalue
appearasanemergentphenomenonfromlocaland
Although economists are sometimes dismissive of distributed market exchanges [33].
conservationlaws,disparaginglycalled‘accounting
identities’, these identities can still throw useful
1.2 The phase space of finance
light on the financial crisis that has been unfold-
ing these last few years. But to do this we need to Abasictoolofconceptualanalysisinstatisticalme-
uncover the specific laws of motion, that is to say chanics is the concept of phase space. If you con-
boththeconservationlawsandtheparticledynam- sider a collectionof particles (for example stars)in
ics that govern the financial system. aclosedvolume,eachparticlecanbedescribedby6
Thatwehavetothinkofthefinancialsystemus- numberswhich specify its positionandmomentum
ing tools derived from statistical mechanics should in terms of a three-dimensional Cartesian coordi-
beobviousbynow. Itisoveraquarterofacentury natesystem: 3numberstospecifythepositionand
since it was shown that the regulation of prices by 3 numbers to specify its momentum. We say that
labour content arises directly from statistical me- each particle has 6 degrees of freedom.
chanical considerations [11]. So if we have a million particles, for instance if
Ifwelookatthemorerecentworkonthestatisti- one is considering the dynamics of a galaxy, the
calmechanicsofmoney[8,10],wecanseeasimilar systemhas6milliondegreesoffreedomandwecan
structure of argumentation – pushed somewhat by consider these to be a coordinate system such that
theuseofmoresophisticatedphysics. Thisresearch every possible configuration of molecular positions
argues that if we treat trades between commodity and moments constitutes a point in this 6 million
owners as a random process that conserves money, dimensional space. We call such a space a phase
then you canuse statistical mechanics to make de- space. Thelawsofmotionthenspecifyatrajectory
ductions about the distribution of money. Money of the whole system through this phase space.
as a conservedquantity randomlytransferedinex- The overall system is governed by conservation
changes between agents, models the transfer of en- laws. The mass is conserved, and relative to the
ergy between gas molecules and it follows that the center of gravity of the system as a whole the sum
maximum entropy distribution of money will be a of the momenta in each of the directions of our
Gibbs-Boltzmannone. Thestatisticalmechanicsof Cartesian system must sum to zero.
moneyshowsthatthisdistributionfitstheobserved Why is this relevant to finance?
distribution of money for most of the population, Well we are again dealing with a system with
but that a small minority of very rich people fall verylargenumbersofagentsandwehaveanalogues
off this distribution – their wealthfollows a power- of position and momentum. The total debt/credit
law. TheGibbsdistributionfallsofsharplyathigh position of an agent is analogous to its mass, and
levels of wealth, whereas the the tail of the power therateofchangeofitsdebt/creditpositionisanal-
law distribution extends much further. ogousto its momentum. Thus if two billion people
The probability of anyone being as rich as Bill in the world are enmeshed in debt/credit relations
Gates or Warren Buffet as a result of simple com- thenthewholesystemcanbethoughtofasaphase
modity trading is vanishingly small, so [9, 24] con- space of 2 billion dimensions.
cludethattherehastobe somemechanismoutside It is impossible to visualise a space with high
of equivalent exchange that gives rise to their ex- numbersofdimensions,sotherearegraphicaltech-
traordinarywealth: theeffectofcompoundinterest niques that people use to reason about them. One
which is a non-random process. trickistoprojectthehighdimensionalphasespace
3
downonto onlytwodimensions: forexample,posi- opposite reaction’ effect.
tion and momentum in the direction of one of the
axes of the coordinate system. This allows one to ∞
create a phase diagram. Applied to the financial 0=Z yPydy (2)
system, a possible phase diagram is shown in Fig- −∞
ure 1.
Increasing Debt These very basic points establish that there is no
net value or net wealth embodied in the financial
a system and that there is no flow of value into or
out of the financial system. It shows the fallacy
Net Credit Net Debt
of the conception, popular among some political
economists that capital has ‘moved into finance’
because of the low rate of profit pertaining in in-
b
dustry.
This is a fundamental misconception, capital is
value,anditcannotflowintothefinancialsystem,
Decreasing Debt
since the sum of value here is always zero. A mo-
ment’s thought about the materiality of value con-
firms this. Real-economic value – what the classi-
Figure 1: A phase diagram for financial space re-
caleconomistsunderstoodtobethelabourcontent
latingdebttotherateofchangeofdebt. Agentais
of physical products [22] – can not be converted
currently a net creditor,but it is borrowing and as
into financial instruments which are just informa-
such moving to the right towards becoming a net
tion structures.
debtor. Agent b has debts which it is paying off
and moving to the left to become a net creditor. A similar dimensional argument shows the fal-
lacyoftheideaofthe‘moneysupply’usedinortho-
dox economics. The notion of a supply originates
We could show every agent (firm, individual,
with physical flows like the supply of water to a
state) as a point on this plane. Or in a more ab-
town, or the supply of cars provided by all the car
stractwaywecouldsaythatthereisadensityfunc-
factoriesinthe world. Thereareflowsinthe finan-
tion P which gives the probability of finding an
x,y cial system, e.g. flows of agents towards greater
agentinagivenareainthephaseplane. Usingthis
debt, but these are exactly balanced by flows to-
probablility density function (PDF) we can formu-
wards greater credit positions, so the net flow is
latetwoconservationlawsanalogoustotheconser-
zero. If the term money supply is taken instead to
vation of mass and momentum.
meanastockofmoney,andthisistakentoinclude
bank deposits,one then hasthe problemthatboth
i. Thetotal‘mass’ontheleftoftheoriginequals
negative and positive money exist: liabilities and
the mass on the right of the origin. Since the
assets of the banking system respectively. Taken
mass to the left is credit, and that to the right
as a whole the positive and negative stocks cancel.
is debt, this is another way of saying that the
total debt and total credit must balance. We believeitisbetter to tryandunderstandthe
system in terms of its laws of motion. These laws
∞
areboththeconservationlaws(1)and(2),andthe
0= xP dx (1)
Z x forces acting on the individual particles (capitalist
−∞ firms, states, etc.). We will argue that the degree
of ‘disorder’ or entropy of a financial system tends
ii. The total ‘mass’ above the origin must equal to increaseovertime. We wouldexpect this ofany
the mass below the origin, that is to say that chaotic system governed by conservation laws, but
any growth in debt must be compensated for anexaminationoftheforcefieldsactingonthepar-
by a growth in credit. This is an ‘equal and ticles will show why this takes place.
4
1.3 Tendancy of financial entropy to headofproductive firmsanda tail ofrentierfirms,
rise who earn their revenue from financial rather than
productive assets. Therefore, as the dispersion or
WiththedensityfunctionP wecancomputethe
x,y spreadoftheprobabilitydensityfunctionincreases,
entropyofasystem,denotedH,usingthestandard
the entropy H rises, representing more disorder.
Boltzman formula,
In previous work [5] we presented a numerical
simulationmodel basedon the methodologydevel-
H =−Z Px,ylnPx,ydxdy, (3) oped in [32] that models a simple capitalist econ-
omywithalargenumberofcapitalistsandworkers.
andweassertthatforafinancialsystemH willrise Thestateofindebtedness/creditofeachofthecap-
over time. itals is tracked as the economy evolves. The cap-
Why does the entropy tend to increase? italists interact via a very simple financial system
First a common-sense explanation. Consider a representedbyasinglebankwhichmaintainsdebit
collectionoffirmsorenterprises,distributedonthe and credit accounts for agents based on a certain
phase plane diagramas in Figure 1. Eachfirm can amount of base money which acts as its reserve.
be consideredaparticlesubjecttoforceswhichde- The evolution can be visualised in a phase plane
termine its rate of change of debt. There are three diagram. For clarity we normalise the net debt of
cases to consider: eachfirmbyits totalcapitalstock,whichisknown
as the ‘debt ratio’.3 Similarly the rate ofchange of
(A) A firm whose debt is rising because its profits
debt is normalised by its total capital stock. Ini-
aretoo lowevento meetits interestpayments
tiallythecapitalistsareclusteredaroundtheorigin
to the banks. Such a firm has to borrow more
of the phase plane diagram,but as time passes the
from the bank to stay in operation. This firm
distribution becomes elongated with head of rela-
is an involuntary borrower.
tively indebted capitalists and long ‘rentier tail’ of
capitalistswith a negativedebt ratio. This process
(B) A firm may be voluntarily borrowing because
is illustrated in Figure 2. The increase in entropy
ithasahighrateofprofit,wellinexcessofthe
of the debt ratio PDF over time is shown.4
interest rate, and thus can increase its profit
ofenterprisebytakingonbankloanstoinvest The greater is the dispersion of the rates of
and expand its business. profit5 and the smaller the gap between the rate
of profit and the rate of interest, the stronger will
(C) Afirmmayreckonthattherateofprofititcan bethispolarisationprocessandthemorerapidwill
earn is lower than the rate of interest, but its be the growth in financial entropy.6
current debt level may be quite low so that it The polarisation process generates a tadpole
isinapositiontopayoffitsdebts tothebank
with some of its retained profit. A firm may
3Notethatafirmwithanetcreditpositionhasanegative
even have no net borrowing and find that it
debt ratio, D/K. Thecapital stock K was calculated from
is more profitable to earn interest on its cash thecurrentvalueofthecommoditystocksandequipmentof
thanitistoinvestitproductively. Suchafirm theenterprise.
4CalculatedusingaperpixelbinningofthePDF.
is a voluntary lender.
5Technicallywhatwemeanhereisitscoefficientofvari-
ation,itsstandarddeviationrelativetoitsmean.
The total amount of borrowing must equal to the 6Aswe saidearlierthe net lendingalways sums tozero.
totalamountoflending,thusifthequantityofvol- As such it is analogous to a motorway with a stream of
untary borrowing by firms in group (B) falls be- carsofequalweightheading pastoneanother at100kph in
low the quantity of lending by firms in group (C), oppositedirections. Thesumofthemomentumsofthecars
iszero. Butifwesquaretheirpositiveornegativevelocities
thelackofdemandfrominvestmentswillautomat-
times their weights we get the energy stored in the traffic.
icallycreatesufficientfirmsin(A)tryingtostayin Onecanviewthesumofthesquaresofthelendingpositions
operationthroughinvoluntaryborrowing,ensuring of all agents as a bitlike energy inthat itdoes not sum to
zeroastheactivityofthefinancialsystemincreasesbutwith
that equation (2) is met. The net effect of this is
the important proviso, that this quantity is not conserved.
to polarise capital in the phase plane as borrowers
Itcan grow without immediatelimit. We willexplainlater
and lenders, giving rise to a tadpole shape with a whythisgrowthinfinancialenergyleadstocrises.
5
T PDF in the phase plane Px,y H realassets,occurseveninaverysimplemodel. The
entropyofthesystemwillincrease,polarisationwill
occur, and a rentier class will be precipitated out,
unless social work is done to curtail the growth of
2 3.29
entropy.
In a more complex model with joint stock firms
asimilarpolarisationwilltendtooccur,butinthis
case there may be pressure for firms with a very
5 3.72
negative debt ratio (lots of cash) to distribute this
to their shareholders.
This distribution is unlikely to put a halt to the
polarisationprocessbecauseinthe caseofcashbe-
20 4.74
ing distributed from firms to individual capitalists
Figure 2: The formation of a rentier tail due to the totalofpositivebalanceswiththe bankingsys-
the polarisation of capitals in the phase plane. T temdoesnotchange,itjustshiftsfromabstractle-
is timestep, H is entropy. The images show a plot gal persons to concrete ones. The only mechanism
of the probability density function of capitals in by which the polarisationcanbe conservativelyre-
the phase plane. The horizontalaxisshowsthe net ducedisbytheclassofcreditorfirmsandcapitalists
debt,normalisedbythetotalcapitalstock,i.e.,the to purchase commodities from the class of debtor
‘debt ratio’. The vertical axis shows the rate of firms and capitalists. This will happen only to the
changeofthedebt,alsonormalisedbytotalcapital extent that a distribution of money from cash-rich
stock. Astime passestheentropyofthesystemin- firms to rentiers results in an increase in the con-
creases. Note that the colouris nonlinearlyrelated sumption of the rentier class.
to the actual value of P in order to display the Commodity exchange is a conservative system,
x,y
areas of very low but non-zero probability in the i.e., one governed by conservation laws. This does
tail. notapplytotaxation. Taxationisanon-equivalent
transfer of value. Heavy taxation of the rentier
class is a form of social work that reduces the en-
shape in the phase plane7 with a body of active tropy of the system.8 The introduction of a regu-
firms clustered round the origin and a rentier tail latedorplannedeconomyisanevenmorepowerful
of firms that progressively enlongates as the sim- form of social work. In a planned economy the de-
ulation goes on. Why do we get this asymetrical gree of chaos and disorder is reduced and coherent
distribution? patterns are established which curb the growth of
Becausethe debt ratio ofa capitalistcannotfor entropy characteristic of the free market.
long exceed unity. A capitalist with more debts
thanassetsistechnicallybankruptandwillshortly
1.4 Relation to the productive econ-
cease trading. There is on the other hand no limit
omy
to how negative the debt ratio of a capitalist can
be. That is to say, no limit to how much money a Themodelaboveisverysimple,itinvolvesnointer-
capitalist can have in the bank. banklendingnortheissueofanycomplexfinancial
What the argument above shows is that it is instruments. All growth in debt arises from the
possible to derive a small set of laws of motion behavior of basic actors in the real economy: capi-
that characterise the basic development of a cap- talists and workers. But it is still able to generate
italist financial system. The essentials of the phe- the polarisation of the capitalist class into produc-
nomenonthathasbeencalled‘financialisation’,i.e., tive capitalists and financiers.
the growth of financial assets/liabilities relative to In a physical system, as it moves from a low en-
tropy state to a high entropy state we are in prin-
7It should be noted that so far this conclusion is based
on theoretical arguments and the evidence from numerical 8Thestatisticalmechanicaleffectsonmoneydistribution
simulations. An empirical investigation of the distribution under different taxation schemes has recently been studied
offirmsonthephaseplaneremainstobedone. by[7].
6
ciple able extractworkfrom it. Is there any equiv- million oz of gold would have lain in their safe at
alent in the financial system? the bus factory and those purchasers who lacked
Does it release any analogue of free energy as it cash(thosewhoareontherightofthephaseplane
evolves? diagraminFig.1)wouldnothavebeenabletobuy
Itisacommonplaceobservationthataneconomy the buses. The sale would thus never have taken
with a low initial level of debt can grow rapidly as place,andthetotaloutputofbuseswouldhavehad
the debt builds up, but what is happening here? tobe10,000lower. Busescouldstillhavebeensold
We have said that there is no value absorbed in to firms who had ready cash, but this would have
or contained in the financial system. The finan- been a smaller number.
cial system is an information structure recording ReadersofMarx’sCapital [20]mayrecallthathe
themutualobligationsofagents. Butthisdoesnot analysedthecirculationofcommoditiesasbeingof
meanthattheremaynotberealvaluecorrelatesof the form
financial relations. If we look at all the firms with C →M →C,
net debt – the integral over the right hand side of
i.e., commodity, money, commodity. He argues
the phase plane in Fig. 1 – then these firms have
that this form already contains the possibility of
all absorbed real resources from the left hand side
10
crisis. Thepotentialcrisisiscausedbytheforma-
of the plane. When capitalists on the bottom half
of the phase plane fail to invest and capitalists on 10“Nothing can be more childish than the dogma, that
the tophalfdoinvestinexcessoftheir income,the becauseeverysaleisapurchase,andeverypurchaseasale,
financialsystemsetsupasystemofobligationsbe- therefore the circulationof commodities necessarily implies
tween the debtors and the saving capitalists. But anequilibriumofsalesandpurchases. Ifthismeansthatthe
numberofactual salesisequaltothenumberofpurchases,
at the same time, the firms onthe bottom are pro-
it is mere tautology. But its real purport is to prove that
vided with a market for their output on the top of every seller brings his buyer to market with him. Nothing
the phaseplane. Thereatransferofrealcommodi- ofthekind. Thesaleandthepurchaseconstitute oneiden-
tical act, an exchange between a commodity-owner and an
ties from the bottom to the top.
owner of money, between two persons as opposed to each
Afirmonthebottom,produces10,000busescon-
otherasthetwopolesofamagnet. Theyformtwodistinct
taining perhaps 100 million hours of labour which acts, of polar and opposite characters, when performed by
areboughtbyagentsonthetophalf. Inreturnthe one single person. Hence the identity of sale and purchase
implies that the commodity is useless, if, on being thrown
buscompanyobtainsnotvaluebutacreditaccount
intothealchemisticalretortofcirculation,itdoesnotcome
at the bank. This is not strictly speaking a com-
out again inthe shape of money; if,inother words, itcan-
modityexchange. Acreditaccountinabankisnot not be sold by its owner, and therefore be bought by the
value. Had they been paid in gold and got back 1 owner of the money. That identity furtherimpliesthat the
exchange,ifitdotakeplace,constitutesaperiodofrest,an
million oz of gold bullion, that would have been a
interval, long or short, in the life of the commodity. Since
commodity exchange, an exchange of equivalents, thefirstmetamorphosisofacommodityisatonceasaleand
sincethe goldwouldhavecontainedrealvalue: the a purchase, it is also an independent process in itself. The
human energy, labour, required to make it. purchaserhasthecommodity,thesellerhasthemoney,i.e.,
a commodity ready to go into circulation at any time. No
The sale of the buses for say 1,000 million Eu-
one can sell unless some one else purchases. But no one is
ros is a nonequivalent transaction in real terms forthwithboundtopurchase,becausehehasjustsold. Cir-
sinceembodiedlabouristransferedbetweenowners culationburststhroughallrestrictionsastotime,place,and
withoutacompensatingmovementoflabourinthe individuals, imposedby directbarter, and this iteffects by
splittingup,intotheantithesisofasaleandapurchase,the
other direction. And, by our previous assumption,
direct identity that in barter does exist between the alien-
it is a transfer between a bus firm who were decid- ation ofone’s ownand the acquisitionof someother man’s
ing to save 1,000 million rather than invest it pro- product. To say that these two independent and antithet-
ical acts have an intrinsic unity, are essentially one, is the
ductively. Thistransferisthusonewhichwouldnot
sameastosaythat this intrinsiconeness expresses itselfin
have occured in the absence of the credit system.
an external antithesis. If the interval in time between the
Had goldcoins been the medium ofexchange9, the two complementary phases of the complete metamorphosis
of a commodity become too great, if the split between the
9The existence of gold as a standard of value is not the saleandthepurchasebecometoopronounced,theintimate
same thing as its use as a medium of exchange. The gold connexionbetweenthem,theironeness,assertsitselfbypro-
standard persisted long after commodity circulation was ducing — a crisis. The antithesis, use-value and value; the
generallycarriedoutoncredit. contradictions that private labour is bound to manifest it-
7
tion of gold hoards, gold which is withdrawn from the credit system is social, it is work to overcome
circulation and saved. This interruption of the cir- the potential barrier that private property would
cuit C →M →C by money lying idle means that otherwise impose on the expansion of production.
goodscannotbesold: ‘Noonecansellunlesssome Commodity exchange requires and exchange of
one else purchases’. equivalents. Wheretheseequivalentsarenotinthe
With credit the circuit C →M →C is replaced hands of the purchasers, the financial system al-
from the standpoint of the seller with one of the lowstransfersthatareinrealtermsnon-equivalent
form C →Fa →C where Fa is a financial asset: a exchanges, whilst creating instead a symbolic rec-
bill of exchange, or a record of credit with a bank. ompensation for the seller.
If both the purchaser and the seller have financial This symbolic recompensation in Euros or Dol-
assetsthis is the sameas the oldmonetarycircula- lars is a theoretical command over future labour.
tion: The borrower in this case is the real appropriator
C F
a of the labour value embodied in the capital goods
ց ր
they acquire. The lender obtains merely a formal
ր ց
or symbolic appropriation of value.
F C
a Private ownership creates a potential barrier to
The financial asset has just changed places, but if the movement of goods which credit overcomes.
we have purchase on credit we get: The increasing entropy of the financial system re-
flects the ‘work’ that has been extracted in over-
C Fa comingthisbarrierandiswhyitappearsto‘create
ց ր wealth’. It allows the creation of wealth by labour
ր ց whose expenditure would otherwise have been in-
a† → → C+Fl hibitedbythe privateorganisationofthe economy.
If one were to ask a bankerwhat productive role
Here the purchase is funded by the spontaneous
they paid in the economy the answer wouldproba-
creation of a financial asset/liability pair by the
bly be in terms of the banks providing the finance
debt creation operation a† giving rise to Fa and that the economy needs.11 Money according to
F . Within this whole process real value is con-
l Adam Smith is the ability to command the labour
served, since the only real value entering was C of others.12 The provision of credit gives a capi-
and C leaves having merely changed owner whilst
the liability and asset cancel: Fl+Fa =0. 11“Now let’s turn to the purpose of banks in a capital-
The ‘work’ done by credit is thus to allow the isteconomy. Finance is an intermediary good: You cannot
production and distribution of goods embodying eat it, experience it, or physically use it. The purpose of
financeistosupportotheractivitiesintheeconomy. Banks
real labour that could not otherwise occur given
are meant to allocate capital (funds) to the best possible
the private organisation of production. This is the
use. In a capitalist economy, this means allocating money
free energy extracted by the increase in entropy of tothepeopleorentitiesthatwillcreatethegreatestwealth
thefinancialsystem. Ofcoursethefinancialsystem forthe overall society. Atthe same time, riskmanagement
is supposedly a primary skill for bankers. When capital is
itselfdoesnotdoanyrealwork. Therealadditional
allocated well and available to wealth creating entities, so-
physical work is done by the employees of compa- cietiesflourish. Whencapitalispoorlyallocated,economies
nies who are net lenders. The ‘work’ done by by cancollapse.” [16]
12“Wealth, as MrHobbes says, ispower. But the person
self as direct social labour, that a particularised concrete whoeitheracquires,orsucceedstoagreatfortune,doesnot
kind of labour has to pass for abstract human labour; the necessarilyacquireorsucceedtoanypoliticalpower,either
contradictionbetweenthepersonificationofobjectsandthe civil or military. His fortune may, perhaps, afford him the
representationofpersonsbythings;alltheseantithesesand means of acquiring both; but the mere possession of that
contradictions, which are immanent in commodities, assert fortunedoesnotnecessarilyconveytohimeither. Thepower
themselves,anddeveloptheirmodesofmotion,intheanti- which that possession immediately and directly conveys to
theticalphasesofthemetamorphosisofacommodity. These him,isthepowerofpurchasingacertaincommandoverall
modesthereforeimplythepossibility,andnomorethanthe the labour, or over all the produce of labour which is then
possibility,ofcrises. Theconversionofthismerepossibility in the market. His fortune is greater or less, precisely in
intoarealityistheresultofalongseriesofrelations,that, proportion to the extent of this power, or to the quantity
from our present standpoint of simple circulation, have as either of other men’slabour, or, what isthe samething, of
yetnoexistence.” [20,ch.2,sec.2] the produce of other men’s labour, whichitenables him to
8
talist the authority or permission to commandeer 1.5 Contradiction between real and
part of the pool of social labour to his project. formal appropriation of value
In this sense the provision of a line of credit by
Why do capitalists seek profits?
a bank is like any other official act of giving per-
mission. It is like for example a building control On the one hand it is something that is imposed
office issuinga permitallowingahouse to be built. bythenatureofcompetition. Onlyprofitablefirms
But the right to hand out such permissions does survive,themoreprofitabletheyarethemorelikely
notmakethe personhandingthemoutproductive. they are to survive, so a mechanism analogous to
natural selection establishes the profit motive as
It is bricklayer’s and carpenters that actually
the driving force of the system.
produce the house, not the bureaucrat who signs
it off. When such permissions are in demand, the But there is another way of looking at this.
official handing them out may ask for a cut: “You Whatever its historical form – gold, banknotes,
want to have this house built, you know your ap- bankaccounts–moneyhasbeenthepowerofcom-
plication might go much more smoothly were you mand over labour. In all class societies, members
to show your generosity in some way”. In an anal- oftheupperclasshadbeendriventoincreasetheir
ogous fashion bankers ask for their cut: interest. power over the labouring classes.
It may appear that a loan to a builder, unlike Slave owners tried to obtain as many slaves as
a building permit, actually gives the resources to they could. Feudal landowners sought to do this
build a house but this is an illusion generated by indirectlybybuildinguptheirlandedestates,since
the legal relations underwhich it is done. The loan attachedtothelandwereserfs. Capitalistsdoitby
does not give the resources to proceed. The means accumulating money. A billion Euros gives a cap-
are bricks and workers, the loan gives the right to italist command over about 100,000 person years
commandthese,this isagainthe removalofalegal of labour, say 2000 working lifetimes of indirect
impediment in that a private citizen can not print labour in commodities, perhaps twice that if they
theirownmoneyorissuegenerallyacceptablecred- employpeopledirectly. Themoremoneyyouhave,
itstoauthorisethework,whilstbanks,unlikeother the more people are at your command.
agents,can do this without legalimpediment. The Buildingupa bankbalancegivesyouasymbolic
right to command labour is in the end a juridical command over lots of future labour but this is dif-
relation,amorecomplexandindirectonethanthat ferentfromreallyhavingtheproductofthislabour,
given by a building warrant, but still ultimately a as the fable of Midas long ago pointed out. By the
legal one backed in the end by the acceptance by nature of credit, a thrifty symbolic appropriator
the tax authorities of drafts on the private bank. depends for his very existence on the spendthrift
The fact that the bank holds an account with the debtors.
state bank is what ultimately gives the bank an The credit system socialises this dependence,
ability to issue the authority to command labour. makesitimpersonal,sothatmoneyseemstosimply
Thisisintheendalegaldelegationofauthorityby represent abstract value, abstract command over
the state. labour. But the labour it is command over,is that
At one time the charging of interest (usury) as ofthedebtorclassesasawhole. Thesub-primecri-
regarded as the moral equivalent of an official tak- sis,likeallcreditcrises,bringstotheforethefragile
ing a bribe. With the rise of bankers to political and mirage-likequality of this symbolic command,
dominance, their verywealth, obtainedin this way which can grow beyond any possibility of conver-
comes to be seen as a token of social respectabil- sion into a real appropriation.
ity.13 Think back to the phase diagram. The symbolic
wealthofthe rentierclassesisthetadpolestail. As
purchaseorcommand.”[26,ch.5].
13“Thisdispositiontoadmire,andalmosttoworship,the That wealth and greatness are often regarded with the re-
richandthepowerful,andtodespise,or,atleast,toneglect spect and admiration which are due only to wisdom and
personsofpoorandmeancondition,thoughnecessaryboth virtue;andthatthecontempt,ofwhichviceandfollyarethe
toestablishandtomaintainthedistinctionofranksandthe only proper objects, is often most unjustly bestowed upon
order of society, is, at the same time, the great and most poverty and weakness, has been the complaint of moralists
universal cause of the corruption of our moral sentiments. inallages.” [25,p.53]
9
it wiggles and extends, it drives the head towards where C ⇒ (C +∆C) represents the production
therighttowardsthewallofbankruptcy(Figure3). process that generates a physical surplus product
Hit the wall and the credit creation operator a† ∆C after the consumption of the present working
becomesitsterribletwintheanihilationoperatora population has been met. Moreover, through the
which cancels out the debt of the bankrupt at the compulsion of market dependency capitalist firms
sametimeasitwipesouttheassetofthecreditor.14 seek an indefinite expansion
M →C →M′ →C′ →M′′ →C′′ →M′′′ →···
by reinvesting the profit in greater productive ca-
pacity. This process is therefore governed by non-
conservative laws of exponential growth. Relative
growthrates are measuredas per unit of time, i.e.,
[time−1],andasmallchangeinsucharatemaypro-
Figure 3: Capitals pushed against the wall of duce dramatic differences over time. For instance,
bankruptcy lead to debt/credit annihilation. if some quantity grows at 1% per annum it dou-
bles in size approximately every 70 years. But if it
grows at 10% per annum it doubles every 7 years.
As we show below, the nonconservative laws of
2 Nonconservation laws of capitalaccumulationinteractswithsystemsoutside
the capitalist sector which provide it with labour,
capital accumulation
natural resources and the material conditions for
habitability in general.
If the characteristic or signature of commodity ex-
change, C → M → C, implies a conservation law,
2.1 Profit rate constraints
then the signature of capital,
M →C →M′, Capitalist firms reinvest their profit – and rentiers
finance expansion in various branches of produc-
breaks that conservation as M′ = M + ∆M de- tion – based on the rate of return on the capital
invested. Consider a firm i earning annual profit
notes an increase in the money above the initial
flow of P Euros per annum, before interest, rents
sumspentoncommoditiesinproductionM. Marx i
and tax expenditure, with a stock of fixed capital
famouslyattemptedtoexplainhowsuchexpansion
K Euros invested in the form of buildings, ma-
is possible [20, ch. 5-6]. It could not, he argued, i
chines, equipment etc. The firm then earns an an-
come about in the sphere of commodity exchange,
nual profit rate R = P /K on its capital stock
since this was governed by a law of conservation i i i
and the dimension of this rate is [time−1]. If new
of values. Thus, he argued, profit ∆M could only
investmentinthefirmistobeattractive,theprofit
be explained outside the realm of commodity ex-
rate should exceed the real interest rate or else it
change, by the extraction of surplus labour in the
wouldbemoreprofitabletosimplyearnintereston
productionprocess: Withincapitalistfirms–where
saved profits.15
Freedom, Equality and Bentham do not prevail –
Next, consider the aggregate of all capitalist
the working day is extended beyond the time re-
firms in the economy. The total capital stock in-
quired to produce the workers’means of consump-
vestedearnsdifferentratesofprofitinvariousfirms
tion, in order to provide a surplus that funds prof-
and branches as illustrated in Figure 4. Due to
its.
varying technical conditions in production and the
If one takes the aggregate of all capitalist firms,
random churning of the market, the distribution
the signature of this process can be represented as
will always be dispersed. The process of finan-
M →[C ⇒(C+∆C)]→M′, (4) cial polarisation of capital into net creditors and
debtors,describedinthe previoussection,willalso
14Weadmitto‘coquetting’withDiracinourterminology
asMarxadmittedtodoingwithHegel. 15AspointedoutbyMarxandKeynes[23].
10