Post on 25-Jun-2018
Laws of Motion in Capitalism
CMS Stockholm
Stockholm
October 19, 2016
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 1 / 23
Laws of motion
[I]t is the ultimate aim of this work, to lay bare the economiclaw of motion of modern society
– K. Marx, 1867 Preface to Capital, vol. 1.
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 2 / 23
Laws of motion
[I]t is the ultimate aim of this work, to lay bare the economiclaw of motion of modern society
– K. Marx, 1867 Preface to Capital, vol. 1.
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 2 / 23
Laws of motion
[I]t is the ultimate aim of this work, to lay bare the economiclaw of motion of modern society
– K. Marx, 1867 Preface to Capital, vol. 1.
Concepts from classical physics in political economy
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 2 / 23
Signatures of capitalist market economy
1 Equivalence in exchange:
C→ C
2 Exchange with money:
C → M → C
3 Expanding money:
M → C → M ′
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 3 / 23
Signatures of capitalist market economy
1 Equivalence in exchange:
C→ C
2 Exchange with money:
C → M → C
3 Expanding money:
M → C → M ′
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 3 / 23
Signatures of capitalist market economy
1 Equivalence in exchange:
C→ C
2 Exchange with money:
C → M → C
3 Expanding money:
M → C → M ′
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 3 / 23
Symmetry and conservation in exchange
C C
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 4 / 23
Symmetry in exchange
Example from Volume 1:If 1 coat =̇ 20 yards of linen
then 20 yards of linen =̇ 1 coat
The exchange relation is symmetric:
C︸︷︷︸1 coat
C︸︷︷︸20 yards of linen
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 5 / 23
Symmetry in exchange
Example from Volume 1:If 1 coat =̇ 20 yards of linen
then 20 yards of linen =̇ 1 coat
The exchange relation is symmetric:
C︸︷︷︸1 coat
C︸︷︷︸20 yards of linen
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 5 / 23
Marx after Noether
Emmy Noether (1882 - 1935)
Symmetry and conservation
If a system has a symmetry property, thenit possesses a quantity that is unchanged
S S ′→
mm
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 6 / 23
Marx after Noether
Emmy Noether (1882 - 1935)
Symmetry and conservation
If a system has a symmetry property, thenit possesses a quantity that is unchanged
Marxian hypothesis
In a system of symmetric exchanges,
C C,
the conserved quantity is social labour time
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 6 / 23
Labour time as the conserved quantity
Social production system
corn
iron
labour
sugar
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 7 / 23
Labour time as the conserved quantity
Social production system
corn
iron
labour
sugar
Labour is a universal and redeployable resource
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 7 / 23
Labour time as the conserved quantity
Social production system
corn
iron
labour
sugar
Social labour is therefore an abstract quantity
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 7 / 23
Labour time as the conserved quantity, cont’d
O
Figure : An object O with a mass ...
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 8 / 23
Labour time as the conserved quantity, cont’d
O
Figure : ... has weight only interaction with gravitational field
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 8 / 23
Labour time as the conserved quantity, cont’d
C
Figure : A commodity C with a use value ...
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 8 / 23
Labour time as the conserved quantity, cont’d
labour
corn
iron sugar
C
Figure : ... has labour value only interaction with social production field
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 8 / 23
Labour time as the conserved quantity, cont’d
labour
sugar
corn
iron
C
C
Figure : Labour value is conserved under symmetric exchange
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 8 / 23
Labour content as conserved quantity, cont’d
Testable law
Market prices of a commodity-type C are statistically linked to itslabour value
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 9 / 23
Labour content as conserved quantity, cont’d
Testable law
Market prices of a commodity-type C are statistically linked to itslabour value
1 2 3 4 5 6 7 80
0.5
1
1.5
ratio
pd
f
Japan, 2000
1 2 3 4 5 6 7 80
0.2
0.4
0.6
0.8
1
1.2
1.4
ratio
pd
f
Sweden, 1995
Figure : Proportion of commodities with different ratios P (C)/Λ(C)
Zachariah, D.: Labour value and equalisation of profit rates: a multi-country study. Indian
Development Review, vol. 4, June 2006.
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 9 / 23
Conservation laws of market exchange
C M C
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 10 / 23
Colliding agents of market exchange
Exchange with money commodity
CAgent A:
MAgent B:
M
C
Labour value of C + M is conserved
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 11 / 23
Colliding agents of market exchange
Exchange with financial asset
CAgent A:
FaAgent B:
Fa
C
Labour value of C is conserved
Asset Fa represents claim on value
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 11 / 23
Marx after Boltzmann
Ludwig Boltzmann (1844 - 1906)
Large systems with energy constraints
Uncoordinated interactions amongparticles produce stable distribution ofenergy
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 12 / 23
Marx after Boltzmann
Ludwig Boltzmann (1844 - 1906)
Large systems with energy constraints
Uncoordinated interactions amongparticles produce stable distribution ofenergy
Marxian hypothesis
Uncoordinated market exchange,
C Fa C,
will by itself produce stable distribution of money Fa
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 12 / 23
Marx after Boltzmann, cont’d
Testable law
The distribution of money across exchanging agents is Boltzmann
0 500 1000 1500 2000 2500 30000
1
2
3
4
5x 10
5
Money F a
#Agents
Figure : Proportion of agents with different amounts of money
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 13 / 23
Marx after Boltzmann, cont’d
Testable law
The distribution of money across exchanging agents is Boltzmann
Figure : Distribution of income in USA
Silva, A. C., and Yakovenko, V. M. Temporal evolution of the ‘thermal’ and ‘superthermal’ income
classes in the USA during 1983-2001. Europhysics Letters, v. 69, pp. 304-310, 2005.
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 13 / 23
Agents of exchange: credit and debt
Exchange using credit and debt
CAgent A:
oAgent B:
Fa
C+D
Labour value of C is conserved
Legal obligation o that creates D and Fa
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 14 / 23
Agents of exchange: credit and debt
Debt
Pay off debt
a b
Figure : Two agents with mutual debt obligations
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 15 / 23
Agents of exchange: credit and debt
Debt
a
b
Pay off debt
Figure : Repaying debt has symmetric effect on asset
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 15 / 23
Agents of exchange: credit and debt
Debt
a
b
Pay off debt
Figure : Increasing debt has symmetric effect on asset
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 15 / 23
Laws of credit and debt
Testable law
The financial surpluses of all economic sectors sum to 0
Testable law
In a credit system with interest, firms with different rates of profit willpolarize into rentiers and debtors
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 16 / 23
Laws of credit and debt
Testable law
The financial surpluses of all economic sectors sum to 0
Testable law
In a credit system with interest, firms with different rates of profit willpolarize into rentiers and debtors
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 16 / 23
Laws of credit and debt
Testable law
The financial surpluses of all economic sectors sum to 0
Testable law
In a credit system with interest, firms with different rates of profit willpolarize into rentiers and debtors
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 16 / 23
Non-conservation laws of capital accumulation
M→ C→M + ∆M
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 17 / 23
Breaking symmetry in production and consumption
Production
Exchange
Workers Capitalists
Cw ∆C∆MMw
Figure : Symmetry and conservation reigns in market exchange
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 18 / 23
Breaking symmetry in production and consumption
Production
Exchange
Workers Capitalists
∆C
L
Cw
Figure : Surplus labour and product extracted via market mechanism
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 18 / 23
Breaking symmetry in production and consumption
Production
Exchange
Workers Capitalists
Mw M′
∆MMw
M
Figure : Profit income is a symbolic claim on surplus product
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 18 / 23
Breaking symmetry in production and consumption
Production
Exchange
Workers Capitalists
Cw ∆C∆MMw
Testable law
Real profit income arises through the extraction of surplus labour
Testable law
Aggregate profit income is determined by capitalist expenditure
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 18 / 23
General signature of capital
The general signature of capital
M → → M′C
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 19 / 23
General signature of capital
hides its material basis
M → → M′C C+∆C⇒
L↑
C
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 19 / 23
Exponential growth through reinvestment
Exponential growth of claims on value
M→ C→M′ → C→M′′ → C→M′′′ → · · ·
must be backed by material expansion of
M → → M′C C+∆C⇒
L↑
C
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 20 / 23
Exponential growth through reinvestment
Exponential growth of claims on value
M→ C→M′ → C→M′′ → C→M′′′ → · · ·
must be backed by material expansion of
M → → M′C C+∆C⇒
L↑
C
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 20 / 23
Constraints on average profitability
Testable law
Average profit rate is determined by investment level and exponentialgrowth of labour and productivity
1965 1970 1975 1980 1985 1990 1995 2000 200510
12
14
16
18
20
22
24
26
28
30
% p
er
an
nu
m
USA
R
R*
R* (g
L=0)
R* (g
L=g
P=0)
1965 1970 1975 1980 1985 1990 1995 2000 200510
15
20
25
30
35
40
% p
er
an
nu
m
UK
R
R*
R* (g
L=0)
R* (g
L=g
P=0)
Figure : Trajectory of average profit rates in US and UK
Zachariah, D.: Determinants of the average profit rate and the trajectory of capitalist economies.
Bulletin of Political Economy, Vol.3, No.1, 2009
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 21 / 23
Constraints on average profitability
Testable law
Average profit rate is determined by investment level and exponentialgrowth of labour and productivity
1965 1970 1975 1980 1985 1990 1995 2000 200510
12
14
16
18
20
22
24
26
28
30
% p
er
an
nu
m
USA
R
R*
R* (g
L=0)
R* (g
L=g
P=0)
1965 1970 1975 1980 1985 1990 1995 2000 200510
15
20
25
30
35
40
% p
er
an
nu
m
UK
R
R*
R* (g
L=0)
R* (g
L=g
P=0)
Figure : Trajectory of average profit rates in US and UK
Zachariah, D.: Determinants of the average profit rate and the trajectory of capitalist economies.
Bulletin of Political Economy, Vol.3, No.1, 2009
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 21 / 23
Summary
By applying concepts from classical physics, the signatures
C → C C →M → C M → C →M ′,
can generate fruitful hypotheses and testable laws of capitalist marketeconomies
For more details:
Cockshott, P. and Zachariah, D.: Conservation laws, financialentropy and the Eurozone crisis. Economics, 8 (2014-5): 1-55.
Thank you for listening!
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 23 / 23
Summary
By applying concepts from classical physics, the signatures
C → C C →M → C M → C →M ′,
can generate fruitful hypotheses and testable laws of capitalist marketeconomies
For more details:
Cockshott, P. and Zachariah, D.: Conservation laws, financialentropy and the Eurozone crisis. Economics, 8 (2014-5): 1-55.
Thank you for listening!
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 23 / 23
Summary
By applying concepts from classical physics, the signatures
C → C C →M → C M → C →M ′,
can generate fruitful hypotheses and testable laws of capitalist marketeconomies
For more details:
Cockshott, P. and Zachariah, D.: Conservation laws, financialentropy and the Eurozone crisis. Economics, 8 (2014-5): 1-55.
Thank you for listening!
CMS Stockholm Laws of Motion in Capitalism October 19, 2016 23 / 23