Download XIV. Internationale InkriT-Tagung Demokratische Planung

4th International Vanguard Science Congress
The role of Science, Technology and Geo-Politics
in the Self-Determination of Mankind
Ciudad de México, May 28-30, 2013
Universidad Autónoma Metropolitana Unidad Xochimilco
El papel de los servicios en las economías
contemporáneas:
Una formulación consistente dentro de los marcos
de la teoría del valor del trabajo de Marx.
The role of services in contemporary economies:
A consistent formulation within the framework of Marx´s labour
theory of value.
Peter Fleissner, catedrático de cibernética social, Viena, Austria
contacto: [email protected]
Outline
• Some basics of the labor theory of value
• Input-output tables and Marxian schemes of
reproduction
• Commodities and services
• How to determine the value of services?
• Marx’ prices of production (transformation
problem)
• Empirical results (Austria 2008)
How to analyse the economy?
• Main method:
• Creating Layers of Various Degrees of Abstraction.
– The kind of abstraction is inspired by insights into history and the
logic of the field.
– For logical reasons we take goods (use values) produced under the
existing division of labor as the most abstract layer.
• Layers of high degrees of abstraction do not necessarily
correspond to observed data, but they grasp essential
aspects of reality.
– Analogy to physics: The Law of Gravitation (all bodies fall with the
same rate of acceleration) is contrary to evidence (compare the
fall of a feather and a coin).
Economic Reality – A Complex Construction
7
Contemporary Capitalism
6 Information Society: Finance market capitalism
information as commodity, communication as commercial service
5 Public sector: State monopoly capitalism
Globalized economy: Finance capitalism
4 International financial capital
Capitalism with perfect competition
3 and fixed capital
Commodity production
2 of self employed
Physical
1 basis
market prices
(observed)
commodification
of information
goods/services
taxes, subventions
transfers, social insurance
markets for money,
credit, stocks, derivatives
prices of production
labor market
exchange values
prices ~ labor values
commodity/service markets
use values, environmental issues
measured by mass, exergy or ecological footprint
The Economy – seen as a self organization process
(historical and logical view)
7
Contemporary Capitalism
6 Information Society:
information as commodity, communication as commercial service
market prices
(observed)
commodification
of information
goods/services
5 Public sector
Globalized economy
4 International financial capital
Commodity production
2 of self employed
Physical
1 basis
Inspired by: Hofkirchner , W. (2002):
Projekt Eine Welt: Kognition –
Kommunikation – Kooperation.
LIT-Verlag Münster-HamburgLondon. p. 166
History: Emergence
Logic: Dominance
Capitalism with perfect competition
3 and fixed capital
Economic Reality – A Complex Construction
7
Contemporary Capitalism
6 Information Society:
information as commodity, communication as commercial service
5 Public sector
Globalized economy
4 International financial capital
Capitalism with perfect competition
3 and fixed capital
Commodity production
2 of self employed
Physical
1 basis
market prices
(observed)
commodification
of information
goods/services
taxes, subventions
transfers, social insurance
markets for money,
credit, stocks, derivatives
prices of production
labor market
exchange values
prices ~ labor values
commodity/service markets
use values, environmental issues
measured by mass, exergy or ecological footprint
Layer 1: Use values, produced and consumed under a certain
division of labor
•
•
•
•
Mathematical description in terms of Leontief’s input-output scheme to
represent the economy in terms of use values.
Each row and each column represent one branch of production or firm
It reflects the degree of division of labor.
The matrix of technical coefficients A represents the technology of the
economy. The element aij gives the amount of goods of industry i needed
to produce one unit of output of industry j.
x (output vector) contains all use values produced. It can be split by kind of
use of goods into Ax (demand for intermediate goods) and y (final
demand). The following famous formula is called the primal problem
Ax + y = x
y (final demand) can be split it into c (consumption) and s (surplus product =
capital investment)
y = c + s.
or in matrix notation
Ax + Cx + Sx = x ,
where C, and S represent matrices of consumption coefficients and surplus
coefficients respectively.
Economic Reality – A Complex Construction
7
Contemporary Capitalism
6 Information Society:
information as commodity, communication as commercial service
5 Public sector
Globalized economy
4 International financial capital
Capitalism with perfect competition
3 and fixed capital
Commodity production
2 of self employed
Physical
1 basis
market prices
(observed)
commodification
of information
goods/services
taxes, subventions
transfers, social insurance
markets for money,
credit, stocks, derivatives
prices of production
labor market
exchange values
prices ~ labor values
commodity/service markets
use values, environmental issues
measured by mass, exergy or ecological footprint
Layer 2: Labour values, small commodity production
The dual Leontief model deals with
the unit prices
pA + q = p
p …row vector of unit prices
q … unit value added.
After substitution of q by life unit
labor input l we get the basic formula
how to compute Marx’ labor values v
vA + l = v.
v = l (E – A)-1
We can split l into wages, w, and
profits p and get
l = w + p.
Marx used other symbols
W = C + V + M,
where W is the labor value,
• C constant capital,
• V variable capital and
• M surplus value.
In our notation:
v = vA + w + p.
Production
Consumption
Labor
Money
Self-employed
laborers
Commodities
&
Services
Basic terms in Marxian Political
Economics
• commodity
• value in use
• value in
exchange
•
•
•
•
(labor)value
constant capital
variable capital
surplus value
• rate of surplus value/rate of
exploitaiton
• organic composition of capital
• rate of profit
two aspects of a commodity
Aristotle (“De Rep.” l. i. c. 9, ~ 350 BC):
“The one is peculiar to the object as such, the other is not, as a sandal
which may be worn, and is also exchangeable. Both are uses of the
sandal, for even he who exchanges the sandal for the money or food he
is in want of, makes use of the sandal as a sandal. But not in its natural
way. For it has not been made for the sake of being exchanged”
Adam Smith (The Wealth of Nations, 1776):
“The word value, it is to be observed, has two different meanings, and
sometimes expresses the utility of some particular object, and
sometimes the power of purchasing other goods which the possession
of that object conveys. The one may be called ‘value in use’; the other,
‘value in exchange.’”
Karl Marx (Das Kapital, Volume One, 1867)
The wealth of those societies in which the capitalist mode of production
prevails, presents itself as ‘an immense accumulation of commodities,’
its unit being a single commodity. Our investigation must therefore
begin with the analysis of a commodity.”
On commodities and markets
• A commodity is a product of human labour
Since Aristotle we know that it has two essential properties (also Adam
Smith and Karl Marx)
• It has value in use
Things or activities/services are useful for somebody for some reason
• and value in exchange
Things or activities have a value for others. They pay a price for it in
the market.
• In the market individual values are compared to each other ->
market value is based on social necessary labor
competition the market creates a tendency
towards more efficiency
• If there is
the composition of labor value w
new labor
(live
labor)
n
w=
c+n
pre-done labor
c
labor value w and its composition
new labor
(live
labor)
pre-done labor
m
surplus value
(profit)
v
variable
capital
(wages)
c
constant
capital
(fix and
circulating
capital)
n
c
w=
c+n=
c+v+m
Three essential indices: rate of exploitation,
organic composition of capital and rate of profit
Rate of exploitation
=m/v
new labor
(live
labor)
pre-done labor
m
surplus value
(profit)
v
variable
capital
(wages)
n
c
c
constant
capital
(fix and
circulating
capital)
Organic composition
of capital
= v / (c + v)
Rate of profit
= m / (c + v)
Rate of profit = rate
of exploitation *
Organic composition
of capital
= m / v * v / (c + v)
New aspects of the labour theory of value
1.
2.
3.
4.
Empirical estimates of labour values
Simple and complex labour
Treating services as value consuming
Transformation of values into prices




Marxian
Von Bortkiewicz
Geometric interpretation
Less abstract transformation
Nr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Industry
Agriculture, hunting
Forestry, logging
Fishing, fish farms
Mining of coal and lignite
Extract. o. crude petrol. a. nat. gas, min. o. metal ores
Other mining and quarrying
Manufacture of food products and beverages
Manufacture of tobacco products
Manufacture of textiles
Manufacture of wearing apparel
Manufacture of leather, leather products, footwear
Manufacture of wood and of products of wood
Manufacture of paper and paper products
Publishing, printing and reproduction
Manufacture of coke, refined petroleum products
Manufacture of chemicals and chemical products
Manufacture of rubber and plastic products
Manufacture of other non-metallic mineral products
Manufacture of basic metals
Manufacture of fabricated metal products
Manufacture of machinery and equipment n.e.c.
Manufacture of office machinery and computers
Manufacture of electrical machinery and apparatus n.e.c.
Manufacture of radio, television equipment
Manuf. of medical, precision, optical instruments, clocks
Manufacture of motor vehicles and trailers
Manufacture of other transport equipment
Manufacture of furniture; manufacturing n.e.c.
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
Recycling
Electricity, gas, steam and hot water supply
Collection, purification and distribution of water
Construction
Sale and repair of motor vehicles; automotive fuel
Wholesale and commission trade
Retail trade, repair of household goods
Hotels and restaurants
Land transport; transport via pipelines
Water transport
Air transport
Supporting a. auxiliary transport activities; travel agencies
Post and tele-communications
Financial intermediation, except insur.
Insurance and pension funding, except social security
Activities auxiliary to financial intermediation
Real estate activities
Renting of machinery and equipment without operator
Computer and related activities
Research and development
Other business activities
Public administration; compulsory social security
Education
Health and social work
Sewage and refuse disposal,sanitation and similar act.
Activities of membership organizations n.e.c.
Recreational, cultural and sporting activities
Other service activities
Private households with employed persons
Stucture of gross output (observed)
c - constant capital, v - variable capital, m - surplus value
Austria 2008: 75 industries (percent)
d
m
v
c
Stucture of gross output (observed)
c - constant capital, v - variable capital, m - surplus value
Austria 2008: 75 industries (percent)
d
m
v
c
Simple and extended reproduction (Marx)
simple reproduction
MEW Bd 24, 396
Extended reproducción
MEW Bd 24, 505
intermediate
inputs
Final demand
(consumption,
„+“ Investment, „=“
exports
minus imports)
Output
Distribucion: costs and income
Use of output
„+“
Value addded
(wages, profits,
depreciation,
taxes)
„=“
Output
Input-Output-Table
Input-Output scheme by Leontief
(1905-1999, Nobel Laureat 1973)
• Primal Problem: Quantities
Ax + y = x
• Dual Problem: Unit-Prices
pA + q = p
A
x
y
p
q
(quadratic) Matrix of techn. coefficients (Leontief Matrix)
output (in quantities), column vector
final demand (in quantities), column vector
unit-price, row vector
unit-value added, row vector
Input-Output
Table
(official
statistics)
„rectangular “:
commodities times
activities
Berechnung einer „quadratischen“ Input-Output
Tabelle nach Sektoren
Statistische Originaltafeln sind „rechteckig“
U...Use-Matrix ... Inputs (Güter x Sektoren)
V...Make-Matrix ... Outputs (Güter x Sektoren)
F...Endnachfrage, W.. Wertschöpfung
Umrechnung in eine quadratische Struktur
(Sektoren x Sektoren) - Standardverfahren
Vorleistungen Ao = V diag(q)-1U diag(g)-1
Wertschöpfung Wo = W
Endnachfrage Fo = V diag(q)-1F
Arbeitszeit no = n
intermediate
inputs
Final demand
(consumption,
„+“ investment,
„=“
exports minus
imports.)
Output
Distribution: costs and incomes
Use of output:
„+“
Value added
(wages, profits,
depreciation,
taxes)
„=“
Output
Input-Output-Table
konstantes
Vorleistungen
Endnachfrage
zirkulierendes
Inputs
(Konsum,
„+“ Investitionen, „=“
Kapital
(Lieferungen
Extended
reproduction
c
zwischen
Exporte
minus
Unternehmen)
Importe)
Output
Distribution: costs and incomes
Marxian terminology
Use of output
„+“
Wertschöpfung
variables
Lebendige
Kapital v
Arbeit
(Löhne,
Gewinn
n
Abschreibung
Mehrwert
Steuern
metc.)
„=“
Output
Wert
w
Input-Output Table
in Marxian terms
Marx: composition of value
Matrix
Ao
Endnachfrage
Output
Constant
Vorleistungen
circulating
Inputs
(Konsum,Vorleistungen
„+“ Investitionen, „=“
Capital
(Lieferungen
c
zwischen
Exporte minus
Unternehmen)
Importe)
consumption
Matrix
„+“
Co
Konsum der
Wertschöpfung
Variable
Lohnabhängigen
Lebendige
capital v
Arbeit
(Löhne,
Gewinn
n value
Abschreibung
Surplus
Steuern
Surplus
metc.)
Matrix
product
S
„=“
o
Output
Value
w
Surplus
Das Marxsche Wertschema
c
+
v
+
m
=
w
Constant
Vorleistungen
circulating
Inputs
(Konsum,Vorleistungen
„+“ Investitionen, „=“
Capital
(Lieferungen
c
zwischen
Exporte minus
Unternehmen)
Importe)
Matrix
„+“
Co
Konsum der
Wertschöpfung
variable
Lohnabhängigen
Lebendige
capital v
Arbeit
(Löhne,
Gewinn
Abschreibung
surplusn value
Steuern
metc.)
Matrix
So
„=“
Output
Value
w
Surplus
Output
Matrix
Ao
Endnachfrage
Consumption
Surplus
product
Observed data:
Current prices, Austria
2008,75 sectors
1
andwirtschat und
Jagd
2
Forstwirtschat und
Holzeinschlag
3
Fischerei und
Aquakultur
4
Kohlenergau
ew..
Erdl.Erdgas
Erzg
Sonst.
Fahrzeugau
27 H.. Meln
26
28
29
30
31
5
ew.. Steinen u.
Erden ienstlstg 
Bergau
6
H.. Nahrungs- und
Futteritteln
7
etrnkeherstellung
8
aakerareitung
9
H.. extilien
36
1
0
H.. Bekleidung
37
1
1
H.. eder
ederwaren und
Schuhen
38
1
2
H.. Holzwaren
Korwaren
1
3
H.. Paier Pae
und Waren daraus
1
4
H..
ruckerzeugnissen
1
5
32
33
34
35
39
40
41
42
5 Versicherungen und
1 Pensionskassen
Mit Finanz- u.
52
Vers.ttigk. er. 
H.. sonst. Waren
rundstcks- und
53
Wohnungswesen
Rearatur u.
5 Rechtseratung und
nstallation .
Wirtschatsrung
4
Maschinen
nternehenshrung Energieersorgung 55 eratung
Architektur- und
Wasserersorgung
56
ngenieurros
Awasser- u.
5 Forschung und
Aallentsorgung
7 Entwicklung
5 Werung und
Rckgewinnung
8 Marktorschung
Hochau
Sonst. reierul.
ieau
5 wiss. u. techn.
Bauinstallation u. 9 tigkeiten
Veterinrwesen
sonst.
6 Verietung .
Ausauttigkeiten
eweglichen Sachen
0
Kz-Handel und 6 Areitskrteerlassun
Rearatur
1g
rohandel o.
Reiseros und
62
Kz)
Reiseeranstalter
Einzelhandel
Err. .
o. Kz)
wirtschatlichen
63
anderkehr u.
ienstleistungen
rans. in
a.n.g.
Rohrernleitungen
entliche
Verwaltung
6
Schiahrt
4 Verteidigung u.
utahrt
Sozialersicherung
Erziehung und
agerei Err.
65
nterricht
. sonst.  r
den Verkehr
Post- und
Kokerei und
43
Minerallerareitung
Kurierdienste
66 esundheitswesen
Alters- und
6
Plegeheie
Structure of „classical“ labour values
all industries are value producers
c - constant capital, v - variable capital, m - surplus value
Austria 2006: 57 industries (percent), r = 0.819
m
v
c
Matrix
Co
Matrix
So
Vorleistungen
Konsum der
Lohnabhängigen
Surplus
Matrix
Co
Konsum der
Lohnabhängigen
Matrix
So
Surplus
=
Output P
=
Output P‘
Matrix
Ao
Generalized Leontief Schema
primal:
(Ao + Co + So)1 = P‘
Quadratic
Input-Output Table
Marx:
c+n=c+v+m=w
where
c = 1‘Ao, v = 1‘Co, m = 1‘So, w = P
Leontief Scheme dual:
1‘(Ao + Co + So) = P
w Ap + n = w
solution:
w = n (E – Ap)-1
Matrix
Ap
Matrix
Ao
Intermediary
goods
Intermediary
goods
in labor time
observed
Matrix
Co
+
Live labor n
value w =
Live labor n times
Leontief-Inverse
(E – Ap)-1
+
=
Value added
“classical“
calculation of labor
values
Po =
1‘(Ao + Co + So)
consumption
+
Matrix
So
surplus
=
Value w
Output at current
prices
Output Po
Output Po at
current prices =
Sum of
intermediate
products,
consumption
and
investment
Labor values and observed data
Empirical results Austria 2005-2008
 Classical definition
 Material definition
Geometric representation of prices and values
Transformation problem a la Marx and von
Bortkiewicz
observed prices and
classic labor values
Austria 2008
75 sectors
Correlation
Coefficient
= 0,883
Structure of labor values, classic, Austria 2008
d
m
v
c
How are the differences produced?
d
v
Prices,
observed 2008
c
d
m
m
v
Labor values,
classic, 2008
c
w Ap + n = w
solution:
w = n (E – Ap)-1
Matrix
Ap
Matrix
Ao
Intermediary
goods
Intermediary
goods
in labor time
observed
Matrix
Co
+
Live labor n
value w =
Live labor n times
Leontief-Inverse
(E – Ap)-1
+
=
Value added
“classical“
calculation of labor
values
Po =
1‘(Ao + Co + So)
consumption
+
Matrix
So
surplus
=
Value w
Output at current
prices
Output Po
Output Po at
current prices =
Sum of
intermediate
products,
consumption
and
investment
The shape of the surplus matrix S determines the
structure of relative prices
• Assumptions:
• A) the basic socio-technical
structure is identical for all
S11 <>0
S12 <> 0
systems of feasible prices.
• B) The sum of the surplus prouct
is constant
• C) Sum of Prices = sum of values
S21 empty S22 empty
• Origin of price changes is a
different allocation of the surplus
product among branches of
production
• Values of commodities and
services are essentially different
Services
• Z.B: Austria 2008: 45 out of 75 Sektoren Commodity
do not sell any investment goods
production
production
S12
The systems of prices
differ by different
allocation of the
S21 empty S22 empty
surplus product
Commodity
production
Services
Production
Services
Surplus
product
Commodities
S11
Surplus matrix
partitioned
General assumptions to determine labour values
• Each hour of labour has the same value
• The labour value of the output of a sector is
proportionate to directly and indirectly spent
average labor time = sum of past and actual labor
• The computation of the labor values are based on
the concept of equivalent exchange: the
enterprises receive for their commodities / services
the full amount of the labor they have used.
• The sum of values = sum of prices, therefore a
comparison of relative prices is possible
Consequences for services
• Enterprises who produce and sell services actually
appropriate parts of the surplus product without
contributing to it with their own production.
• In an economy in equilibrium commodity producing
sectors are therefore unable to realise the full value of
their product in the market – this means a violation of
the principle of equal exchange
• The only possibility for them to realise the full value is to
evaluate services under the condition of simple
reproduction – without appropriation of surplus product
• Therefore we have to evaluate the value of services at
reproduction cost
The labour of some of the most respectable orders in the society
is, like that of menial servants, unproductive of any value, and
does not fix or realize itself in any permanent subject; or vendible
commodity, which endures after that labour is past, and for which
an equal quantity of labour could afterwards be procured...…In
the same class must be ranked, some both of the gravest and
most important, and some of the most frivolous professions:
churchmen, lawyers, physicians, men of letters of all kinds;
players, buffoons, musicians, opera-singers, opera-dancers, &c.
…Like the declamation of the actor, the harangue of the orator,
or the tune of the musician, the work of all of them perishes in
the very instant of its production.
Smith, Adam, An Inquiry into the Nature and Causes of the Wealth of Nations, Book
II, Chapter III, Of the Accumulation of Capital, or of Productive and Unproductive
Labour, http://www.econlib.org/LIBRARY/Smith/smWN.html.
S21 empty S22 empty
S21 empty
S22 empty
Matrix
Co
Matrix
So
Intermediate
products
Consumption of
workers
Surplus
Matrix
Co
Consumption of
workers
Matrix
So
S21 empty
S22 empty
Surplus
=
Output P
=
Output P‘
Matrix
Ao
Generalized Leontief Scheme
primal:
(Ao + Co + So)1 = P‘
Quadratic
Input-Output Table
Marx:
c+n=c+v+m=w
where
c = 1‘Ao, v = 1‘Co, m = 1‘So, w = P
Leontief Scheme dual:
1‘(Ao + Co + So) = P
How to determine labor values where the principle of
equivalent exchange is not violated?
The economy is partitioned into commodity producing sectors
(index 1) and services producing ones (index 2).
A...
C...
D...
A = {
Partitioned matrix of technical coefficients
Partitioned matrix of consumption
Partitioned matrix of depreciation
A 11, A12
A21, A22
n...
w...
E....
},
C=
{
C11, C12
C21, C22
},
D={
D 11, D12
D21, D22
Partitioned row vector of live labor = { n1, n2 }
Partitioned row vector of labor values = { w1, w2 }
Unit matrix
}
Production of value in commodity producing sectors only
Value of output of commodity producers
w1 (A11 + D11) + w2 (A21 + D21) + n1 = w1
Value of output of services (at reproduction cost)
w1 (A12 + D12 + C12) + w2 (A22 + D22 + C22) = w2
=>
Value of output of services w2:
w2 = w1(A12 + D12 + C12). (E22 – A22 - D22 - C22)-1
Value of output of commodity producers w1:
w1 = n1 { E11 – (A11+ D11) – (A12+ D12+ C12).
(E22 – A22 - D22 - C22)-1 (A21 + D21) } -1
Observed prices,
classic labor values and
labor values with
services at reproduction
cost Austria 2008
75 sectors
Coefficients of
correlation
classic:0.883
material:0.839
Structure of labor values, services at reproduction
costs, Austria ,2008
d
m
v
c
No surplus value
31 service sectors without producing investment goods
Branchen
code
Sektor
Branchen
code
46
Großhandelsleistungen (o. Kfz)
73
47
Einzelhandelsleistungen (o. Kfz)
74-75
49
Landverkehrsleist. u. Tranportleist. in
Rohrfernleitungen
50
Schifffahrtsleistungen
51
Luftfahrtleistungen
52
Lagereileistungen, sonst. DL für den Verkehr
53
Post- und Kurierdienste
55-56
Beherbergungs- und Gastronomie-DL
60
Rundfunkveranstaltungsleistungen
61
Telekommunikationsdienstleistungen
64
Finanzdienstleistungen
65
DL v.Versicherungen und Pensionskassen
66
Sektor
Werbe- und Marktforschungs-DL
So. freiberufl., wiss. u. techn. DL; DL d.
Veterinärwesens
77
DL der Vermietung v. beweglichen Sachen
78
DL der Arbeitskräfteüberlassung
79
Reisebüro- und Reiseveranstaltungs-DL
84
DL der öffentl. Verwaltung, Verteidigung u.
Sozialvers.
85
Erziehungs- und Unterrichtsdienstleistungen
86
DL des Gesundheitswesens
87-88
DL von Heimen u.des Sozialwesens
91
DL von Bibliotheken und Museen
92
DL des Spiel-, Wett- und Lotteriewesens
93
DL des Sports, der Unterhaltung und der Erholung
94
DL v. Interessenvertretungen, Kirchen u.a.
Mit Finanz- u. Versicherungsleistungen verb. DL
95
Reparatur von EDV-Geräten und Gebrauchsgütern
70
DL d. Unternehmensführung u. -beratung
96
Sonstige überwiegend persönliche DL
72
Forschungs- und Entwicklungs-DL
Four sectors, producing immaterial investments
Branchencode
58
59
62-63
90
Sektor
DL des Verlagswesens
DL d. Filmherstellung, d. -vertriebs u. -verleihs; Kino-DL
DL d. Informationstechnologie; Informations-DL
Kreative, künstlerische und unterhaltende DL
Sum of output prices of the sectors 58, 59, 62/63 und 90
4.709.586,00
Total sum of all investments in Euro
61.144.849,00
Consequences
• The extension the services is ceteris paribus
connected with a lower accumulation rate in the
average, because the produced surplus product
will become relatively more scarce as the
advances of capital increase
• Eventually this could be an explanation of the
smaller growth rates in developed economies with
a high share of services.
• In addition to that there is also a self-strangulation
of effective demand by restrictive wage policy
Transformation problem
By Marx and von Bortkiewicz
Transformation problem
Transition from level 2 (labor values)
To level 3 (prices of production)
The physical parameters (primal problem) are not
changed by Marx
Captalism of perfect competition
Small commodity
production
Physical
basis
Prices of production, labor market
Labor values,
commodity and
services markets
use values,
materials, energy, ecologic dimension
Transformation problem can be seen as “experiment of
thought”
There are two different ideal types of economic systems
1. Small commodity production: producers work for their
own, without fixed capital, without wage labor. Prices will
finally become proportionate to labor values
2. Capitalistic Produktion: wage labor exists, capitalists
invest in sectors with higher rate of profit than their own.
Expectation by Marx: Rates of profit approach a general
rate of profit. Prices change to prices of production,
proportionate to capital advanced.
3. Quantities remain invariant by transformation
Transformation problem
• Marx explained the modification of values by competition of
capitalists
• He assumed that the movements come to an end if all the rates of
profit are equal.
• In a mathematical perspective he described the first step of an
iterative process – similar to Andrew Kliman’s Temporal Single
System Interpretation (TSSI).
• The repeated application of Marx’ method (but also of TSSI) leads to
the solution by von Bortkiewicz resp. to the Simultaneous Single
System Interpretation (SSSI) (i. e. input prices become equal to
output prices)
• One should not see SSSI and TSSI in Opposition, but as a process
which contains both moments.
Transformation problem: from labor values to prices of
production
Marx‘ solution
pp(0) = w or w* (classic or material labor values, in general: any starting
value can be chosen)
pp(1) = pp(0) R [1 + r(i)], R = A + C + D ... Matrix of reproduktion r(i) Profitrate
1 + r(i) = pp(i) x / [pp(i) R x],
i...counter for iteration
Problem: prices of input ≠ prices of output
von Bortkiewicz‘ solution
two identical solutions
a)
Eigenvector solution: pp ... left-Eigenvector of R
pp R (1 + r) = pp,
largest Eigenvector ofR: λ=1/(1+r)
b) iterative solution: i -> ∞
pp = pp(∞)
pp(i) = pp(i-1) R [1 + r(i-1)], 1 + r(i) = pp(i) x / [pp(i) R x]
Under the condition pp(i) x = const for all price systems =>
location of all prices vectors is a hyperplane in an ndimensional space.
Several Price Systems
• Prices observed:
P (Az + Cz + Sz) = P
• Classic labor values (all sectors produce value)
Pk = n (E-Az)-1
• „Material“ labor values (material production only produces
value)
Ps
• Prices of production with circulating capital only, equal rates of
profit)
Pzk
• Prices of production with fixed capital, equal rates of profit
Pfk
The different price systems are linked to different distributions of
the surplus product resp. surplus value.
The sum of the surplus product is always constant
Geometric Interpretation
of volume and price vectors
Sector 3
x quantities
pw classic labor values
p observed prices
The hyperplane
1-2-3 is the
location of all
feasible price
systems where
pi x = const
Assumption: total
sum of values
and prices are
pp prices of production
always equal
ps „material“ labor values
O
Sector 1
Sector 2
Layer 3: prices of production, capitalist economy at perfect
competition („Transformation Problem“)
Marx provided us with the following solution for p:
p = v (K + A + C) (1 + r), where r = v (I - A - C) x / v (K + A + C) x
and v = l (I – A)-1
K…matrix of capital coefficients per unit of output, I …identity matrix with ones in
its main diagonal, otherwise zeros, and r is the average rate of profit.
This method can be generalized to an iteration process which leads us to the
solution proposed by von Bortkiewicz in the beginning of the 20th century (which
is equal to the solution of an eigenvector/eigenvalue problem). The generalized
iteration scheme inspired by Marx is:
pi (K + A + C) (1 + ri) = pi+1 where ri = pi (I - A - C) x / pi (K + A + C) x,
ri … average profit rate at iteration step i.
Different turnover times neglected, and assumed that they are all equal to one.
The link to labor time is kept up because the iteration scheme starts from the
solution of equation (3) for v
p0 = v = l (I – A)-1, where r0 = p0 (I - A - C) x / p0 (K + A + C) x
Prices of production:
Empirical results for Austria
2005 - 2008
Structure of prices of production a la Marx
Austria 2008, only one iteration
d
m
v
Rates of profit can be negativ.
They are not equal.
c (measured in terms of output
prices)
Structure of prices of production a la Marx
2008, 2nd Iteration
d
m
v
c
Structure of prices of production a la Marx
2008, 3rd Iteration
d
m
v
c
Structure of prices of production a la Marx
2008, 4th Iteration
d
m
v
c
Structure of prices of production a la Marx
2008, 5th Iteration
d
m
v
c
Structure of prices of production a la Bortkiewicz
Austria 2008, (without fixed Capital)
d
m
v
c
Observed prices
and prices of
production without
fixed capital
Austria 2008
75 sectors
Coeff.of
correlation:
0,978
Structure of prices of production a la Bortkiewicz
Austria 2007, with fixed and circulating constant capital,
57 Sectors
d
m
v
c
Structure of prices of production a la Bortkiewicz
Austria 2007, with fixed and circulating constant capital
Standardized to total advanced capital plus
surplus value m/(cfix+czirk+v+m)
Observed prices, prices
of production with and
without fixed capital,
Austria 2007
57 sectors
Koeff. Of corr:
Without K_fix: 0.978
with K_fix: 0.970
Summary:
correlations of specific price systems with observed
prices: Austria 2005-2008
Year
Labor value Labor value PriceofProd PriceofProd PriceofProd
classic
„material“ Marx 1 Iter. circ Cap circ+fix cap
2005
0.872
0.829
0.920
0.980
0.971
2006
0.877
0.834
0.920
0.979
0.970
2007
0.895
0.857
0.933
0.978
0.970
2008
0.883
0.839
0.924
0.979
-
Indicators for labor values and worked minutes per
Euro in Austria 2005-2008
Year
Euro per
hour
classic
Euro per
hour
material
Minutes per
Euro
classic
Minutes
per Euro
material
Unit Value
(Index
2005 = 100)
2005
28,85
35,96
2,08
1,67
100
2006
30,66
38,79
1,96
1,55
95,05
2007
31,77
40,96
1,89
1,46
91,52
2008
32,82
44,38
1,83
1,35
88,48
Thanks for your attention!
Contact:
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