Peter Fleissner, catedr

1
4th International Vanguard Science CongressThe
role of Science, Technology and Geo-Politics in
the Self-Determination of Mankind  Ciudad de
México, May 28-30, 2013Universidad 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 Marxs labour theory of
value.

• Peter Fleissner, catedrático de cibernética
  social, Viena, Austria
• contacto fleissner_at_arrakis.es

2
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)

3
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).

4
Economic Reality A Complex Construction
Contemporary Capitalism
market prices (observed)
7 6 5 4 3 2 1
commodification of information goods/services
Information Society Finance market
capitalism information as commodity,
communication as commercial service
Public sector State monopoly capitalism
taxes, subventions transfers, social insurance
Globalized economy Finance capitalism Internation
al financial capital
markets for money, credit, stocks, derivatives
Capitalism with perfect competition and fixed
capital
prices of production labor market
Commodity production of self employed
exchange values prices labor values commodity/se
rvice markets
Physical basis
use values, environmental issues measured by
mass, exergy or ecological footprint
5
The Economy seen as a self organization process
(historical and logical view)
market prices (observed)
Contemporary Capitalism
7 6 5 4 3 2 1
commodification of information goods/services
Information Society information as commodity,
communication as commercial service
Public sector
Globalized economy International financial capital
Capitalism with perfect competition and fixed
capital
older newer
Logic Dominance
Commodity production of self employed
Inspired by Hofkirchner , W. (2002) Projekt
Eine Welt Kognition Kommunikation
Kooperation. LIT-Verlag Münster-Hamburg- London.
p. 166
Physical basis
History Emergence
6
Economic Reality A Complex Construction
market prices (observed)
Contemporary Capitalism
7 6 5 4 3 2 1
commodification of information goods/services
Information Society information as commodity,
communication as commercial service
Public sector
taxes, subventions transfers, social insurance
Globalized economy International financial capital
markets for money, credit, stocks, derivatives
Capitalism with perfect competition and fixed
capital
prices of production labor market
Commodity production of self employed
exchange values prices labor values commodity/se
rvice markets
Physical basis
use values, environmental issues measured by
mass, exergy or ecological footprint
7
Layer 1 Use values, produced and consumed under
a certain division of labor

• Mathematical description in terms of Leontiefs
  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.

8
Economic Reality A Complex Construction
market prices (observed)
7 6 5 4 3 2 1
Contemporary Capitalism
commodification of information goods/services
Information Society information as commodity,
communication as commercial service
Public sector
taxes, subventions transfers, social insurance
Globalized economy International financial capital
markets for money, credit, stocks, derivatives
Capitalism with perfect competition and fixed
capital
prices of production labor market
Commodity production of self employed
exchange values prices labor values commodity/se
rvice markets
Physical basis
use values, environmental issues measured by
mass, exergy or ecological footprint
9
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.

10
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

11
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12
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.

13
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 -gt market value is based on social
  necessary labor
• If there is competition the market creates a
  tendency towards more efficiency

14
the composition of labor value w
new labor (live labor)
n
w c n
c
pre-done labor
15
labor value w and its composition
m
surplus value (profit)
new labor (live labor)
n
w c n c v m
variable capital (wages)
v
c
c
constant capital (fix and circulating capital)
pre-done labor
16
Three essential indices rate of exploitation,
organic composition of capital and rate of profit
Rate of exploitation m / v 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)
m
surplus value (profit)
new labor (live labor)
n
variable capital (wages)
v
c
c
constant capital (fix and circulating capital)
pre-done labor
17
New aspects of the labour theory of value

• 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

18
Nr Industry
1 Agriculture, hunting
2 Forestry, logging
3 Fishing, fish farms
4 Mining of coal and lignite
5 Extract. o. crude petrol. a. nat. gas, min. o. metal ores
6 Other mining and quarrying
7 Manufacture of food products and beverages
8 Manufacture of tobacco products
9 Manufacture of textiles
10 Manufacture of wearing apparel
11 Manufacture of leather, leather products, footwear
12 Manufacture of wood and of products of wood
13 Manufacture of paper and paper products
14 Publishing, printing and reproduction
15 Manufacture of coke, refined petroleum products
16 Manufacture of chemicals and chemical products
17 Manufacture of rubber and plastic products
18 Manufacture of other non-metallic mineral products
19 Manufacture of basic metals
20 Manufacture of fabricated metal products
21 Manufacture of machinery and equipment n.e.c.
22 Manufacture of office machinery and computers
23 Manufacture of electrical machinery and apparatus n.e.c.
24 Manufacture of radio, television equipment
25 Manuf. of medical, precision, optical instruments, clocks
26 Manufacture of motor vehicles and trailers
27 Manufacture of other transport equipment
28 Manufacture of furniture manufacturing n.e.c.
29 Recycling
30 Electricity, gas, steam and hot water supply
31 Collection, purification and distribution of water
32 Construction
33 Sale and repair of motor vehicles automotive fuel
34 Wholesale and commission trade
35 Retail trade, repair of household goods
36 Hotels and restaurants
37 Land transport transport via pipelines
38 Water transport
39 Air transport
40 Supporting a. auxiliary transport activities travel agencies
41 Post and tele-communications
42 Financial intermediation, except insur.
43 Insurance and pension funding, except social security
44 Activities auxiliary to financial intermediation
45 Real estate activities
46 Renting of machinery and equipment without operator
47 Computer and related activities
48 Research and development
49 Other business activities
50 Public administration compulsory social security
51 Education
52 Health and social work
53 Sewage and refuse disposal,sanitation and similar act.
54 Activities of membership organizations n.e.c.
55 Recreational, cultural and sporting activities
56 Other service activities
57 Private households with employed persons
19
Stucture of gross output (observed) c - constant
capital, v - variable capital, m - surplus
valueAustria 2008 75 industries (percent)
d
m
v
c
20
Stucture of gross output (observed) c - constant
capital, v - variable capital, m - surplus
valueAustria 2008 75 industries (percent)
21
Simple and extended reproduction (Marx)
simple reproduction
MEW Bd 24, 396
Extended reproducción
MEW Bd 24, 505
22
Input-Output-Table
Use of output
intermediate inputs
Final demand (consumption, Investment, exports
minus imports)


Output
Distribucion costs and income

Value addded (wages, profits, depreciation,
taxes)

Output
23
Input-Output scheme by Leontief(1905-1999, Nobel
Laureat 1973)

• Primal Problem Quantities
• Ax y x
• Dual Problem Unit-Prices
• pA q p
• A (quadratic) Matrix of techn. coefficients
  (Leontief Matrix)
• x output (in quantities), column vector
• y final demand (in quantities), column vector
• p unit-price, row vector
• q unit-value added, row vector

24
Input-Output Table (official statistics)
rectangular commodities times activities
25
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

26
Input-Output-Table
Use of output
intermediate inputs
Final demand (consumption, investment, exports
minus imports.)


Output
Distribution costs and incomes

Value added (wages, profits, depreciation, taxes)

Output
27
Input-Output Tablein Marxian terms
Marxian terminology
Use of output
konstantes zirkulierendes Kapital c
Vorleistungen Inputs (Lieferungen zwischen
Unternehmen)
Endnachfrage (Konsum, Investitionen, Exporte
minus Importe)


Output
Extended reproduction
Distribution costs and incomes

Lebendige Arbeit n
Wertschöpfung (Löhne, Gewinn Abschreibung Steuer
n etc.)

Output
Wert w
28
Marx composition of value
Matrix Ao Vorleistungen
Constant circulating Capital c
Vorleistungen Inputs (Lieferungen zwischen
Unternehmen)
Endnachfrage (Konsum, Investitionen, Exporte
minus Importe)


Output
Matrix Co Konsum der Lohnabhängigen
consumption

Lebendige Arbeit n
Wertschöpfung (Löhne, Gewinn Abschreibung Steuer
n etc.)
Surplus product
Matrix So Surplus

Output
Value w
29
Das Marxsche Wertschema
Matrix Ao Vorleistungen
Constant circulating Capital c
Vorleistungen Inputs (Lieferungen zwischen
Unternehmen)
Endnachfrage (Konsum, Investitionen, Exporte
minus Importe)


Output
c v m w
Matrix Co Konsum der Lohnabhängigen
Con-sumption

Lebendige Arbeit n
Wertschöpfung (Löhne, Gewinn Abschreibung Steuer
n etc.)
Surplus product
Matrix So Surplus

Output
Value w
30
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31
51 Versicherungen und Pensionskassen
52 Mit Finanz- u. Vers.tätigk. verb. DL
53 Grundstücks- und Wohnungswesen
54 Rechtsberatung und Wirtschaftsprüfung
55 Unternehmensführung, -beratung
56 Architektur- und Ingenieurbüros
57 Forschung und Entwicklung
58 Werbung und Marktforschung
59 Sonst. freiberufl., wiss. u. techn. Tätigkeiten Veterinärwesen
60 Vermietung v. beweglichen Sachen
61 Arbeitskräfteüberlassung
62 Reisebüros und Reiseveranstalter
63 Erbr. v. wirtschaftlichen Dienstleistungen a.n.g.
64 Öffentliche Verwaltung, Verteidigung u. Sozialversicherung
65 Erziehung und Unterricht
66 Gesundheitswesen
67 Alters- und Pflegeheime Sozialwesen
68 Künstlerische Tätigkeiten
69 Bibliotheken und Museen
70 Spiel-, Wett- und Lotteriewesen
71 Erbr. v. DL d. Sports, d. Unterhaltung u. Erholung
72 Interessensvertretungen und Vereine
73 Reparatur v. Gebrauchsgütern
74 Erbr. v. sonst. pers. DL
75 Private Haushalte mit Hauspersonal
1 Landwirtschaft und Jagd
2 Forstwirtschaft und Holzeinschlag
3 Fischerei und Aquakultur
4 Kohlenbergbau Gew.v. Erdöl,.Erdgas Erzbgb
5 Gew.v. Steinen u. Erden Dienstlstg f Bergbau
6 H.v. Nahrungs- und Futtermitteln
7 Getränkeherstellung
8 Tabakverarbeitung
9 H.v. Textilien
10 H.v. Bekleidung
11 H.v. Leder, Lederwaren und Schuhen
12 H.v. Holzwaren Korbwaren
13 H.v. Papier, Pappe und Waren daraus
14 H.v. Druckerzeugnissen
15 Kokerei und Mineralölverarbeitung
16 H.v. chemischen Erzeugnissen
17 H.v. pharmazeutischen Erzeugnissen
18 H.v. Gummi- und Kunststoffwaren
19 H.v. Glas u. Glaswaren, Keramik u. Ä.
20 Metallerzeugung und -bearbeitung
21 H.v. Metallerzeugnissen
22 H.v. Datenverarbeitungsgeräten, elektron. u
23 H.v. elektrischen Ausrüstungen
24 Maschinenbau
25 H.v. Kraftwagen und -teilen
26 Sonst. Fahrzeugbau
27 H.v. Möbeln
28 H.v. sonst. Waren
29 Reparatur u. Installation v. Maschinen
30 Energieversorgung
31 Wasserversorgung
32 Abwasser- u. Abfallentsorgung, Rückgewinnung
33 Hochbau
34 Tiefbau
35 Bauinstallation u. sonst. Ausbautätigkeiten
36 Kfz-Handel und -Reparatur
37 Großhandel (o. Kfz)
38 Einzelhandel (o. Kfz)
39 Landverkehr u. Transp. in Rohrfernleitungen
40 Schifffahrt
41 Luftfahrt
42 Lagerei, Erbr. v. sonst. DL für den Verkehr
43 Post- und Kurierdienste
44 Beherbergung u. Gastronomie
45 Verlagswesen
46 Herst., Verleih u. Vertrieb v. Filmen Kinos
47 Rundfunkveranstalter
48 Telekommunikation
49 Erbr. v. DL d. Informations-technologie Informations-DL
50 Erbr. v. Finanzdienstleistungen
Verzeichnis der 75 Sektoren der
österreichischen Wirtschaft
32
Structure of classical labour values all
industries are value producers c - constant
capital, v - variable capital, m - surplus
valueAustria 2006 57 industries (percent), r
0.819
m
v
c
33
Matrix Ao Vorleistungen
Matrix Co Konsum der Lohnabhängigen
Matrix So Surplus
Output P

Generalized Leontief Schema primal (Ao Co
So)1 P Marx c n c v m w where c
1Ao, v 1Co, m 1So, w P
Matrix Co Konsum der Lohnabhängigen
Quadratic Input-Output Table
Leontief Scheme dual 1(Ao Co So) P
Matrix So Surplus

Output P
34
classical calculation of labor values w Ap
n w solution w n (E Ap)-1 value w
Live labor n times Leontief-Inverse (E Ap)-1
Matrix Ap Intermediary goods in labor time
Matrix Ao Intermediary goods observed
Output at current prices Po 1(Ao Co
So) Output Po at current prices Sum of
intermediate products, consumption and
investment
Marx
Input-Output

Matrix Co consumption

Live labor n

Value added
Matrix So surplus


Output Po
Value w
35

• 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

36
observed prices and classic labor values
Austria 2008 75 sectors
Correlation Coefficient 0,883
37
Structure of labor values, classic, Austria 2008
d
m
v
c
38
How are the differences produced?
Prices, observed 2008
Labor values, classic, 2008
39
classical calculation of labor values w Ap
n w solution w n (E Ap)-1 value w
Live labor n times Leontief-Inverse (E Ap)-1
Matrix Ap Intermediary goods in labor time
Matrix Ao Intermediary goods observed
Output at current prices Po 1(Ao Co
So) Output Po at current prices Sum of
intermediate products, consumption and
investment
Marx
Input-Output

Matrix Co consumption

Live labor n

Value added
Matrix So surplus


Output Po
Value w
40
The shape of the surplus matrix S determines the
structure of relative prices

• Assumptions
• A) the basic socio-technical structure is
  identical for all systems of feasible prices.
• B) The sum of the surplus prouct is constant
• C) Sum of Prices sum of values
• Origin of price changes is a different allocation
  of the surplus product among branches of
  production
• Values of commodities and services are
  essentially different
• Z.B Austria 2008 45 out of 75 Sektoren do not
  sell any investment goods

S11 ltgt0
S12 ltgt 0
S21 empty
S22 empty
Commodity production
Services production
41
Surplus matrix partitioned
S11
S12
Surplus product
Commodities
The systems of prices differ by different
allocation of the surplus product
S21 empty
S22 empty
Services
Services Production
Commodity production
42
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

43
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

44
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.

• 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.

45
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46
Matrix Ao Intermediate products
Matrix Co Consumption of workers
Matrix So Surplus
Output P

Generalized Leontief Scheme primal (Ao Co
So)1 P Marx c n c v m w where c
1Ao, v 1Co, m 1So, w P
Matrix Co Consumption of workers
Quadratic Input-Output Table
Leontief Scheme dual 1(Ao Co So) P
Matrix So Surplus

Output P
47
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... Partitioned matrix of technical coefficients
• C... Partitioned matrix of consumption
• D... Partitioned matrix of depreciation
• A 11, A12 C11, C12
  D 11, D12
• A , C , D
  
• A21, A22 C21, C22
  D21, D22
• n... Partitioned row vector of live labor
  n1, n2
• w... Partitioned row vector of labor values
  w1, w2
• E.... Unit matrix

48
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
• gt 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

49
Coefficients of correlation classic0.883
material0.839
Observed prices, classic labor values and labor
values with services at reproduction cost Austria
2008 75 sectors
50
Structure of labor values, services at
reproduction costs, Austria ,2008
No surplus value
d
m
v
c
51
31 service sectors without producing investment
goods
Branchen code Sektor
46 Großhandelsleistungen (o. Kfz)
47 Einzelhandelsleistungen (o. Kfz)
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 Mit Finanz- u. Versicherungsleistungen verb. DL
70 DL d. Unternehmensführung u. -beratung
72 Forschungs- und Entwicklungs-DL
Branchen code Sektor
73 Werbe- und Marktforschungs-DL
74-75 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.
95 Reparatur von EDV-Geräten und Gebrauchsgütern
96 Sonstige überwiegend persönliche DL
97 DL privater Haushalte mit Hauspersonal
52
Four sectors, producing immaterial investments
Branchencode Sektor
58 DL des Verlagswesens
59 DL d. Filmherstellung, d. -vertriebs u. -verleihs Kino-DL
62-63 DL d. Informationstechnologie Informations-DL
90 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
53
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

54

• Transformation problem
• By Marx and von Bortkiewicz

55
Transformation problem

• Transition from level 2 (labor values)
• To level 3 (prices of production)
• The physical parameters (primal problem) are not
  changed by Marx

56
Transformation problem can be seen as experiment
of thought

• There are two different ideal types of economic
  systems
• Small commodity production producers work for
  their own, without fixed capital, without wage
  labor. Prices will finally become proportionate
  to labor values
• 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.
• Quantities remain invariant by transformation

57
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 Klimans 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.

58
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 ?1/(1r)
• b) iterative solution i -gt 8
• pp pp(8)
• 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 gt location of all prices vectors
  is a hyperplane in an n-dimensional space.

59
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

60
Geometric Interpretation of volume and price
vectors
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 always equal
ps material labor values
61
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 Kmatrix 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)
pi1 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  
62

• Prices of production
• Empirical results for Austria
• 2005 - 2008

63
Structure of prices of production a la Marx
Austria 2008, only one iteration
64
Structure of prices of production a la Marx
2008, 2nd Iteration
d
m
v
c
65
Structure of prices of production a la Marx
2008, 3rd Iteration
d
m
v
c
66
Structure of prices of production a la Marx
2008, 4th Iteration
d
m
v
c
67
Structure of prices of production a la Marx
2008, 5th Iteration
d
m
v
c
68
Structure of prices of production a la
BortkiewiczAustria 2008, (without fixed Capital)
d
m
v
c
69
Observed prices and prices of production without
fixed capital Austria 2008 75 sectors
Coeff.of correlation 0,978
70
Structure of prices of production a la
BortkiewiczAustria 2007, with fixed and
circulating constant capital, 57 Sectors
d
m
v
c
71
Structure of prices of production a la
BortkiewiczAustria 2007, with fixed and
circulating constant capital
Standardized to total advanced capital plus
surplus value m/(cfixczirkvm)
72
Koeff. Of corr Without K_fix 0.978 with K_fix
0.970
Observed prices, prices of production with and
without fixed capital, Austria 2007 57 sectors
73
Summary correlations of specific price systems
with observed prices Austria 2005-2008
Year Labor value classic Labor value material PriceofProd Marx 1 Iter. PriceofProd circ Cap PriceofProd circfix 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 -
74
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
75

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