peter fleissner, catedrático de cibernética social, viena, austria contacto : fleissner@arrakis.es

Peter Fleissner, catedrático de cibernética social, Viena, Austria

contacto: fleissner@arrakis.es

4th International Vanguard Science CongressThe 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.

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

use values, environmental issuesmeasured by mass, exergy or ecological footprint

exchange valuesprices ~ labor values

commodity/service markets

prices of productionlabor market

markets for money,credit, stocks, derivatives

Commodity productionof self employed

Physical basis

Public sector: State monopoly capitalism taxes, subventions

transfers, social insurance

Globalized economy: Finance capitalismInternational financial capital

market prices(observed)

Capitalism with perfect competitionand fixed capital

Information Society: Finance market capitalisminformation as commodity, communication as commercial service

commodificationof information

goods/services

7

6

5

4

3

2

1

Contemporary Capitalism

The Economy – seen as a self organization process (historical and logical view)

Commodity productionof self employed

Physical basis

Public sector

Globalized economyInternational financial capital

market prices(observed)

Capitalism with perfect competitionand fixed capital

Information Society: information as commodity, communication as commercial service

commodificationof information

goods/services

7

6

5

4

3

2

1

History: Emergence

Logic: Dom

inance

older

newer

Inspired by: Hofkirchner , W. (2002): Projekt Eine Welt: Kognition – Kommunikation – Kooperation.LIT-Verlag Münster-Hamburg-London. p. 166

Contemporary Capitalism

Economic Reality – A Complex Construction

use values, environmental issuesmeasured by mass, exergy or ecological footprint

exchange valuesprices ~ labor values

commodity/service markets

prices of productionlabor market

markets for money,credit, stocks, derivatives

Commodity productionof self employed

Physical basis

Public sector taxes, subventions

transfers, social insurance

Globalized economyInternational financial capital

Contemporary Capitalismmarket prices

(observed)

Capitalism with perfect competitionand fixed capital

commodificationof information

goods/services

7

6

5

4

3

2

1

Information Society: information as commodity, communication as commercial service

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

use values, environmental issuesmeasured by mass, exergy or ecological footprint

exchange valuesprices ~ labor values

commodity/service markets

prices of productionlabor market

markets for money,credit, stocks, derivatives

Commodity productionof self employed

Physical basis

Public sector taxes, subventions

transfers, social insurance

Globalized economyInternational financial capital

market prices(observed)

Capitalism with perfect competitionand fixed capital

Information Society: information as commodity, communication as commercial service

commodificationof information

goods/services

7

6

5

4

3

2

1

Contemporary Capitalism

Layer 2: Labour values, small commodity production

Production Consumption

Self-employed laborersMoney

Labor

Commodities&

Services

The dual Leontief model deals with the unit prices

pA + q = pp …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 and get

l = w + .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 + .

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

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.”

two aspects of a commodity

On commodities and markets

• A commodity is a product of human labourSince 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 exchangeThings 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

• If there is competition the market creates a tendency towards more efficiency

the composition of labor value w

n

c

w = c + n

new labor(live labor)

pre-done labor

new labor(live labor) n

pre-done labor

m

c

v

c

constantcapital(fix and

circulatingcapital)

variablecapital

(wages)

surplus value(profit)

w = c + n =

c + v + m

labor value w and its composition

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)

new labor(live labor) n

pre-done labor

m

c

v

c

constantcapital(fix and

circulatingcapital)

variablecapital

(wages)

surplus value(profit)

New aspects of the labour theory of value

1. Empirical estimates of labour values 2. Simple and complex labour3. Treating services as value consuming4. Transformation of values into prices

Marxian Von Bortkiewicz Geometric interpretation Less abstract transformation

29 Recycling30 Electricity, gas, steam and hot water supply31 Collection, purification and distribution of water32 Construction33 Sale and repair of motor vehicles; automotive fuel34 Wholesale and commission trade35 Retail trade, repair of household goods36 Hotels and restaurants37 Land transport; transport via pipelines38 Water transport39 Air transport40 Supporting a. auxiliary transport activities; travel agencies41 Post and tele-communications42 Financial intermediation, except insur. 43 Insurance and pension funding, except social security44 Activities auxiliary to financial intermediation45 Real estate activities46 Renting of machinery and equipment without operator47 Computer and related activities48 Research and development49 Other business activities50 Public administration; compulsory social security51 Education52 Health and social work53 Sewage and refuse disposal,sanitation and similar act.54 Activities of membership organizations n.e.c.55 Recreational, cultural and sporting activities56 Other service activities57 Private households with employed persons

Nr Industry

1 Agriculture, hunting2 Forestry, logging3 Fishing, fish farms4 Mining of coal and lignite5 Extract. o. crude petrol. a. nat. gas, min. o. metal ores6 Other mining and quarrying7 Manufacture of food products and beverages8 Manufacture of tobacco products9 Manufacture of textiles

10 Manufacture of wearing apparel11 Manufacture of leather, leather products, footwear12 Manufacture of wood and of products of wood13 Manufacture of paper and paper products14 Publishing, printing and reproduction15 Manufacture of coke, refined petroleum products16 Manufacture of chemicals and chemical products17 Manufacture of rubber and plastic products18 Manufacture of other non-metallic mineral products19 Manufacture of basic metals20 Manufacture of fabricated metal products21 Manufacture of machinery and equipment n.e.c.22 Manufacture of office machinery and computers23 Manufacture of electrical machinery and apparatus n.e.c.24 Manufacture of radio, television equipment25 Manuf. of medical, precision, optical instruments, clocks26 Manufacture of motor vehicles and trailers27 Manufacture of other transport equipment28 Manufacture of furniture; manufacturing n.e.c.

Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus value

Austria 2008: 75 industries (percent)

c

v

m

d

Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus value

Austria 2008: 75 industries (percent)

c

v

m

d

Simple and extended reproduction (Marx)

MEW Bd 24, 396

MEW Bd 24, 505

simple reproduction

Extended reproducción

Input-Output-Table

„+“

„+“

„=“

„=“

intermediate inputs

Final demand(consumption, Investment, exports minus imports)

Out

put

Value addded (wages, profits, depreciation,

taxes)

Dis

trib

ucio

n: c

osts

and

inco

me

Use of output

Output

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

• Primal Problem: QuantitiesAx + y = x

• Dual Problem: Unit-PricespA + q = p

A (quadratic) Matrix of techn. coefficients (Leontief Matrix)x output (in quantities), column vectory final demand (in quantities), column vectorp unit-price, row vectorq 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) - StandardverfahrenVorleistungen Ao = V diag(q)-1U diag(g)-1

Wertschöpfung Wo = W

Endnachfrage Fo = V diag(q)-1F

Arbeitszeit no = n

Input-Output-Table

„+“

„+“

„=“

„=“

intermediate inputs

Final demand(consumption, investment, exports minus imports.)

Out

put

Value added (wages, profits, depreciation,

taxes)

Dis

trib

utio

n: c

osts

and

inco

mes

Use of output:

Output

Output

Input-Output Tablein Marxian terms

„+“

„+“

„=“

„=“

Vorleistungen Inputs(Lieferungen zwischen Unternehmen)

Endnachfrage(Konsum, Investitionen,Exporte minusImporte)

Out

put

Wertschöpfung (Löhne, GewinnAbschreibungSteuern etc.)

Wert w

Marxian terminology

konstanteszirkulierendes

Kapitalc

LebendigeArbeit

n

Extended reproduction

variables Kapital v

Mehrwertm

Use of output

Dis

trib

utio

n: c

osts

and

inco

mes

Output

„+“

„+“

„=“

„=“

Vorleistungen Inputs(Lieferungen zwischen Unternehmen)

Endnachfrage(Konsum, Investitionen,Exporte minusImporte)

Out

put

Wertschöpfung (Löhne, GewinnAbschreibungSteuern etc.)

Value w

Marx: composition of value

Constant circulating

Capital c

LebendigeArbeit

n

Variable capital v

Surplus value

m

MatrixAo

Vorleistungen

MatrixCo

Konsum der

Lohnabhängigen

MatrixSo

Surplus

consumption

Surplus product

Output

„+“

„+“

„=“

„=“

Vorleistungen Inputs(Lieferungen zwischen Unternehmen)

Endnachfrage(Konsum, Investitionen,Exporte minusImporte)

Out

put

Wertschöpfung (Löhne, GewinnAbschreibungSteuern etc.)

Value w

Das Marxsche Wertschema

Constant circulating

Capital c

LebendigeArbeit

n

variable capital v

surplus valuem

MatrixAo

Vorleistungen

MatrixCo

Konsum der

Lohnabhängigen

MatrixSo

Surplus

Con-sumption

Surplusproduct

c

+

v

+

m

=w

Observed data: Current prices, Austria2008,75 sectors

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

c

v

m

MatrixAo

Vorleistungen

MatrixCo

Konsum der

Lohnabhängigen

MatrixSo

Surplus

Output P

MatrixCo

Konsum der

Lohnabhängigen

MatrixSo

Surplus

Out

put

P‘

=

=

Generalized Leontief Schema primal:(Ao + Co + So)1 = P‘

Marx:c + n = c + v + m = w wherec = 1‘Ao, v = 1‘Co, m = 1‘So, w = P

Leontief Scheme dual:1‘(Ao + Co + So) = P

Quadratic Input-Output Table

MatrixAp

Intermediary

goods

in labor time MatrixCo

consumption

MatrixSo

surplus

Value w

=

“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

Live labor n

+

MatrixAo

Intermediary

goods

observed

+

+

Output Po

=

Val

ue a

dded

Output at current prices

Po =1‘(Ao + Co + So)

Output Po at current prices =Sum of intermediate products, consumption and investment

Labor values and observed data

Empirical results Austria 2005-2008Classical definitionMaterial 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

c

v

m

d

How are the differences produced?

c

v m

d c

v

m

d

Labor values,classic, 2008

Prices, observed 2008

MatrixAp

Intermediary

goods

in labor time MatrixCo

consumption

MatrixSo

surplus

Value w

=

“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

Live labor n

+

MatrixAo

Intermediary

goods

observed

+

+

Output Po

=

Val

ue a

dded

Output at current prices

Po =1‘(Ao + Co + So)

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 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

Commodityproduction

Servicesproduction

S21 empty S22 empty

S11 <>0 S12 <> 0

S21 empty S22 empty

S11 S12

Services Production

Commodityproduction

Ser

vice

sC

omm

oditi

es

Sur

plus

pr

oduc

t

Surplus matrixpartitioned

The systems of pricesdiffer by different allocation of thesurplus product

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

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.

MatrixAo

Intermediate

products

MatrixCo

Consumption of

workers

MatrixSo

Surplus

Output P

MatrixCo

Consumption of

workers

MatrixSo

Surplus

Out

put

P‘

=

=

Generalized Leontief Scheme primal:(Ao + Co + So)1 = P‘

Marx:c + n = c + v + m = w wherec = 1‘Ao, v = 1‘Co, m = 1‘So, w = P

Leontief Scheme dual:1‘(Ao + Co + So) = P

QuadraticInput-Output Table

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 coefficientsC... Partitioned matrix of consumptionD... 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

Production of value in commodity producing sectors only

Value of output of commodity producersw1 (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

c

v

m

d No surplus value

31 service sectors without producing investment goods

Branchencode

Sektor

46 Großhandelsleistungen (o. Kfz)

47 Einzelhandelsleistungen (o. Kfz)

49Landverkehrsleist. 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

Branchencode

Sektor

73 Werbe- und Marktforschungs-DL

74-75So. freiberufl., wiss. u. techn. DL; DL d. Veterinärwesens

77 DL der Vermietung v. beweglichen Sachen

78 DL der Arbeitskräfteüberlassung

79 Reisebüro- und Reiseveranstaltungs-DL

84DL 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

Four sectors, producing immaterial investments

Branchencode Sektor58 DL des Verlagswesens59 DL d. Filmherstellung, d. -vertriebs u. -verleihs; Kino-DL

62-63 DL d. Informationstechnologie; Informations-DL90 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

use values, materials, energy, ecologic dimension

Labor values, commodity and

services markets

Prices of production, labor market

Small commodity production

Physical basis

Captalism of perfect competition

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

• 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

Transformation problem: from labor values to prices of production

Marx‘ solutionpp(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) Profitrate1 + 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 Rpp 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 n-dimensional 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 profitPfk

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

p observed pricespw classic labor values

x quantities

O

pp prices of production

Sector 1

Sector 2

Sector 3

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

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

c

v

m

d

Rates of profit can be negativ. They are not equal.(measured in terms of output prices)

Structure of prices of production a la Marx 2008, 2nd Iteration

c

v

m

d

Structure of prices of production a la Marx 2008, 3rd Iteration

c

v

m

d

Structure of prices of production a la Marx 2008, 4th Iteration

c

v

m

d

Structure of prices of production a la Marx 2008, 5th Iteration

c

v

m

d

c

v

m

d

Structure of prices of production a la BortkiewiczAustria 2008, (without fixed Capital)

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 BortkiewiczAustria 2007, with fixed and circulating constant capital,

57 Sectorsd

c

v

m

Structure of prices of production a la BortkiewiczAustria 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 valueclassic

Labor value„material“

PriceofProd Marx 1 Iter.

PriceofProd circ Cap

PriceofProd 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

YearEuro per

hour classic

Euro per hour

material

Minutes per Euro

classic

Minutes per Euromaterial

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:fleissner@arrakis.es