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Peter Fleissner, catedrático de cibernética social, Viena, Austria contacto: 4th International Vanguard Science Congress The role.

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Präsentation zum Thema: "Peter Fleissner, catedrático de cibernética social, Viena, Austria contacto: 4th International Vanguard Science Congress The role."—  Präsentation transkript:

1 Peter Fleissner, catedrático de cibernética social, Viena, Austria contacto: 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.

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 use values, environmental issues measured by mass, exergy or ecological footprint exchange values prices ~ labor values commodity/service markets prices of production labor market markets for money, credit, stocks, derivatives Commodity production of self employed Physical basis Public sector: State monopoly capitalism taxes, subventions transfers, social insurance Globalized economy: Finance capitalism International financial capital market prices (observed) Capitalism with perfect competition and fixed capital Information Society: Finance market capitalism information as commodity, communication as commercial service commodification of information goods/services Contemporary Capitalism

5 The Economy – seen as a self organization process (historical and logical view) Commodity production of self employed Physical basis Public sector Globalized economy International financial capital market prices (observed) Capitalism with perfect competition and fixed capital Information Society: information as commodity, communication as commercial service commodification of information goods/services History: Emergence Logic: Dominance older newer Inspired by: Hofkirchner, W. (2002): Projekt Eine Welt: Kognition – Kommunikation – Kooperation. LIT-Verlag Münster-Hamburg- London. p. 166 Contemporary Capitalism

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

7 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 a ij 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 use values, environmental issues measured by mass, exergy or ecological footprint exchange values prices ~ labor values commodity/service markets prices of production labor market markets for money, credit, stocks, derivatives Commodity production of self employed Physical basis Public sector taxes, subventions transfers, social insurance Globalized economy International financial capital market prices (observed) Capitalism with perfect competition and fixed capital Information Society: information as commodity, communication as commercial service commodification of information goods/services Contemporary Capitalism

9 Layer 2: Labour values, small commodity production Production Consumption Self-employed laborers Money Labor Commodities & Services 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  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 + .

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

12 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

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 -> 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 n c w = c + n new labor (live labor) pre-done labor

15 new labor (live labor) n pre-done labor m c v c constant capital (fix and circulating capital) variable capital (wages) surplus value (profit) w = c + n = c + v + m labor value w and its composition

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) new labor (live labor) n pre-done labor m c v c constant capital (fix and circulating capital) variable capital (wages) surplus value (profit)

17 New aspects of the labour theory of value 1.Empirical estimates of labour values 2.Simple and complex labour 3.Treating services as value consuming 4.Transformation of values into prices Marxian Von Bortkiewicz Geometric interpretation Less abstract transformation

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

19 Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus value Austria 2008: 75 industries (percent) c v m d

20 c v m d

21 Simple and extended reproduction (Marx) MEW Bd 24, 396 MEW Bd 24, 505 simple reproduction Extended reproducción

22 Input-Output-Table „+“ „=“ intermediate inputs Final demand (consumption, Investment, exports minus imports) Output Value addded (wages, profits, depreciation, taxes) Distribucion: costs and income Use of output Output

23 Input-Output scheme by Leontief ( , Nobel Laureat 1973) Primal Problem: Quantities Ax + y = x Dual Problem: Unit-Prices pA + q = p A(quadratic) Matrix of techn. coefficients (Leontief Matrix) xoutput (in quantities), column vector yfinal demand (in quantities), column vector punit-price, row vector qunit-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 A o = V diag(q) -1 U diag(g) -1 Wertschöpfung W o = W Endnachfrage F o = V diag(q) -1 F Arbeitszeit n o = n

26 Input-Output-Table „+“ „=“ intermediate inputs Final demand (consumption, investment, exports minus imports.) Output Value added (wages, profits, depreciation, taxes) Distribution: costs and incomes Use of output: Output

27 Input-Output Table in Marxian terms „+“ „=“ Vorleistungen Inputs (Lieferungen zwischen Unternehmen) Endnachfrage (Konsum, Investitionen, Exporte minus Importe) Output Wertschöpfung (Löhne, Gewinn Abschreibung Steuern etc.) Wert w Marxian terminology konstantes zirkulierendes Kapital c Lebendige Arbeit n Extended reproduction variables Kapital v Mehrwert m Use of output Distribution: costs and incomes

28 Output „+“ „=“ Vorleistungen Inputs (Lieferungen zwischen Unternehmen) Endnachfrage (Konsum, Investitionen, Exporte minus Importe) Output Wertschöpfung (Löhne, Gewinn Abschreibung Steuern etc.) Value w Marx: composition of value Constant circulating Capital c Lebendige Arbeit n Variable capital v Surplus value m Matrix A o Vorleistungen Matrix C o Konsum der Lohnabhängigen Matrix S o Surplus consumption Surplus product

29 Output „+“ „=“ Vorleistungen Inputs (Lieferungen zwischen Unternehmen) Endnachfrage (Konsum, Investitionen, Exporte minus Importe) Output Wertschöpfung (Löhne, Gewinn Abschreibung Steuern etc.) Value w Das Marxsche Wertschema Constant circulating Capital c Lebendige Arbeit n variable capital v surplus value m Matrix A o Vorleistungen Matrix C o Konsum der Lohnabhängigen Matrix S o Surplus Con- sumption Surplus product c+v+m=wc+v+m=w

30 Observed data: Current prices, Austria 2008,75 sectors

31 5151 Versicherungen und Pensionskassen 52 Mit Finanz- u. Vers.tätigk. verb. DL 53 Grundstücks- und Wohnungswesen 5454 Rechtsberatung und Wirtschaftsprüfung 55 Unternehmensführung, - beratung 56 Architektur- und Ingenieurbüros 5757 Forschung und Entwicklung 5858 Werbung und Marktforschung 5959 Sonst. freiberufl., wiss. u. techn. Tätigkeiten; Veterinärwesen 6060 Vermietung v. beweglichen Sachen 6161 Arbeitskräfteüberlassung 62 Reisebüros und Reiseveranstalter 63 Erbr. v. wirtschaftlichen Dienstleistungen a.n.g Öffentliche Verwaltung, Verteidigung u. Sozialversicherung 65 Erziehung und Unterricht 66Gesundheitswesen 6767 Alters- und Pflegeheime; Sozialwesen 6868 Künstlerische Tätigkeiten 6969 Bibliotheken und Museen 7070 Spiel-, Wett- und Lotteriewesen 7171 Erbr. v. DL d. Sports, d. Unterhaltung u. Erholung 7272 Interessensvertretungen und Vereine 7373 Reparatur v. Gebrauchsgütern 7474 Erbr. v. sonst. pers. DL 7575 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 1010 H.v. Bekleidung 1 H.v. Leder, Lederwaren und Schuhen 1212 H.v. Holzwaren; Korbwaren 1313 H.v. Papier, Pappe und Waren daraus 1414 H.v. Druckerzeugnissen 1515 Kokerei und Mineralölverarbeitung 1616 H.v. chemischen Erzeugnissen 1717 H.v. pharmazeutischen Erzeugnissen 1818 H.v. Gummi- und Kunststoffwaren 1919 H.v. Glas u. Glaswaren, Keramik u. Ä Metallerzeugung und -bearbeitung 2121 H.v. Metallerzeugnissen 2 H.v. Datenverarbeitungsger äten, elektron. u 2323 H.v. elektrischen Ausrüstungen 2424 Maschinenbau 2525 H.v. Kraftwagen und -teilen 26 Sonst. Fahrzeugbau 27H.v. Möbeln 28H.v. sonst. Waren 29 Reparatur u. Installation v. Maschinen 30Energieversorgung 31Wasserversorgung 32 Abwasser- u. Abfallentsorgung, Rückgewinnung 33Hochbau 34Tiefbau 35 Bauinstallation u. sonst. Ausbautätigkeiten 36 Kfz-Handel und - Reparatur 37 Großhandel (o. Kfz) 38 Einzelhandel (o. Kfz) 39 Landverkehr u. Transp. in Rohrfernleitungen 40Schifffahrt 41Luftfahrt 42 Lagerei, Erbr. v. sonst. DL für den Verkehr 43 Post- und Kurierdienste 44 Beherbergung u. Gastronomie 45Verlagswesen 46 Herst., Verleih u. Vertrieb v. Filmen; Kinos 47 Rundfunkveranstalt er 48Telekommunikation 49 Erbr. v. DL d. Informations- technologie; Informations-DL 50 Erbr. v. Finanzdienstleistun gen

32 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 = c v m

33 Matrix A o Vorleistungen Matrix C o Konsum der Lohnabhängigen Matrix S o Surplus Output P Matrix C o Konsum der Lohnabhängigen Matrix S o Surplus Output P‘ = = Generalized Leontief Schema primal: (A o + C o + S o )1 = P‘ Marx: c + n = c + v + m = w where c = 1‘A o, v = 1‘C o, m = 1‘S o, w = P Leontief Scheme dual: 1‘(A o + C o + S o ) = P Quadratic Input-Output Table

34 Matrix A p Intermediary goods in labor time Matrix C o consumption Matrix S o surplus Value w = “classical“ calculation of labor values w A p + n = w solution: w = n (E – A p ) -1 value w = Live labor n times Leontief-Inverse (E – A p ) -1 Live labor n + Matrix A o Intermediary goods observed + + Output P o = Value added Output at current prices P o = 1‘(A o + C o + S o ) Output P o at current prices = Sum of intermediate products, consumption and investment

35 Labor values and observed data Empirical results Austria 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 sectors Correlation Coefficient = 0,883

37 Structure of labor values, classic, Austria 2008 c v m d

38 How are the differences produced? c v m d c v m d Labor values, classic, 2008 Prices, observed 2008

39 Matrix A p Intermediary goods in labor time Matrix C o consumption Matrix S o surplus Value w = “classical“ calculation of labor values w A p + n = w solution: w = n (E – A p ) -1 value w = Live labor n times Leontief-Inverse (E – A p ) -1 Live labor n + Matrix A o Intermediary goods observed + + Output P o = Value added Output at current prices P o = 1‘(A o + C o + S o ) Output P o at current prices = Sum of intermediate products, consumption and investment

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 Commodity production Services production S21 emptyS22 empty S11 <>0S12 <> 0

41 S21 emptyS22 empty S11S12 Services Production Commodity production Services Commodities Surplus product Surplus matrix partitioned The systems of prices differ by different allocation of the surplus product

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, Inquiry into the Nature and Causes of the Wealth of Nationshttp://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 S21 emptyS22 empty S21 empty S22 empty

46 Matrix A o Intermediate products Matrix C o Consumption of workers Matrix S o Surplus Output P Matrix C o Consumption of workers Matrix S o Surplus Output P‘ = = S21 empty S22 empty Generalized Leontief Scheme primal: (A o + C o + S o )1 = P‘ Marx: c + n = c + v + m = w where c = 1‘A o, v = 1‘C o, m = 1‘S o, w = P Leontief Scheme dual: 1‘(A o + C o + S o ) = P Quadratic Input-Output Table

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, A 12 C 11, C 12 D 11, D 12 A = { }, C = { }, D = { } A 21, A 22 C 21, C 22 D 21, D 22 n... Partitioned row vector of live labor = { n 1, n 2 } w...Partitioned row vector of labor values = { w 1, w 2 } E....Unit matrix

48 Production of value in commodity producing sectors only Value of output of commodity producers w 1 (A 11 + D 11 ) + w 2 (A 21 + D 21 ) + n 1 = w 1 Value of output of services (at reproduction cost) w 1 (A 12 + D 12 + C 12 ) + w 2 (A 22 + D 22 + C 22 ) = w 2 => Value of output of services w 2 : w 2 = w 1 (A 12 + D 12 + C 12 ). (E 22 – A 22 - D 22 - C 22 ) -1 Value of output of commodity producers w 1 : w 1 = n 1 { E 11 – (A 11 + D 11 ) – (A 12 + D 12 + C 12 ). (E 22 – A 22 - D 22 - C 22 ) -1 (A 21 + D 21 ) } -1

49 Observed prices, classic labor values and labor values with services at reproduction cost Austria sectors Coefficients of correlation classic:0.883 material:0.839

50 Structure of labor values, services at reproduction costs, Austria,2008 c v m d No surplus value

51 31 service sectors without producing investment goods Branchen code Sektor 46Großhandelsleistungen (o. Kfz) 47Einzelhandelsleistungen (o. Kfz) 49 Landverkehrsleist. u. Tranportleist. in Rohrfernleitungen 50Schifffahrtsleistungen 51Luftfahrtleistungen 52Lagereileistungen, sonst. DL für den Verkehr 53Post- und Kurierdienste 55-56Beherbergungs- und Gastronomie-DL 60Rundfunkveranstaltungsleistungen 61Telekommunikationsdienstleistungen 64Finanzdienstleistungen 65DL v.Versicherungen und Pensionskassen 66Mit Finanz- u. Versicherungsleistungen verb. DL 70DL d. Unternehmensführung u. -beratung 72Forschungs- und Entwicklungs-DL Branchen code Sektor 73Werbe- und Marktforschungs-DL So. freiberufl., wiss. u. techn. DL; DL d. Veterinärwesens 77DL der Vermietung v. beweglichen Sachen 78DL der Arbeitskräfteüberlassung 79Reisebüro- und Reiseveranstaltungs-DL 84 DL der öffentl. Verwaltung, Verteidigung u. Sozialvers. 85Erziehungs- und Unterrichtsdienstleistungen 86DL des Gesundheitswesens 87-88DL von Heimen u.des Sozialwesens 91DL von Bibliotheken und Museen 92DL des Spiel-, Wett- und Lotteriewesens 93DL des Sports, der Unterhaltung und der Erholung 94DL v. Interessenvertretungen, Kirchen u.a. 95Reparatur von EDV-Geräten und Gebrauchsgütern 96Sonstige überwiegend persönliche DL 97DL privater Haushalte mit Hauspersonal

52 Four sectors, producing immaterial investments BranchencodeSektor 58DL des Verlagswesens 59DL d. Filmherstellung, d. -vertriebs u. -verleihs; Kino-DL 62-63DL d. Informationstechnologie; Informations-DL 90Kreative, künstlerische und unterhaltende DL Sum of output prices of the sectors 58, 59, 62/63 und ,00 Total sum of all investments in Euro ,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 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

56 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

57 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

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: 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.

59 Several Price Systems Prices observed: P (A z + C z + S z ) = P Classic labor values (all sectors produce value) P k = n (E-A z ) -1 „Material“ labor values (material production only produces value) P s Prices of production with circulating capital only, equal rates of profit) P zk Prices of production with fixed capital, equal rates of profit P fk 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 p observed prices p w classic labor values x quantities O pp prices of production Sector 1 Sector 2 Sector 3 The hyperplane is the location of all feasible price systems where p i x = const Assumption: total sum of values and prices are always equal p s „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 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 20 th century (which is equal to the solution of an eigenvector/eigenvalue problem). The generalized iteration scheme inspired by Marx is: p i (K + A + C) (1 + r i ) = p i+1 where r i = p i (I - A - C) x / p i (K + A + C) x, r i … 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 p 0 = v = l (I – A) -1, where r 0 = p 0 (I - A - C) x / p 0 (K + A + C) x

62 Prices of production: Empirical results for Austria

63 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)

64 Structure of prices of production a la Marx 2008, 2nd Iteration c v m d

65 Structure of prices of production a la Marx 2008, 3rd Iteration c v m d

66 Structure of prices of production a la Marx 2008, 4th Iteration c v m d

67 Structure of prices of production a la Marx 2008, 5th Iteration c v m d

68 c v m d Structure of prices of production a la Bortkiewicz Austria 2008, (without fixed Capital)

69 Observed prices and prices of production without fixed capital Austria sectors Coeff.of correlation: 0,978

70 Structure of prices of production a la Bortkiewicz Austria 2007, with fixed and circulating constant capital, 57 Sectors d c v m

71 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/(c fix +c zirk +v+m)

72 Observed prices, prices of production with and without fixed capital, Austria sectors Koeff. Of corr: Without K_fix: with K_fix: 0.970

73 Summary: correlations of specific price systems with observed prices: Austria Year Labor value classic Labor value „material“ PriceofProd Marx 1 Iter. PriceofProd circ Cap PriceofProd circ+fix cap

74 Indicators for labor values and worked minutes per Euro in Austria Year Euro per hour classic Euro per hour material Minutes per Euro classic Minutes per Euro material Unit Value (Index 2005 = 100) ,8535,962,081, ,6638,791,961,5595, ,7740,961,891,4691, ,8244,381,831,3588,48

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