Seminar SE 2 st. Uni Klagenfurt: 814. 005 und TU Wien: 187 Seminar SE 2 st. Uni Klagenfurt: 814.005 und TU Wien: 187.234 Mathematische Modellbildung und Simulation Ökonometrische, systemdynamische, Input-Output Modelle sowie agent-based systems http://peter.fleissner.org/MathMod/web.htm Peter Fleissner fleissner@arrakis.es

Termine immer mittwochs, 14:00-17:30 (pktl) 1. Block Mittwoch 6. Okt 2010, 14:00 bis 16:00 Uhr Vorbspr. im SR 4a 2. Block: Mittwoch, 20.10.2010 14:00 bis 17:30 im SR 4a 3. Block: Mittwoch, 3.11.2010 14:00 bis 17:30 im SR 4a 4. Block: Mittwoch, 17.11.2010 14:00 bis 17:30 im SR 4c 5. Block: Mittwoch, 1.12.2010 14:00 bis 17:30 im SR 6 6. Block: Mittwoch, 15.12.2010 14:00 bis 17:30 im SR 4a 7. Block: Mittwoch, 12.01.2011 14:00 bis 17:30 im SR 4a 8. Block: Mittwoch, 26.01.2011 14:00 bis 17:30 Prüfung im SR 6 Alle Termine finden am IFF, Schottenfeldgasse 29, 1070 Wien, entweder im Seminarraum 3 oder 6 statt.

Inhalt des Seminars (optional) Teil 1 Grundzüge der mathematischen Modellierung (Sozialkybernetik) Modellierungspraxis mit dem Softwarepaket STELLA anhand kleiner Projekte Teil 2 Datensammlung/Parameterschätzung (Ökonometrie; neuronale Netze) Praktische Übungen anhand ökonometrischer Modelle Teil 3 Grundzüge der Input-Output-Analyse, Mehrebenenökonomie Anwendungen auf volkswirtschaftliche Modelle, Stoffstromrechnung Teil 4 Agent-based modelling Praktische Beispiele Abschluss Prüfung

websites Allgemeines Laufende Ereignisse, Skripten, Termine https://campus.uni-klu.ac.at/studien/lvkarte.jsp?sprache_nr=35&rlvkey=66132 Laufende Ereignisse, Skripten, Termine http://peter.fleissner.org/MathMod/web.htm Meine persönliche website http://members.chello.at/gre/fleissner/default.htm

Fachgebiete/Projektvorschläge der TeilnehmerInnen (2010) Stefan: Sozök, Soziologie, Polwiss; Biomasse-Handel Irene: Sozök, Publizistik, Kommw Polwiss: mit Alexander_R und Johannes: Pensionsmodell Alexander_R: Soziologie, Diss Sozök: Pensionsmodell Markus: Physik, Diss Sozök Modellierung Materialflüsse: Urbane Transportmodelle Peter: Techn Math: mit Andrea Kommunikationsnetzwerke Johannes: Wirtschaftsinformatik: Pensionsmodell Alexander_H: Soziologie: Pensionsmodell Nikolaus: ?? Andrea: Kommunikationsnetzwerke Julian: Inst f Elektrische Anlagen + Boku Energiewirtschaft: Biomasse-Handel

Projekt A: Pensionsmodell mit Irene, Alexander_H, Alexander_R und Johannes

Projekt B: Kommunikationsnetzwerk Andrea und Peter

Projekt C: Urbanes Transportmodell mit Markus

Projekt D: Biomasse-Handel mit Stefan und Julian

Teil 1 Grundzüge der mathematischen Modellierung (siehe Skriptum Sozialkybernetik http://peter.fleissner.org/MathMod/Skriptum_Sozkyb.pdf) Modellierungspraxis mit dem Softwarepaket STELLA anhand kleiner Projekte

Exkurs: Zur intuitiven Lösung von gewöhnlichen Differentialgleichungen

Intuitive Lösung von nichtlinearen Differentialgleichungen dx/dt dx/dt = f(x) Differentialgleichung darstellbar im (x, dx/dt) Koordinatensystem x x0

Intuitive Lösung von nichtlinearen Differentialgleichungen x(t) x0 t Trajektorie im (t , x) Koordinatensystem

Graphische „Lösung“ von nichtlinearen Differentialgleichungen als Differenzengleichungen Δx/Δt = f(x) Δx x0

Graphische Lösung von nichtlinearen Differentialgleichungen Δx/Δt = f(x) Δx x0

Graphische Lösung von nichtlinearen Differentialgleichungen Δx/Δt = f(x) Δx Δx x0

Graphische Lösung von nichtlinearen Differentialgleichungen X2 = ??? Δx/Δt = f(x) Δx Δx x1= x0+Δx x0

Graphische Lösung von nichtlinearen Differentialgleichungen Δx/Δt = f(x) Stationäre Punkte??

Graphische Lösung von nichtlinearen Differentialgleichungen Stationäre Punkte x*: dx/dt = f(x)=0

Graphische Lösung von nichtlinearen Differentialgleichungen Sind die stationären Punkte stabil?

Was bedeutet Stabilität? Ein stationärer Punkt x* ist stabil, wenn er bei jeder kleinen Auslenkung wieder angenommen wird x*

Was bedeutet Stabilität? Ein stationärer Punkt x* ist stabil, wenn er bei jeder kleinen Auslenkung wieder angenommen wird instabil stabil x*

Ein Anwendungsbeispiel Die nordamerikanische Passagiertaube: ausgestorben 1914

Die natürliche Reproduktion der nordamerikanischen Passagiertauben dx/dt x Schwarmgröße http://www.loe.org/series/gap_in_nature/

Die natürliche Reproduktion der nordamerikanischen Passagiertauben dx/dt x In welchen Bereichen wächst der Schwarm und wo schrumpft er? Wo sind die stationären Punkte?

Die natürliche Reproduktion der nordamerikanischen Passagiertauben dx/dt Hier wächst der Schwarm x In welchen Bereichen wächst der Schwarm und wo schrumpft er? Wo sind die stationären Punkte?

Die natürliche Reproduktion der nordamerikanischen Passagiertauben dx/dt Hier wächst der Schwarm x instabil stabil Stabilität der stationären Punkte?

Die Jagd auf die nordamerikanischen Passagiertauben dx/dt x Abschussrate

Reproduktionsrate minus Abschussrate der Passagiertauben dx/dt x

Reproduktionsrate minus Abschussrate = Nettoreproduktionsrate dx/dt x

Erhöhte Abschussrate dx/dt x

Erhöhte Abschussrate dx/dt x

Erhöhte Abschussrate dx/dt x

Erhöhte Abschussrate dx/dt x

Resultat Ein einziger weiterer Schuss führt (unerwartet) zur Katastrophe: zum Aussterben des Schwarms

Teil 2 Input-Outputanalyse im Kontext der Widerspiegelungstheorie Grundelemente der Volkswirtschaftlichen Gesamtrechnung Grundzüge der Input-Output-Analyse, Mehrebenenökonomie

Kontext: Widerspiegelungstheorie

Veränderungszyklus und Simulation Widerspiegelung = Abbildung und Entwurf die „Welt“ §x“?+* ~$}[% Vergegenständlichung Versprachlichung Verbildlichung °^^‚#* .:->>| Vergegenständlichung Widerspiegelung Diffusion

Basic Relations in simulation models Strictly deterministic relations (inspired by Rainer Thiel) Definition equations Static balance equations Dynamic balance equations Behavioral equations Stochastic relations (inspired by Herbert Hörz) Randomness as residual/error, Randomness essential, but constant Randomness essential, but variable

Mathemathic codification 0: Definition equations Main element: “variable” with an associated quality/dimension and a certain quantity Types of definition equations: A: A new variable of same dimension is constructed by other variables of the same dimension, but different quantities Example: Circumference of a triangle is equal to the sum of the length of the three sides. B: A new variable of new dimension is constructed by other variables of the same dimension, but different quantities Example: Area of a rectangle is the product of its length and width. C: A new variable of new dimension is constructed by other variables of the different dimension and different quantities. wir Example: Labour is force times distance, turnover equals unit price times volumes. Although definition equations look simple, their identification was a cumbersome and erroneous process (like “energy” or “force”)

Mathemathic codification 1: Static Balance Equation conservation laws; e.g. input-output-tables, national accounting schemes L := l1 + l2 + l3 + l4 R := r1 + r2 + r3 l3 „Unequal quantities of equal qualities sum up to a quantity of equal quality“ l1 l2 l4 r1 r2 „Only the unequal becomes equal“ „Equal quantities must consist of unequal qualities“ r3 L = R

Mathemathic codification 2: Dynamic Balance Equation inventory equation, dynamic population balance, capital accumulation, dynamic accounting schemes Dx(t, t+1) x(t+Dt) = x(t) + Dx(t, t+1) The only qualitative difference between left and right: Position in time reality is constructed by „stocks“ and „flows“ Basis for the mirroring of dynamic processes (difference and/or differential equations) x(t) x(t+Dt) t -> t +Dt

Mathemathic codification 3: Behavioral equations cause-effect-schemes; e.g. multi-variate Blalock-model, econometric equations, neural networks x1 D + y y(t) = f [ x1(t), x2(t),…] D - x2 y x Modifications: linear nonlinear stochastic delays Feedback -> y x y x D

Causal Loop Diagrams Negative feedback: goal seeking, oscillations (D) Target value State value D Positive feedback: exponential growth reaction discrepancy wages Demand for higher wages cost pressure prices

Examples: Input-Output-Model Econometric model

Combined Example: Input-Output and Econometric Model BMWF (Ed Combined Example: Input-Output and Econometric Model BMWF (Ed.) Mikroelektronik - Anwendungen, Verbreitung und Auswirkungen am Beispiel Österreichs, Wien 1981

Wassily W. Leontief, Scientific American, Sept.1982, pp.152-164; Nobelpreis für Ökonomie1973

10-years forecast/comparison with actual data 1990 fast diffusion of micro-electronics in Austria Indikator 1990 actual 1990 standard 1990 forecast with m-electronics GDP prices 1976 1051 Mrd ATS 1113 Mrd ATS 1190 Mrd ATS unemployed 165.795 220.000 386.000! Wage labour 2.925.396 3.221.000 3.056.000 male 1.716.754 1.883.000 1.802.000 female 1.208.642 1.338.000 1.254.000 Working hours Hours/week 39,4 39,6 39,9 Exports 526 Bill ATS 619 Bill ATS 624! Bill ATS Imports 470 Bill ATS 631 Bill ATS 648! Bill ATS

Grundelemente der Volkswirtschaftlichen Gesamtrechung

Babylonische Tabelle Plimpton 322, dated from between 1900 and 1600 B Babylonische Tabelle Plimpton 322, dated from between 1900 and 1600 B.C.

Volkswirtschaftliche Gesamtrechung: Grundschema Vorleistungen Endnachfrage Bruttoproduktion Wertschöpfung

Volkswirtschaftliche Gesamtrechung: Entstehung Vorleistungen Endnachfrage Bruttoproduktion Wertschöpfung Sektor n1 Sektor n2 ….. Sektor n… = BIP=n1+n2+………=

Volkswirtschaftliche Gesamtrechung: Verwendung Endnachfrage Vorleistungen Bruttoproduktion Privater Konsum c Öffentl. Konsum g Investitionen i Exporte ex minus Importe im Wertschöpfung = BIP=c+g+i+ex-im = Sektor n1 Sektor n2 ….. Sektor n… = BIP=n1+n2+………=

Volkswirtschaftliche Gesamtrechung: Verteilung Endnachfrage Vorleistungen Bruttoproduktion Privater Konsum c Öffentl. Konsum g minus Importe im Investitionen i Exporte ex Wertschöpfung Löhne v Unv. Gewinne pr Abschreibungen d Eink Selbständiger s Ind Steuern min Sub = BIP=c+g+i+ex-im = = BIP=v+pr+s+ind+d = = BIP=n1+n2+………=

National Economic Accounting: Input-Output Scheme Endnachfrage Vorleistungen Bruttoproduktion Bruttoproduktion Privater Konsum c Öffentl. Konsum g minus Importe im Investitionen i Exporte ex Wertschöpfung Löhne v Unv. Gewinne pr Abschreibungen d Eink Selbständiger s Ind Steuern min Sub = BIP=c+g+i+ex-im = = BIP=v+pr+s+ind+d = = BIP=n1+n2+………=

Current prices: Example Austria 1976 million ATS Sector j=1 j=2 j=3 final dmd Y Output X i=1 18396,73 77305,34 11773,13 4724,80 112200,00 i=2 19404,07 210142,46 75713,31 307308,15 612568,00 i=3 9569,20 72819,19 99498,56 361828,05 543715,00 sum 1+2+3 47370,00 360267,00 186985,00 value added 64830,00 252301,00 356730,00 output Direct labor Persons 369610 1207657 1594369 Vorleistungsmatrix Z = { Zij } End- nach- frage Brutto- Produk- tion Wertschöpfung V Bruttoproduktion X‘

Empirical view: matrix notation [monetary units] Vorleistungen Endnachfrage Bruttoproduktion Z = { Zij } Y = { Yi } X = { Xi } Wertschöpfung Zeilen: Z 1 + Y = X Spalten: 1’Z + V = X’ Symbols in caps!! V = { Vj } X‘ = { Xj }

How can we characterize the I-O system? Try to find invariants which will increase the understanding of the economy and allow also for comparisons -> standardize the figures Easy procedure: divide each figure of the intermediary table by the corresponding output of the sector. Be aware of the units of measurement! The figures of one column are divided by the same numbers: aij = zij/xj Result: Matrix A = {aij } of technical coefficients: input needed for the production of one unit of output (in this case in monetary units, e.g. Euro or ATS)

Standardized I-O: Example Austria 1976 ATSi per ATSj Sector j=1 j=2 j=3 i=1 0,16 0,13 0,02 i=2 0,17 0,34 0,14 i=3 0,09 0,12 0,18 sum 1+2+3 0,42 0,59 value added/ output 0,58 0,41 0,66 Stand. 1,00 l = labor/ Persons per mill ATS 3,29 1,97 2,93 Technol. coeff matrix A = { aij}

Ax + Cx + Sx = x Simplified two-class model of extended reproduction There are only two loops in the system, accumulation of capital and reproduction of labor power No explicit public sector, closed economy All capital investment goes to capitalists All consumption goes to laborers Final demand approximated by two matrices C = c w‘ /(1‘c) (consumption matrix, w wages) S = i p‘ / (1‘i) (surplus matrix, i investmt, p profits) Fixed capital is represented by K = i k‘ / (1‘i) (capital matrix, k fixed capital) Ax + Cx + Sx = x

Extended Reproduction Fixed Capital Intermed. goods Intermed. products Labor Power Capital investment Intermed. goods Consumer goods

Consumption matrix C: Example Austria 1976 million ATS sector j=1 j=2 j=3 consum- tion c con- i=1 1027 9859 13733 24619 sumpti-on i=2 6536 62710 87353 156598 matrix i=3 7254 69601 96952 173807 wages (sum) 14817 142169 198038 output 112200 612568 543715 C 0,009158 0,0160939 0,0252573 standar 0,058250 0,1023715 0,1606593 dized 0,064651 0,1136215 0,1783146

Idealized view: matrix notation [amounts, unit prices] Vorleistungen Endnachfrage Bruttoproduktion Z = { pi aij xj } = Y = { piyi } = X = {pixi} Wertschöpfung x…amount (Stück, Anzahl), (column) p…unit price, v…unit value added (row) Zeilen: Ax + y = x Spalten: pA + v = p Summen: pAx + vx = px V = { vj xj } = X‘ = {pjxj}

Leontief-Inverse (I – A)-1= I + A + A2 + A3 +.. Von Neumann Reihe Inverse view Vorleistungen Endnachfrage Bruttoproduktion Z = { pi aij xj } = Y = { piyi } = X = {pixi} Wertschöpfung Zeilen: x = (I – A)-1y Leontief-Inverse (I – A)-1= I + A + A2 + A3 +.. Von Neumann Reihe Spalten: p = v(I – A)-1 V = { vj xj } =

Excursion: Linear Programming: standard form Primal and dual problem with volumes x and prices p Primal Linear Program Maximize the Objective Function (P) P = c‘x subject to Ax <= b, x >= 0 Dual Linear Program Minimize the Objective Function (D) D = p‘b subject to p‘A >= c‘, p >= 0

Excursion: Linear Programming: standard form Primal and dual problem with amounts x and prices p Max: 2.x1 + 1.x2 subject to 3x1 + 8 x2 <= 24 8x1 + 3 x2 <= 24 1x1 + 1 x2 <= 4 x >=o

Mehrebenenanalyse

Multilevel Economics How to look at the economy? Appearance and Essence A multilevel perspective Labor values and price systems Transformation of values into prices How to handle services? Three ways to understand “productivity”

Looking through the surface General rule From empirical findings to abstractions From appearance to essence and back Application of the rule From observed market prices to labor values and use-values

Economic Reality – A Complex Construction 7 6 5 4 3 2 1 Contemporary Capitalism market prices (observed) Information Society: information as commodity, communication as commercial service commodification of information goods/services 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/service markets Physical basis use values, environmental issues collective production/appropriation

Economic Reality – A Complex Construction 7 6 5 4 3 2 1 Contemporary Capitalism market prices (observed) Information Society: information as commodity, communication as commercial service commodification of information goods/services 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/service markets Physical basis use values, environmental issues collective production/appropriation

Intermediary goods A diag(x) Values in use [observed physical units] 1/3 j=1 2 3 …. i =1 2 3 .. Intermediary goods A diag(x) Final Demand Cons/Inv “ “ “ “ Output Ax + y = x

Intermediary goods A diag(x) Values in use [observed physical units] 2/3 j=1 2 3 …. i =1 2 3 .. Intermediary goods A diag(x) Con- sumption C diag(x) Capital Investment S diag(x) Final Demand Cons/Inv/ Exp/-Imp “ “ “ “ “ “ = Output Ax + Cx + Sx = x (A+C+S)x= Tx = x

Values in use [observed physical units] 3/3 Two physical ways how to make goods commeasurable: By mass/weight By energy content/dissipated heat/entropy If we have commeasurable variables, we can add up the columns of the table, not only the rows Problems: How to handle services, waste? What are the balance equations?

Material flows [physical units] j=1 2 3 …. i =1 2 3 .. Intermediary flows Z Final Demand y Output x other inputs minus waste (i-d) Z 1 + y = x 1’Z +i-d =x’ Output

Material Flows: Example Austria 1983 tons Sector 1 2 3 final dmd output 30545305 18172255 12045635 39127282 99890477 2065667 7593987 5033740 5525759 20219153 sum 1+2+3 32610973 25766242 17079375 input 71757963 7389707 - waste -4478459 -12936796 -17079375 labor 369610 1207657 1594369

Energy Flows: Example Austria 1986 terajoule Sector 1 2 3 final dmd output 181725 122719 43311 116725 464480 53924 181721 62689 190779 489113 5084 1906 912 1788 9690 sum 1+2+3 240734 306346 106912 imports 89982 400735 37899 „value added“ 133764 -217967 -135121

But there is a third way also. It is leading to the societal sphere… But there is a third way also. It is leading to the societal sphere….. Human labor is THE activity which makes human beings different from animals Excursion: what is the difference between labor and other human activities?

Human labor and other human activities Labor is a special human activity which could in principle be performed by someone else. The person performing the activity is replaceable. This is in contrast to human activities which are related to the individual personality and individual experience => Labor bears an internal and an external aspect for the individual worker

Labor does exist formally and informally While formal labor is remunerated by wages (like in the case of employees) or compensated by income via the market (like in the case of self-employed), informal labor is not directly compensated financially (e.g. the work of wives in households or social work during leisure time). The contemporary economic system does not deal with informal labor, nevertheless a comparison between formal and informal labor might be interesting.

Economic Reality – A Complex Construction 7 6 5 4 3 2 1 Contemporary Capitalism market prices (observed) Information Society: information as commodity, communication as commercial service commodification of information goods/services 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/service markets Physical basis use values, environmental issues collective production/appropriation

Fragestellung „Die positive Fragestellung, die sich NUR mit Hilfe der Arbeitswerttheorie beantworten lässt, geht von der Tatsache aus, dass die wachsenden Wirtschaften laufend einen größeren Output als Input erstellen, d.h. der Ertrag übersteigt die Kosten. Ertrag und Kosten können prinzipiell in drei Dimensionen definiert werden, in Mengengrößen, in monetären (Preis-) Größen und Arbeitswertgrößen. Die Mengenrechnung hat nur sehr eingeschränkte Verwendbarkeit, da sie bei den vielen heterogenen Gütern zu keiner einheitlichen Ertrags- bzw. Kostenziffer führt. Anders ist dies bei der monetären und Arbeitswertrechnung. Während jedoch die monetären Größen keine exakte Widerspiegelung der Menge darstellen, sondern sich bei inflationären Entwicklungen davon lösen, bestehen zwischen Gütermengen und den in ihnen steckenden Arbeitsmengen genaue technische Beziehungen. Es liegt somit nahe, zu untersuchen, wie mit einem gegebenen Arbeitsquantum als Input eine wachsende Gütermenge hergestellt werden kann und welche Relation zwischen Arbeitsmenge und Gütermenge besteht. Um den Output (Brutto- oder Nettoproduktion einer Volkswirtschaft) und den Input als Ausdruck von Arbeitsmengen begreifen zu können, ist es notwendig, die Produktionsmittel, also das sogenannte Kapital, auf Arbeit zurückzuführen." (H.G.Zinn, Arbeitswertheorie, Westberlin, 1972, S.10)

Die Ware besitzt Gebrauchswert (value in use, Nutzen) Tauschwert (value in exchange) Wertgröße = durchschnittliche gesellschaftlich notwendige Arbeitszeit (¹ individuellem Arbeitszeitaufwand) Mehrwert = Gesellschaftliche Arbeitszeit, die über jene Arbeitszeit hinausgeht, die für die einfache Reproduktion notwendig ist Technischer Fortschritt reduziert den Stückwert = durchschnittl. Arbeitszeitaufwand pro Stück

Setting the stage: Basic terms in Marxian Political Economics commodity value in use value in exchange (labour)value constant capital variable capital surplus value rate of surplus value/rate of exploitaiton organic composition of capital rate of profit

the composition of labour value w new labour (live labour) n w = c + n pre-done labour c

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

three essential Marxian indicators rate of surplus value = m / v organic composition of capital = v / (c + v) profit rate = m / (c + v) = rate of surplus value * organic = m / v * v / (c + v) m surplus value (profit) new labour (live labour) n variable capital (wages) v c c constant capital (fix and circulating capital) pre-done labour

(Labor time) value of output w = c + n = c + v + m w labor time value of output c constant capital n newly created value = socially necessary labor v variable capital (wage bill) m surplus value

Labor value is fixed in the market w = c + n = c + v + m There is a difference between individual value market value (average value) Market Engine to compare individual performance with the performance of society Rewards the efficient Punishes the less productive Creates a tendency towards more efficiency Labor values shrinking with technical/organis. improvements

Various indicators Capital advanced: K = c + v Capital available after selling: K'= c + v + m Rate of surplus (exploitation rate): e = m/v Organic composition of capital: o = v/(c + v) Classical rate of profit per production period: r = m / (c + v) = e.o Annual rate (dimensions corrected): ra = m / (cf + cz.Tz + v.Tv) cf … fixed constant capital cz … circulating constant capital Tz,Tv … turnover periods

Classical indicators in matrix terms Capital advanced: K = w(A+C)x Capital available after selling: K'=wAx+L Rate of surplus: e = (L - wCx)/wCx Organic composition of capital: o= wCx/w(A+C)x Classical rate of profit per production period: r = (L - wCx)/w(A+C)x = e.o

Labor Values w [labor time] j=1 2 3 …. Use of GDP i =1 2 3 .. Intermediary goods Final Demand Cons/Inv/ Exp/-Imp Output wAx Distribution of GDP Value added { Lj = lj . xj } L=lx wx Output l,w.. row vectors

Labor Unit Values w [labor time] j=1 2 3 …. Use of GDP i =1 2 3 .. Intermediary values Final Demand Cons/Inv/ Exp/-Imp Output Distribution of GDP Value added {Lj=lj.xj} wA + l = w w =l(E-A)-1 Output

Empirical results: Gross-output (P), labour values (W0) and prices of production (PP) Austria 2003: 57 industries (Mio EUR) Correlation coefficient with r classical labour values w 0.883 Prices of production pp (Bort- kiewicz) 0.952 Labour values W0 gross output P (observed) prices of production PP

Mining of coal and lignite 5 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

Structure of „classical“ labour values all industries are value producers c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m v c

Marxian indicators (observed data) rate of surplus value, organic composition of capital, rate of profit Austria 2003: 57 industries (percent) rate of profit rate of surplus value organic composition

Economic Reality – A Complex Construction 7 6 5 4 3 2 1 Contemporary Capitalism market prices (observed) Information Society: information as commodity, communication as commercial service commodification of information goods/services 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/service markets Physical basis use values, environmental issues collective production/appropriation

transformation of labor values into prices (transformation problem) Marx‘ solution pp(0) = w or w* pp(1) = pp(0) R [1 + r ] 1 + r = [pp(0) x] / [pp(0) R x] Difficulty: input prices ≠ output prices von Bortkiewicz solution two identical solutions with different philosophical implications a) Eigenvector solution: pp ... left-hand Eigenvector of R pp R (1 + r) = pp, largest eigenvalue of R: λ=1/(1+r) b) iterative solution: i -> ∞ Marx‘ solution: i = 1 pp = pp(∞); pp(0) = w or w* pp(i) = pp(i-1) R [1 + r(i-1)], 1 + r(i) = [pp(i) x] / [pp(i) R x]

Marx’s solution of the transformation of labor values into prices of production Basis: costs of production In terms of labor values of commodities Profit added Share of total value added proportionally to costs of production Result “prices of production” Intrinsic problem input prices are different from output prices Proposed solution Iterative application of Marx’s method

How to determine the average rate of profit? pp(A+C)(1+r) = pp -> pp[ 1/(1+r) I – A - C ] = 0 Eigenvalue-Equation for l = 1/(1+r) : pp (A + C) = l pp Non-trivial solution for pp, if and only if determinant of the matrix MDET( l I – A - C ) = 0 Hint: Solve it in Excel by its solver-function

r… uniform rate of profit Prices of production pp [currency units] 1/3 j=1 2 3 …. Use of GDP i =1 2 3 .. Intermediary values Final Demand Output Distribution of GDP wages profits pp(A+C)(1+r)=pp r… uniform rate of profit Output

Solutions to the transformation problem Marx’s method, iteratively applied, converges to Bortkiewicz’s solution (1907) Rate of profit Method Labor Values 1.140 Marx’s solution 1.140 First iteration 1.035 Second iteration 1.030 Third iteration 1.025 Bortkiewicz’s solution 1.025

von Bortkiewicz: Prices of production c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m v c

Solutions to the transformation problem Alternative Solution: Variable quantities of consumer goods A combined approach of marginal utility theory (demand function for consumer goods and labor theory of value (to determine prices by labor content and modified by equalized rates of profit) Result: Instead of one solution there are two High price and high profit rate, low consumption level Low price and low profit rate, high consumption level

Does every wage-earner create surplus value? w = c + n = c + v + m Here comes the story of an agrarian society consisting only of a farmers. What will be the effect to the surplus if They bring an additional farmer into their society? They bring a shaman into their society?

the role of services and productivity measures Two sources of inspiration Productive and unproductive labour (Adam Smith) Material Product System (MPS) vs System of National Accounts (SNA – Richard Stone)

Does every worker create additional value? My answer is: “no” Value is a concept to make qualitative different things comparable The common background is labor power embodied in physical goods If there is no physical/material good, there is no surplus, and there is no value nor surplus value Accumulation is based on surplus and surplus value, which is the basis for profits and the profit rate This statement is equivalent to: human beings cannot live without a material environment and without exchange of material flows (metabolism) with nature

There is value creating labor and value consuming labor Value creating labor results in things, which can be stored, resold and accumulated Value consuming labor results in pure use-values, which are useful, but cannot be stored, neither resold nor accumulated A typical sector of value consuming labor is the service sector All the value consuming sectors have zeros in the rows of the S (surplus) matrix = their output cannot be invested But, their output can have important indirect effects (e.g. increasing the productivity of labor)

Examples and borderline cases of value consuming production Services Education Entertainment (opera ticket) Material production The story of the coffee mugs Customer specific production Energy transformation Software production

Labor Values w [labor time] j=1 2 3 …. i =1 2 3 .. A11 A12 A21 A22 * C11 C12 C21 C22 * S11 <= S12 0 0 * Final Demand Cons/Inv/ Exp/-Imp “ “ “ “ “ “ = Output w1C12x2+ w2C22x2 L1 0 *Note: All matrices have to be premultiplied by diag(w) and postmultiplied by diag(x) w1C11x1 + w2C21x1 L1 Total surplus value L1 – (w1C11+w2C21)x1 Output

Possible effects of an expansion of value consuming sectors Effects of first order (ceteris paribus) Decrease of the average rate of profit Reduction of the rate of economic growth Example: Outsourcing and GDP (“vertical” and “horizontal” growth, labor productivity change) Possible secondary effects Services may increase their own productivity of labor and the productivity of other sectors by improving technology and management techniques This may compensate for the effects of first order

The labour of some of the most respectable orders in the society is, like that of menial servants, unproductive of any value, and does not fix or realize itself in any permanent subject; or vendible commodity, which endures after that labour is past, and for which an equal quantity of labour could afterwards be procured...…In the same class must be ranked, some both of the gravest and most important, and some of the most frivolous professions: churchmen, lawyers, physicians, men of letters of all kinds; players, buffoons, musicians, opera-singers, opera-dancers, &c. …Like the declamation of the actor, the harangue of the orator, or the tune of the musician, the work of all of them perishes in the very instant of its production. Smith, Adam, An Inquiry into the Nature and Causes of the Wealth of Nations, Book II, Chapter III, Of the Accumulation of Capital, or of Productive and Unproductive Labour, http://www.econlib.org/LIBRARY/Smith/smWN.html.

treating services as value consuming there is an essential difference between goods (= material products) and services services do not contribute neither to surplus product, nor to surplus value, they as such cannot be resold nor accumulated nor invested, because they are consumed when they are produced In „Das Kapital“, Vol I, Marx dealt only with material products where according to his labour theory of value (LTV) the principle of equivalent exchange holds. principle of equivalent exchange : goods are exchanged according to their content of social necessary labour if service sectors are allowed to make profits (as it is the case under capitalism), the principle of equivalent exchange is violated and LTV is no longer valid

How to determine labour values that obey the principle of equivalent exchange? A... partitioned matrix of technical coefficients C... partitioned matrix of unit consumption R… partitioned matrix of unit reproduction n... partitioned row vector of unit live labour = { n1, n2 } w... partitioned row vector of labour values = { w1, w2 } I.... Identity matrix A 11, A12 C11, C12 A = { }, C = { }, R = A + C A21, A22 C21, C22 w: „classical“ labour values: all industries are value producer w = n (I – A)-1 w*: value production in material sectors only w* = { n1(I – A11)-1 , n1(I – A11)-1 (A12+C12) [I-(A22+C22)]-1 }

Construction of the consumption matrix C in analogy to A Consumption matrix C (on unit-level) C = c v diag(x) / (vx) diag(x)-1 = c v / (vx) c... column vector of consumption v... row vector of unit wages x... column vector of output p... row vector of unit prices pC = v Cx = c

Construction of the surplus matrix S in analogy to A Surplus Matrix S (on unit-level) S = s m diag(x) / (mx) diag(x)-1 = s m / (mx) s... column vector of surplus product m... row vector of unit surplus value (or unit profit) x... column vector of output p... row vector of unit prices pS = m Sx = s

Services in a simplyfied Leontief economy primal: (A + C + S)x = x dual: p(A + C + S) = p S... partitioned matrix of unit surplus product S11, S12 S = { } surplus product s = (I – A - C)x S21, S22 If services are present, S21 = 0 and S22 = 0, because services do not contribute to surplus product Sub-matrix S12 is crucial: If principle of equivalent exchange holds, S12 = 0. Material producers can fully invest, services cannot invest at all

Effects on the service sector Growing S12 -> higher service prices p*2 = p2 + p1S12(E – R22)-1; x*2 = x2 Reallocation of C11x1, consumption in sector 1 towards services -> x2 increases x*2 = x2 + C11 x1 / (A12 + C12); p*2 = p2 Multiple accounting under SNA (seen from MPS) Double accounting, if diagonal matrices=0

Stucture of labour values no surplus for services, variable exploitation rates c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m m v v c c

Structure of labour values no surplus for services, equal exploitation rates c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m v c

Marxian indicators exploitation rates (equal), organic composition of capital, rate of profit Austria 2003: 57 industries (in percent) rate of profit rate of surplus value organic composition

geometric interpretation of prices, values and volumes More variables r... rate of profit g... rate of growth Marx’ notation w = “c” + “v” + “m” row vector on unit level turnover level Constant circulating capital “c” = wA = wA diag(x) Variable capital “v” = wC = wC diag(x) Surplus value “m” = Ws = wS diag(x)

Dual decomposition of output x (left) and unit prices p (right) Ax + Cx + Sx = x = pA + pC + pS = p = = Rx + Sx = x = pR + pS = p x Ax Cx O Sx Rx p pA pC pS pR

Dual decomposition of output x (left) for equilibrium growth and for unit prices of production p (right) x = Rx (1 + g) = p = pR (1 + r) = = Rx + g Rx = Rx + Sx pR + r pR = pR + pS x Sx p pS Cx Ax Rx pR pC pA O O

Dual decomposition of turnover w “w” = pdiag(x) or “w” = diag(p)x “w” = “c” + “v” + “m”, r = g w = pAdiag(x) + pCdiag(x) + pSdiag(x) w’ = diag(p)Ax + diag(p)Cx + diag(p)Sx „m“=pSdiag(x) „w“ = pdiag(x) = diag(p)x diag(p)Sx „v“=pCdiag(x) pRdiag(x) diag(p)Rx diag(p)Cx „c“=pAdiag(x) diag(p)Ax O

Stucture of labor values no surplus for services, variable exploitation rates c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m m v v c c

Marx‘ solution: Prices of production c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m v c

von Bortkiewicz: Prices of production c - constant capital, v - variable capital, m - surplus value Austria 2003: 57 industries (percent) m v c

Empirical results II: Gross-output (P), labour values (W0) and prices of production (PP) Austria 2003: 57 industries (Mio EUR) Correlation coefficient of p with r w - all sectors 0.883 w* – only mat. production 0.802 pp Marx first iteration 0.901 5th iteration 0,954 pp Bort- kiewicz 0.952 Labour values W0 gross output P (observed) prices of production PP Zum Video

Transformation problem iterative solution Video Iteration Correlation 1 0,80200000 2 0,90131617 3 0,94169690 4 0,95211631 * 5 0,95373425 6 0,95349443 7 0,95306224 8 0,95273999 9 0,95253944 10 0,95242360 11 0,95235923

generalized transformation problem: moving the tip of the value vector in a hyperplane p, observed w, classical x O pp, prices of production Bortkiewicz 1 2 3 hyperplane of all possible non-negative price systems p x = const value of total turnover is invariant pp, prices of production, One iteration a la Marx w*, mat. prod. only

hyperplane (Austria: 3 sectors) Video

set of all feasible prices – corresponding to fixed surplus product, but variable distribution of profits: subset of hyperplane px = const (Austria: 3 sectors)

Prices and labor values (hyperplane px = const) s: von Bortkiewicz‘ solution Marx‘ solution of the transformation problem one iteration only

Conclusions on price systems While A and C may remain constant, Changes in the price system go together with changes of the surplus matrix S Changes of S must leave the row sums of Sdiag(x) invariant (no change in the surplus product, but change in the distribution of profits) In mathematical terms this can be done by post-multiplication of S by an appropriately chosen Markov-matrix The changes result in a change of sectorial profits resp. surplus values, and sectorial rates of profit resp. rates of surplus

Economic Reality – A Complex Construction 7 6 5 4 3 2 1 Contemporary Capitalism market prices (observed) Information Society: information as commodity, communication as commercial service commodification of information goods/services 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/service markets Physical basis use values, environmental issues collective production/appropriation

p(A+C+S)= p different profit rates Observed market prices p [currency units] j=1 2 3 …. Use of GDP i =1 2 3 .. Intermediary values Final Demand Output Distribution of GDP wages profits p(A+C+S)= p different profit rates Output

Three measures of productivity Productivity(1), productivity of use value, number of use-values per working hour (independent of relations of production Productivity(2), productivity of labour value, 0 or 1 (productive vs. unproductive labour: Adam Smith). Important to characterize the difference between goods and services Productivity(3), productivity of profit, measured by profit over live labour in working hours. Productivity measure of capitalism, proposed by Marx

Economic Reality – A Complex Construction 7 6 5 4 3 2 1 Contemporary Capitalism market prices (observed) Information Society: information as commodity, communication as commercial service Public sector Globalized economy International financial capital Capitalism with perfect competition and fixed capital Productivity (3) Profitable Production Commodity production of self employed Productivity (2) Production of values in exchange Physical basis Productivity (1) Production of use-values

Danke für Ihre Aufmerksamkeit! Nächster Termin: 17. November, 14:00 Uhr am IFF, Seminarraum 4c