The Third Forum of the World Association for Political Economy (WAPE)

1. The Third Forum of the World Association for Political Economy (WAPE) Marxism and Sustainable Development May 24-25, 2008 at Langfang City, China Hosted by the Academy of Marxism, Chinese Academy of Social Sciences (CASS) The School of Economics and Management, Tsinghua University, and The U.S. journal Nature, Society, and Thought New aspects of the labor theory of valuePeter Karl Fleissner, Vienna, Austriahttp://transform.or.at

2. Setting the stage: 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

4. two aspects of a commodity Aristotle (“De Rep.” l. i. c. 9, ~ 350 BC): “The one is peculiar to the object as such, the other is not, as a sandal which may be worn, and is also exchangeable. Both are uses of the sandal, for even he who exchanges the sandal for the money or food he is in want of, makes use of the sandal as a sandal. But not in its natural way. For it has not been made for the sake of being exchanged” Adam Smith (The Wealth of Nations, 1776): “The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called ‘value in use’; the other, ‘value in exchange.’” Karl Marx (Das Kapital, Volume One, 1867) The wealth of those societies in which the capitalist mode of production prevails, presents itself as ‘an immense accumulation of commodities,’ its unit being a single commodity. Our investigation must therefore begin with the analysis of a commodity.”

5. 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

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

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

8. New aspects • treating services as value consuming • joint geometric interpretation of prices, values and volumes • visualisations of the transformation of values into prices

9. treating services as value consuming • there is an essential difference between goods (= material products) and services • nota bene: many environmentally relevant activities are services • services do not contribute to surplus product, nor to surplus value, they as such cannot be resold nor accumulated, because they disappear when they are produced and at the same time consumed • In „Das Kapital“, Vol I, Marx dealt only with material products where according to his labor theory of value (LTV) theprinciple of equivalenceholds. • principle of equivalence: goods are exchanged according to their total content of social labor • if service sectors are allowed to make profits(as it is the case under capitalism),the principle of equivalence is violated and LTV is no longer valid

10. How to determine labor values in a Leontief economy mathematically? A... partitioned matrix of technical coefficients C... partitioned matrix of unit consumption n... partitioned row vector of unit live labor = { n1, n2 } p... partitioned row vector of observed prices = { p1, p2 } w... partitioned row vector of labor values = { w1, w2 } pp... row vector of prices of production I.... Identity matrix A11, A12 C11, C12 A = {}, C = {} A21, A22 C21, C22 all industries (classic) are value producers w = n (I – A)-1 onlymaterial production is value producing (services at reproduction cost) w* = { n1(I – A11)-1 , n1(I – A11)-1 (A12+C12) [I-(A22+C22)]-1}

11. Empirical test:Gross-output (P), labor values (W0) and prices of production (PP)Austria 2003: 57 industries (Mio EUR) gross output P (observed) labour values W0 prices of production PP

13. Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m v c

15. Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m v c

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

17. Marxian indicators rate of surplus value, organic composition of capital, rate of profitAustria 2003: 57 industries (percent) rate of profit rate of surplus value organic composition

18. Stucture of labor valuesno surplus for services, variable exploitation rates c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m m v v c c

19. Structure of labor values no surplus for services, equal exploitation rates c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m v c

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

21. Structure of labor values all industries are value producers c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m v c

22. joint geometric interpretation of prices, values and volumes More variables S... partitioned matrix of surplus product R... partitioned reproduction matrix, R = A + C x... column vector of physical output r... rate of profit g... rate of growth pp... row vector of prices of production i...... index of iteration (i=1,2,...) S11, S12 S = {} S21, S22

23. x pS Sx p pC Cx pR Ax Rx pA O O 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

24. 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 + SxpR + r pR = pR + pS x p Sx pS Cx Ax Rx pR pC pA O O

25. 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

26. transformation of labor values into prices (transformation problem) Marx‘ solution pp(0) = w or w* pp(1) = pp(0) R [1 + r(i)] 1 + r(i) = pp(i) x / [pp(i) R x] Difficulty: input prices ≠ output prices von Bortkiewicz solution two identical solutions a) Eigenvector solution: pp ... left-hand Eigenvector of R pp R (1 + r) = pp, largest eigenvector of R: 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]

27. visual representations of thetransformation of labor values into prices of production

28. Stucture of labor valuesno surplus for services, variable exploitation rates c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m m v v c c

29. Marx‘ solution: Prices of productionc - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m v c

30. von Bortkiewicz: Prices of productionc - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent) m v c

31. Video Transformation problem iterative solution

32. 3 x w p pp, prices of production 2 O 1 Geometric interpretationof input-output indicators hyperplane of all possible non-negative price systems p x = const value of total turnover is invariant

33. Video hyperplane (Austria: 3 sectors)

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

35. Prices and labor values (hyperplane px = const) : von Bortkiewicz‘ solution of the transformation problem Marx‘ solution of the transformation problem

36. Thank you for your attention! E-mail: fleissner@transform.or.at Homepagehttp://members.chello.at/gre/fleissner Homepage transform!at: http://transform.or.at