New aspects of the

labor theory of value Peter Karl Fleissner, Vienna, Austria

http://transform.or.at

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

Marxism and Sustainable DevelopmentMay 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, andThe U.S. journal Nature, Society, and Thought

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

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

New aspects

1. treating services as value consuming

2. joint geometric interpretation of prices, values and volumes

3. visualisations of the transformation of values into prices

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) the principle of equivalence holds.

• 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

How to determine labor values in a Leontief economy mathematically?

A... partitioned matrix of technical coefficientsC... 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 productionI.... Identity matrix

A11, A12 C11, C12 A = { }, C = { }

A21, A22 C21, C22

all industries (classic) are value producers w = n (I – A)-1

only material production is value producing (services at reproduction cost)

w* = { n1(I – A11)-1 , n1(I – A11)-1 (A12+C12) [I-(A22+C22)]-1 }

Empirical test:Gross-output (P), labor values (W0) and prices of production (PP)

Austria 2003: 57 industries (Mio EUR)

labour values W0 gross output P (observed)

prices of production PP

Correla-

tion coeff

r with p

w* – mat

production

0.802

w - all sectors

0.883

pp Marx

1 iteration

0.901

pp Bort- kiewicz

0.952

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.

c

v

m

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

Austria 2003: 57 industries (percent)

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.

c

v

m

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

Austria 2003: 57 industries (percent)

three central Marxian indicators

new labor(live labor) n

pre-done labor

m

c

v

c

constantcapital(fix and

circulatingcapital)

variablecapital

(wages)

surplus value(profit)

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)

rate of profit rate of surplus value

organic composition

Marxian indicators rate of surplus value, organic composition of capital, rate of profit

Austria 2003: 57 industries (percent)

c

v

m

c

v

m

Stucture of labor values no surplus for services, variable exploitation rates

c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

Structure of labor values no surplus for services, equal exploitation rates

c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

c

v

m

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

Structure of labor values all industries are value producers

c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

c

v

m

joint geometric interpretation of prices, values and volumes

More variables

S... partitioned matrix of surplus productR... partitioned reproduction matrix, R = A + Cx... column vector of physical outputr... rate of profitg... rate of growthpp... row vector of prices of productioni...... index of iteration (i=1,2,...)

S11, S12S = { }

S21, S22

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

= Rx + Sx = x = pR + pS = px

Ax

Cx

O

Sx

Rx

p

pA

pC

O

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

p

pA

pC

O

pS

pR

x

Ax

Cx

O

Sx

Rx

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

„w“ = pdiag(x) = diag(p)x

diag(p)Ax

diag(p)Cx

O

diag(p)Sx

diag(p)Rx

pRdiag(x)

„c“=pAdiag(x)

„v“=pCdiag(x)

„m“=pSdiag(x)

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 Rpp 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]

visual representations

of thetransformation

of labor values

into prices of production

c

v

m

c

v

m

Stucture of labor values no surplus for services, variable exploitation rates

c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

Marx‘ solution: Prices of productionc - constant capital, v - variable capital, m - surplus value

Austria 2003: 57 industries (percent)

v

c

m

von Bortkiewicz: Prices of productionc - constant capital, v - variable capital, m - surplus value

Austria 2003: 57 industries (percent)

v

c

m

Correlation coefficient between actual prices and production prices (i-th iteration)

0,8

0,82

0,84

0,86

0,88

0,9

0,92

0,94

0,96

0,98

1 2 3 4 5 6 7 8 9 10 11

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

Transformation problem iterative solution

Video

Geometric interpretation of input-output indicators

p

w

x

O

pp, prices of production

1

2

3

hyperplane of all possible non-negative price systems

p x = const

value of total turnover is invariant

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)

Marx‘ solution of the transformation problem

: von Bortkiewicz‘ solution of the transformation problem

Thank you

for your attention!

E-mail: fleissner@transform.or.atHomepage http://members.chello.at/gre/fleissner

Homepage transform!at: http://transform.or.at