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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

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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 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

setting the stage basic terms in marxian political economics
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
two aspects of a commodity
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.”

on commodities and markets
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
the composition of labor value w
the composition of labor value w

new labor

(live

labor)

n

w =

c + n

pre-done labor

c

labor value w and its composition
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

new aspects
New aspects
  • treating services as value consuming
  • joint geometric interpretation of prices, values and volumes
  • visualisations of the transformation of values into prices
treating services as value consuming
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
how to determine labor values in a leontief economy mathematically
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}

slide11
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

slide13
Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

m

v

c

slide15
Stucture of gross output (observed) c - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

m

v

c

three central marxian indicators
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

slide17
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

slide18

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

slide19

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

slide20
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

slide21

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

joint geometric interpretation of prices values and volumes
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

slide23

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

slide24

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

slide25

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

transformation of labor values into prices transformation problem
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]

slide28

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

slide29
Marx‘ solution: Prices of productionc - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

m

v

c

slide30
von Bortkiewicz: Prices of productionc - constant capital, v - variable capital, m - surplus valueAustria 2003: 57 industries (percent)

m

v

c

geometric interpretation of input output indicators

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

slide34

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
Prices and labor values (hyperplane px = const)

: von Bortkiewicz‘ solution of the

transformation problem

Marx‘ solution of the

transformation problem

slide36
Thank you

for your attention!

E-mail: [email protected]

Homepagehttp://members.chello.at/gre/fleissner

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

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