Transcript The Third Forum of the World Association for Political Economy (WAPE) Marxism and Sustainable Development May 24-25, 2008 at Langfang City, China Hosted.

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 value
Peter Karl Fleissner, Vienna, Austria
http://transform.or.at
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
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
• 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
competition the market creates a tendency
towards more efficiency
• If there is
the composition of labor value w
new labor
(live
labor)
n
w=
c+n
pre-done labor
c
labor value w and its
composition
new labor
(live
labor)
pre-done labor
m
surplus value
(profit)
v
variable
capital
(wages)
c
constant
capital
(fix and
circulating
capital)
n
c
w=
c+n=
c+v+m
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...
C...
n...
p...
w...
pp...
I....
partitioned matrix of technical coefficients
partitioned matrix of unit consumption
partitioned row vector of unit live labor = { n1, n2 }
partitioned row vector of observed prices = { p1, p2 }
partitioned row vector of labor values = { w1, w2 }
row vector of prices of production
Identity matrix
A11, A12
A = {
}, C = {
A21, A22
C11, C12
}
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
prices of production PP
gross output P (observed)
Correlation coeff
r with
p
w* – mat
production
0.802
w - all
sectors
0.883
pp Marx
1 iteration
0.901
pp Bortkiewicz
0.952
Nr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Industry
Agriculture, hunting
Forestry, logging
Fishing, fish farms
Mining of coal and lignite
Extract. o. crude petrol. a. nat. gas, min. o. metal ores
Other mining and quarrying
Manufacture of food products and beverages
Manufacture of tobacco products
Manufacture of textiles
Manufacture of wearing apparel
Manufacture of leather, leather products, footwear
Manufacture of wood and of products of wood
Manufacture of paper and paper products
Publishing, printing and reproduction
Manufacture of coke, refined petroleum products
Manufacture of chemicals and chemical products
Manufacture of rubber and plastic products
Manufacture of other non-metallic mineral products
Manufacture of basic metals
Manufacture of fabricated metal products
Manufacture of machinery and equipment n.e.c.
Manufacture of office machinery and computers
Manufacture of electrical machinery and apparatus n.e.c.
Manufacture of radio, television equipment
Manuf. of medical, precision, optical instruments, clocks
Manufacture of motor vehicles and trailers
Manufacture of other transport equipment
Manufacture of furniture; manufacturing n.e.c.
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
Recycling
Electricity, gas, steam and hot water supply
Collection, purification and distribution of water
Construction
Sale and repair of motor vehicles; automotive fuel
Wholesale and commission trade
Retail trade, repair of household goods
Hotels and restaurants
Land transport; transport via pipelines
Water transport
Air transport
Supporting a. auxiliary transport activities; travel agencies
Post and tele-communications
Financial intermediation, except insur.
Insurance and pension funding, except social security
Activities auxiliary to financial intermediation
Real estate activities
Renting of machinery and equipment without operator
Computer and related activities
Research and development
Other business activities
Public administration; compulsory social security
Education
Health and social work
Sewage and refuse disposal,sanitation and similar act.
Activities of membership organizations n.e.c.
Recreational, cultural and sporting activities
Other service activities
Private households with employed persons
Stucture of gross output (observed)
c - constant capital, v - variable capital, m - surplus value
Austria 2003: 57 industries (percent)
m
v
c
Nr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Industry
Agriculture, hunting
Forestry, logging
Fishing, fish farms
Mining of coal and lignite
Extract. o. crude petrol. a. nat. gas, min. o. metal ores
Other mining and quarrying
Manufacture of food products and beverages
Manufacture of tobacco products
Manufacture of textiles
Manufacture of wearing apparel
Manufacture of leather, leather products, footwear
Manufacture of wood and of products of wood
Manufacture of paper and paper products
Publishing, printing and reproduction
Manufacture of coke, refined petroleum products
Manufacture of chemicals and chemical products
Manufacture of rubber and plastic products
Manufacture of other non-metallic mineral products
Manufacture of basic metals
Manufacture of fabricated metal products
Manufacture of machinery and equipment n.e.c.
Manufacture of office machinery and computers
Manufacture of electrical machinery and apparatus n.e.c.
Manufacture of radio, television equipment
Manuf. of medical, precision, optical instruments, clocks
Manufacture of motor vehicles and trailers
Manufacture of other transport equipment
Manufacture of furniture; manufacturing n.e.c.
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
Recycling
Electricity, gas, steam and hot water supply
Collection, purification and distribution of water
Construction
Sale and repair of motor vehicles; automotive fuel
Wholesale and commission trade
Retail trade, repair of household goods
Hotels and restaurants
Land transport; transport via pipelines
Water transport
Air transport
Supporting a. auxiliary transport activities; travel agencies
Post and tele-communications
Financial intermediation, except insur.
Insurance and pension funding, except social security
Activities auxiliary to financial intermediation
Real estate activities
Renting of machinery and equipment without operator
Computer and related activities
Research and development
Other business activities
Public administration; compulsory social security
Education
Health and social work
Sewage and refuse disposal,sanitation and similar act.
Activities of membership organizations n.e.c.
Recreational, cultural and sporting activities
Other service activities
Private households with employed persons
Stucture of gross output (observed)
c - constant capital, v - variable capital, m - surplus value
Austria 2003: 57 industries (percent)
m
v
c
three central Marxian indicators
new labor
(live
labor)
m
n
v
pre-done labor
surplus value
(profit)
c
c
variable
capital
(wages)
constant
capital
(fix and
circulating
capital)
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)
Marxian indicators
rate of surplus value, organic composition of capital, rate of profit
Austria 2003: 57 industries (percent)
rate of profit
organic composition
rate of surplus value
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
Structure of labor 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
organic composition
rate of surplus value
Structure of labor values
all industries are value producers
c - constant capital, v - variable capital, m - surplus value
Austria 2003: 57 industries (percent)
m
v
c
joint geometric interpretation of
prices, values and volumes
More variables
S...
R...
x...
r...
g...
pp...
i......
partitioned matrix of surplus product
partitioned reproduction matrix, R = A + C
column vector of physical output
rate of profit
rate of growth
row vector of prices of production
index of iteration (i=1,2,...)
S11, S12
S =
{
}
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 = p
x
pS
Sx
pC
Cx
pR
Ax
Rx
pA
O
O
p
Dual decomposition of
output x (left) for equilibrium growth
and for unit prices of production p (right)
x = Rx (1 + g) =
= Rx + g Rx = Rx + Sx
p = pR (1 + r) =
pR + r pR = pR + pS
x
p
Sx
pS
Cx
Ax
Rx
pR
pA
O
O
pC
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
„c“=pAdiag(x)
O
diag(p)Ax
diag(p)Cx
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,
b)
largest eigenvector of R: λ=1/(1+r)
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 the
transformation
of
labor values
into
prices of production
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
Transformation problem
iterative solution
Iteration Correlation
1
0,80200000
2
0,90131617
Video
Correlation coefficient between actual
prices and production prices (i-th iteration)
0,98
0,96
3
0,94169690
0,94
*
4
0,95211631
5
0,95373425
6
0,95349443
7
0,95306224
0,88
8
0,95273999
0,86
9
0,95253944
0,84
10
0,95242360
0,82
11
0,95235923
0,8
0,92
0,9
1
2
3
4
5
6
7
8
9
10
11
Geometric interpretation
3
of input-output indicators
x
w
p
hyperplane of all
possible nonnegative price
systems
p x = const
value of total
turnover is invariant
pp, prices of
production
2
O
1
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)
: von Bortkiewicz‘
solution of the
transformation problem
Marx‘ solution of the
transformation problem
Thank you
for your attention!
E-mail: [email protected]
Homepage http://members.chello.at/gre/fleissner
Homepage transform!at: http://transform.or.at