Journal of Applied Input-Output Analysis, Vol. 15, 2009

Alternative Value Bases and Prices:

Evidence from the Input-Output Tables of the Swedish Economy1
byGeorge Soklis*

Abstract

This paper extends the empirical investigation of the relationships between labour values,
actual prices of production and market prices to the case of alternative 'value bases' using
data from the input-output tables of the Swedish economy. It is found that there exist vec
tors of 'commodity values' that are better approximations of prices than labour values.

INTRODUCTION

In recent years, an increasing number of empirical studies explore the relationships be
tween labour values, actual production prices and market prices.2 The main conclusionof these studies is that the vectors of labour values and production prices are quite
close to that of market prices, as this can be judged by alternative measures of devia
tion. These results are usually interpreted as giving support to the labour theory ofvalue as an analytical tool for the understanding of the laws of motion of actual econo
mies.

Department of Public Administration, Panteion University, Athens, Greece

Correspondence Address: George Soklis, Department of Public Administration, Panteion University,
136 Syngrou Ave, Athens 17671, Greece; Email: gsok@hotmail.gr
Earlier versions of this paper were presented at a Workshop of the 'Study Group on Sraffian
Economics' at the Panteion University, in December 2008, at the '11th Conference of the Greek His
torians of Economic Thought' and at the '1st Conference of the Greek Scientific Association of Po

litical Economy' at the University of Crete, in June 2009: I am indebted to Apostolos Dedousopoulos, Alexis Ioannides, Eleftheria Rodousaki, Nikolaos Rodousakis, Nikos Theocarakis, Lefteris Tsoul-fidis, Andriana Vlachou and, in particular, Theodore Mariolis for helpful discussions and comments. I
am also grateful to three anonymous referees of this journal for helpful comments and suggestions. It
goes without saying that the responsibility for the views expressed and any errors rests entirely withthe author.

See Shaikh (1984, 1998), Petrovic (1987), Ochoa (1989), Cockshott et al. (1995), Cockshott andCottrell (1997), Chilcote (1997), Tsoulfidis and Maniatis (2002), Tsoulfidis and Mariolis (2007),
Tsoulfidis (2008), inter alia.

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Journal ofApplied Input-Output Analysis, Vol. 15, 2009

However, it is well known that any 'basic' (a la Sraffa, 1960, §6) commodity can beconsidered as a 'value base' and, therefore, it is possible to determine the so-called'commodity i values' (Gintis and Bowles, 1981; Roemer, 1986), i.e., the direct and in
direct requirements of commodity / necessary to produce one unit of each commodity
as gross output. To our knowledge, there are two empirical studies (Cockshott and Cottrell, 1997; Tsoulfidis and Maniatis, 2002), based on input-output tables of the UK and
Greek economy, respectively, which have used alternative commodities as value bases.3
The conclusion of the aforesaid studies is that commodity values are, by and large,
considerably worse approximations of prices than labour values. The purpose of thispaper is to estimate the deviations of the vectors of actual production prices and market
prices from the vectors of labour values and commodity values associated with theSymmetric Input-Output tables (SIOT) of the Swedish economy (for the years 1995
and 2005).4 It is important to note that we decided to use Sweden's input-output tables
mainly because there were available comparable tables of not less than ten years
chronological distance, which is a sufficient time interval in order to expect differenti
ated results.

A crucial issue concerning the investigation of the relationships between prices andvalues is the choice of a theoretical appropriate measure of price-value deviation. As iswell known, the results obtained on the basis of the traditional measures of deviation(such as 'correlation coefficient', 'mean absolute deviation', 'mean absolute weighted
deviation', 'root-mean-square-percent-error') depend on the arbitrary choice of either
the numeraire or the physical measurement units.5 In the current study, we avoid thesaid problems by using the so-called 'd -distance' (Steedman and Tomkins, 1998, pp.
381-382), which constitutes a measure of price-value deviation that is free from nu
meraire and measurement-unit dependence.

The remainder of the paper is organized as follows. Section 2 presents the analytic
framework. Section 3 provides the results of the empirical analysis. Section 4 concludes.

Cockshott and Cottrell (1997) considered as value bases the commodities 'Electricity', 'Oil products'
and 'Iron and Steel', whilst Tsoulfidis and Maniatis (2002) considered the commodities 'Agricultural
products', 'Electricity', 'Oil products' and 'Chemicals'.

See Appendix 1 for the available input-output data as well as the construction of relevant variables.
For a detailed discussion of the problem of measuring the deviation of prices from labour values,see, e.g., Steedman and Tomkins (1998) and Diaz and Osuna (2005-2006, 2009). For the theoreticalinvestigation of the relationships between prices and labour values, see Parys (1982) and Bidard andEhrbar (2007), whilst for the so-called problem of transforming values into prices, see, e.g., Pasinetti(1977, ch. 5, Appendix) and Reati (1986). Finally, for a new approach to the relationships between
prices and values, see Mariolis (2010).

Alternative Value Bases and Prices: Evidence from the Input-Output Tables ofthe Swedish Economy

23

THE ANALYTIC FRAMEWORK

We begin with a closed, linear system with only single-product industries, circulating
capital and homogeneous labour, which is not an input to the household sector. The net
product is distributed to profits and wages that are paid at the beginning of the com

mon production period and there are no savings out of this income.6 All commodities
are basic and there are no alternative production techniques. The system is viable, i.e.,
the Perron-Frobenius eigenvalue, /L, of the nxn matrix of input-output coefficients, A,
is less than 1. Finally, the givens in our analysis are (i) the technical conditions of pro
duction, i.e., the pair (A, 1), where 1T is the lx/i vector of direct labour inputs ('T' denotes the transpose of an nx\ vector); and (ii) the real wage rate, which is represented
by the nxl vector b. On the basis of these assumptions, we can write

vT = vTA + f(1)

co = vTb(2)

pT = (l+r)(pTA + wlT)(3)

w = pTb(4)

where v, p are the vectors of labour values and production prices, respectively, co is
the labour value of the real wage bundle, i.e., the direct and indirect input requirementsof labour necessary to produce one unit of labour, w the money wage rate, and r theuniform rate of profit. Relations (1) and (3)-(4) entail thatvT = f [1 - A]"1

(5)

pT(l + r)"' = pTB(6)

where B (=A +blT) represents the matrix of the 'augmented' input-output coefficients,
i.e., each coefficient represents the sum of the respective material and wage good input
per unit of output. Thus, labour values can be estimated from (5). Each element, v,, ofthe vector of labour values expresses the 'vertically integrated labour coefficient' (Pasinetti, 1973) for commodity j, i.e., the direct and indirect requirements of labour necessary to produce one unit of commodity j. The coefficients v, or, more specifically, 1/v,are considered as indices of the productivity of labour (see, e.g., Okishio, 1963). Fi
nally, since a non-positive vector of commodity prices is economically insignificant, (6)implies that (1+r)"1 is the Perron-Frobenius eigenvalue of B and pT is the corresponding left-hand side eigenvector.

6 We hypothesize that wages are paid antefactum (for the general case, see Steedman, 1977, pp. 103105) and that there are no savings out of this income in order to follow most of the empirical studies
on this topic (see footnote 2).

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Journal ofApplied Input-Output Analysis, Vol. 15, 2009

Now define the 'extended' mxm (m=n+l) matrix C = [cy] (see, e.g., Okishio, 1963) asThis matrix is also known as the 'complete' or 'full' matrix (Brody, 1970).7 On the ba
sis of the above matrix, the vector of labour values is defined by

vT = vTC(„o + &(7)where C(m) denotes the matrix derived from C by extracting its m th row and column
and cl denotes the m th row of C if we extract its m th element. Therefore, it can beeasily seen that C(m) = A and cl = 1T. Furthermore, the labour value of the real wage
bundle is given byco = cl(I - Cwr'c"(8)where cm denotes the m th column of C if we extract its m th element, i.e., cm = b.

However, labour is just one of the m production inputs that can be considered as avalue base. In general, the vector of commodity / values (Gintis and Bowles, 1981,
Appendix 1; Roemer, 1986, pp. 24-26) is defined as follows
vj = v7C(0 + J(9)where \J =(vi, Vi,..., vU, v/+i,..., vi), v/ denotes the commodity / value of commodity;,i.e., the total (direct and indirect) requirements of commodity i necessary to produce

one unit of gross output of commodity j,* C0) denotes the matrix derived from C by
extracting its i th row and column (just as we extracted the m th row and column inorder to define the vector of labour values in relation (7) above), and cl denotes the /th row of C if we extract its i th element (and, therefore, represents the vector of direct
input requirements of commodity /). For example, assume that n = 2 and, therefore, C
is a 3x3 matrix, i.e.,

Then, the vector of 'commodity 1 values' is given byy] = vTCd, + Cl

(10)

where v! =(vl vl), C(n =( 22 2j and c[ =(an, bi). From relation (10) we obtain

7 Due to our assumption that labour is not an input to the household sector, the (m, m)th element of
matrix C equals zero. However, there is not an analogous assumption for the other production inputs,i.e., the on diagonal elements of matrix A can be positive.

8 It has been argued (see Mariolis and Rodousaki, 2008) that the concept of total requirements forgross output was introduced by Vladimir K. Dmitriev in his essay, published in 1898, on the theoryof value in Ricardo (see Dmitriev, 1974, Essay I).

Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy

25

V21 = V2022 + V3/2 + <2i2(11)

V31 = vlbi + h

(12)

and

Relation (11) gives the direct and indirect requirements of commodity 1 necessary to
produce one unit of commodity 2 as gross output, whilst relation (12) gives the direct
and indirect requirements of commodity 1 necessary to produce one unit of labour.
Analogously, one may obtain the vector of 'commodity 2 values' by extracting the sec
ond row and column of matrix C. Finally, by extracting the third row and column of C
we may obtain the vector of labour values. Thus, in general, the vector of commodity /values is obtained from relation (9) as follows (see also Manresa et al., 1998, p. 359)vf^cfd-Ccor1(13)

whilst the total input requirements of commodity / necessary to produce one unit of it
self is given by

C0i = v/c' + cu

(14)

where c' denotes the / th column of C if we extract its / th element, and e,- = (1 - co)l

C0i may be defined as the 'rate of exploitation' of commodity / (see also Gintis andBowles, 1981, p. 18). Finally, it can be shown that the conditions

r >0, C0i< 1, Ac< 1(15)where Ac denotes the Perron-Frobenius eigenvalue of C, are all equivalent (see Brody,
1970, Part 1; Manresa et al., 1998, pp. 358-360).9
Although the empirical relationships between prices and labour values have been inten
sively investigated, the relationships between commodity values and prices have notbeen examined to the same extent.10 In the next section we estimate the deviations ofactual prices from labour values and commodity values for the case of the Swedish
economy.

RESULTS AND THEIR EVALUATIONThe results from the application of the previous analysis to the input-output tables of
the Swedish economy for the years 1995 and 2005 are reported in Table 1 and Figures
1-2. Table 1 reports the largest and smallest deviations of prices from values. The vec-

9 Note that the aforesaid condition constitutes a general profitability condition, which includes the wellknown 'Fundamental Marxian Theorem' (see, e.g., Okishio, 1963).

10 For the theoretical relationships between prices and values, see Appendix 2 (which is based on Mari
olis, 2000; 2001).

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Journal of Applied Input-Output i\nalysis, Vol. 15, 2009

Tablel. Deviations of prices from values; Swedish economy, 1995 and 2005^^^^^^^

d-distance (%)'Value bases'^^^^^^

Actual prices of production vs. Market prices vs. values for thevalues for the year 1995 (2005) year 1995 (2005)

Labour

14.0 (13.6)

32.0 (21.8)'Products of forestry' CPA:02

29.0 (30.0)

31.5 (32.2)

17.2 (16.0)

29.8 (23.0)

33.4 (30.8)

47.1 (38.1)

31.0 (30.6)

46.9 (39.8)

14.8 (14.2)

31.8 (19.2)'Wearing apparels; furs'
CPA: 18'Basic metals' CPA: 27'Secondary raw materials'
CPA: 37'Energy products' CPA: 40'Services of water' CPA: 41

20.1 (19.8)

35.9 (19.8)'Construction work' CPA: 45

22.1 (21.0)

23.1 (16.6)

10.9 (10.3)

34.7 (23.0)

15.0 (15.4)

26.6 (15.7)'Wholesale and retail tradeservices'CPA: 50©51©52'Financial intermediation
services' CPA: 65'Insurance services' CPA: 66

17.4 (16.6)

28.9 (17.9)'Real estate services' CPA: 70

18.8 (17.2)

33.9 (20.9)

Average deviation of prices
from 'commodity values'

21.6 (20.4)

37.7 (27.3)

tors of values are estimated from the relation (13), whilst the vectors of actual prices of

production are estimated from the eigenequation (6).n In order to assess the proximityof actual production prices to values, we use a normalization bias-free measure of deviation that has been proposed by Steedman and Tomkins (1998) and is known as the
4d- distance'. The 'd- distance' is defined as d =/2(l-cos0), where 0 is the Euclid
ean angle between the vectors nj(\i)~l and e, v, a diagonal matrix formed from the ele
ments of v, and nl(yi)~x the ratio of prices to values.12

The first row of Table 1 refers to the deviations of prices from labour values,13 whilst
the remaining rows report the deviations of prices from commodity values.14 The last
11 Mathematica 7.0 is used in the calculations. The analytical results are available on request from theauthor.

12 Note that for / f m we get nj = (ph pi,..., /?,-i, /?.-+!,..., w), whilst for / = m we get nj = nl = pT. Fur
thermore, the 'd- distance' between market prices and values is estimated on the basis of the Euclid

ean angle between the vectors (^(v,)-1 and e, where (t^)t = (p,M, p?,..., ptX /?,>,,..., pi1) denotes thevector of market prices. Since market prices are taken to be equal to 1 (see Appendix 1), it follows

that for ifmvte get (nT)T = (l,l,l,l,...,wl), whilst for / = m we get (n™)T = eT. I am grateful to
Theodore Mariolis for an enlightening discussion on this point.
13 The vectors of labour values and actual prices of production for the year 1995 (2005) are reported inAppendix 3, Tables 3.1-3.2 (3.3-3.4). Note that we report the 'complete' a la Brody (1970) vectors,i.e., we include the value/price of the real wage bundle as the last element of the vectors.
14 The price-commodity value deviations that are found to be less than the corresponding price-labour
value deviations are indicated by bold characters.

Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy

27

row refers to the average deviations of prices from commodity values, i.e., the sum of
the deviations divided by the total number of commodities that are used as value bases.
In order to get a complete picture of the price-value deviations, in Figure 1 (2) we dis
play the deviations of the vector of production (market) prices from each vector ofcommodity values for both years of our analysis. The deviations for the year 1995
(2005) are measured in the vertical (horizontal) axis, whilst the price-labour value deviations are taken as the origin of the axes.
The points below (above) the horizontal axes indicate price-commodity value devia
tions less (greater) than the price-labour value deviations for the year 1995, whilst the
points on the left (right) side of the vertical axes indicate price-commodity value devia
tions less (greater) than the price-labour value deviations for the year 2005. Thus, thepoints on the lower-left (upper-right) quadrants of the figures indicate vectors of com
modity values that are better (worse) approximations of prices than labour values forboth years of our analysis.
From the Table 1, Figures 1-2, and the associated numerical results, we arrive at thefollowing conclusions:(i). The deviation of the vector of actual production (market) prices from the vector oflabour values for the year 1995 is almost 14% (32%), whilst that for the year 2005 isalmost 13.6% (21.8%). Furthermore, the actual 'relative rate of profit', p(=rlR),
where R (= (AA)_1-1) denotes the maximum rate of profit, is almost 39.1% (r 33.6%, R - 85.9%) for the year 1995 and almost 36.8% for the year 2005 (r Figure 1. Deviations of actual production prices from values; Swedish economy,
1995 and 2005
1995

30-

25-

20-

2005
20

25

30

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Journal of Applied Input-Output Analysis, Vol. 15, 2009

Figure 2. Deviations of market prices from values; Swedish economy, 1995 and
2005
1995

45

40

35

2005
25

20

30

35

40

30

25

29.7%, R - 80.7%).15(ii). The average deviations of actual production (market) prices from commodity val
ues are in the area of 21.6% (37.7%) for the year 1995 and in the area of 20.4%(27.3%) for the year 2005.
(iii). The deviation of actual production prices from the vector of commodity values associated with the aggregate commodity of sectors16 50 (Trade, maintenance and repair
services of motor vehicles and motorcycles; retail sale of automotive fuel'), 51('Wholesale trade and commission trade services, except of motor vehicles and motor

cycles') and 52 ('Retail trade services, except of motor vehicles and motorcycles; repair services of personal and household goods') is less than the corresponding actual
production price-labour value deviation for both years of our analysis,(iv). The deviations of market prices from the vectors of commodity values associatedwith commodities 40 ('Energy products'), 45 ('Construction work'), 65 ('Financial intermediation services') and 66 ('Insurance services') are less than the corresponding

market price-labour value deviation for both years of our analysis. Furthermore, the deviations of market prices from the vectors of commodity values associated with com
modities (a) 02 ('Products of forestry') and 18 ('Wearing apparels') for the year 1995;

15 It should be noted that these results are in accordance with the findings of all the relevant empiricalstudies (see footnote 2), where the relative rate of profit is in the range of 17%-40%, the actual pro

duction price-labour value deviation is in the range of 6%-20% and the market price-labour value deviation is in the range of 7%-37%.

16 For the degree of sectoral disaggregation of Sweden's input-output tables, see Appendix 1.

Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy29

and (b) 41 ('Services of water') and 70 ('Real estate services') for the year 2005 areless than the corresponding market price-labour value deviations,(v). The smallest actual production price-value deviation for the year 1995 (2005) is
10.9% (10.3%) and corresponds to the vector of commodity values associated with theaggregate commodity of the sectors 50, 51 and 52, whilst the smallest market pricevalue deviation for the year 1995 (2005) is almost 23.1% (15.7%) and corresponds tothe vector of commodity values associated with the commodity 'Construction work'('Financial intermediation services').17(vi). The largest actual production price-value deviation for the year 1995 (2005) is
33.4% (30.8%) and corresponds to the vector of commodity values associated with thecommodity 'Basic metals', whilst the largest market price-value deviation for the year
1995 (2005) is 46.9% (39.8%) and corresponds to the vector of commodity values associated with the commodity 'Basic metals' ('Secondary raw materials').

CONCLUDING REMARKSThis paper explored the relationships between the labour values, actual prices and com
modity values of the Swedish economy for the years 1995 and 2005. Regarding the deviations of prices from labour values, our results are in absolute accordance with thefindings of other empirical studies. However, it has been found that there exist vectorsof commodity values that are better approximations of actual prices than labour values.
The results of this study do not (or, more precisely, cannot) provide support to an alter
native value theory; on the contrary, cast doubts on the logic of the so-called 'empiricallabour theory of value' (Stigler, 1958, p. 361), in the sense that the empirical investiga
tion of the relationships between values and prices should not a priori neglect alterna
tive value bases. Future research efforts should use more disaggregated input-output
data from various countries and concretize the model by including the presence of
fixed capital and the degree of its utilization, depreciation, turnover times, taxes andsubsidies, and joint-product activities.

APPENDIX 1: A NOTE ON THE DATAThe SIOT and the corresponding levels of sectoral employment of the Swedish economy (for the years 1995, 2000 and 2005) are available via the Eurostat website (http://
ec.europa.eu/eurostat). Given that technical change over time could be considered asrather 'slow', we have chosen to apply our analysis to the tables of the years 1995 and2005. As is well known, the SIOT are derived from the 'System of National Accounts'

17 The aforesaid vectors of commodity values are reported in Appendix 4, Tables 4.1-4.4. The direct
and indirect requirements of a commodity necessary to produce one unit of itself are indicated bybold characters.

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Journal ofApplied Input-Output Analysis, Vol. 15, 2009

(SNA) framework of the Supply and Use tables (SUT) (see, e.g., United Nations,
1999, chs 2-4; Eurostat, 2008, ch. 11), whilst the level of sectoral disaggregation depends on the statistical practices of the relevant national offices (e.g., some European
Union member states compile tables that, initially, include 2000 to 3000 products (seeEurostat, 2008, p. 43)). The SIOT published by Eurostat describe 59 products, which
are classified according to CPA ('Classification of Product by Activity'). The described
products of the Swedish economy and their correspondence to CPA are reported in Ta
ble Al below. However, all the elements associated with the product 12 ('Uranium andthorium ores') equal zero and, therefore, we remove them from our analysis. Further
more, Statistics Sweden has aggregated, due to confidentiality reasons, the products 14('Other mining and quarrying products') and 16 ('Tobacco products') with the products
13 ('Metal ores') and 15 ('Food products and beverages'), respectively, whilst the prod
ucts 51 ('Wholesale trade and commission trade services, except of motor vehicles andmotorcycles') and 52 ('Retail trade services, except of motor vehicles and motorcycles;
repair services of personal and household goods') are aggregated with the product 50('Trade, maintenance and repair services of motor vehicles and motorcycles; retail saleof automotive fuel'). Additionally, for the year 2005, the products 32 ('Radio, televi
sion and communication equipment and apparatus') and 74 ('Other business services')are aggregated with the products 31 ('Electrical machinery and apparatus n.e.c.') and
73 ('Research and development services'), respectively. Finally, since the labour inputthat corresponds to the production of the product 11 ('Crude petroleum and naturalgas; services incidental to oil and gas extraction excluding surveying') equals zero forboth of the years, we aggregate the product 11 with the product 13. Thus, we derive
SIOT of dimensions 53x53 for the year 1995 and 51x51 for the year 2005. It goes
without saying that statistical practices, such as (i) the method used to convert SUT
into SIOT (for a review of these methods see, e.g., ten Raa and Rueda-Cantuche(2003, pp. 441-447)); and (ii) the level of sectoral disaggregation, can bias the empiri
cal results of our analysis.

The market prices of all products are taken to be equal to 1; that is to say, the physicalunit of measurement of each product is that unit which is worth of a monetary unit
(see, e.g., Miller and Blair, 1985, p. 356). Thus, the matrix of input-output coefficients,
A, is obtained by dividing element-by-element the inputs of each sector by its gross
output.

It need hardly be said that, in the real world, labour is not homogeneous and, therefore,
the levels of sectoral employment derived from the SIOT correspond to heterogeneous
labour. However, in the case of economic systems with heterogeneous labour, any attempt to explore the price-value deviation(s) is devoid of economic sense. Thus, in ac
cordance with most of the relevant empirical studies, we use wage differentials to homogenize the sectoral employment (see, e.g., Sraffa, 1960, §10; Kurz and Salvadori,
1995, pp. 322-325), i.e., the vector of inputs in direct homogeneous labour, 1 =[/j], isdetermined as follows: /j = (L77*;)(w;M/w22n), where L,, xj9 w,M denote the total employ
ment, gross output and money wage rate, in terms of market prices, of the j th sector,
respectively, and Wmm the minimum sectoral money wage rate in terms of market prices.
Alternatively, the homogenization of employment could be achieved, for example,

Alternative Value Bases and Prices: Evidence from the Input-Output Tables ofthe Swedish Economy

31

through the economy's average wage; in fact, the empirical results are robust to alter
native normalizations with respect to homogenization of labour inputs. The described
reductions of course are only meaningful when the relative wages express with precision the differences in skills and intensity of labour that is employed by each sector of

the economy (ibid.). In any other case the choice of homogenization procedure is, ofnecessity, arbitrary. Furthermore, by assuming that workers do not save and that theirconsumption has the same composition as the vector of the final consumption expenditures of the household sector, hf„ directly obtained from the input-output tables, thevector of the real wage rate, b = [&,•], is determined as follows: b = (widn/eTh«)h«,where eT = [l,l,...,l] denotes the row summation vector identified with the vector ofmarket prices (see also, e.g., Okishio and Nakatani, 1985, pp. 66-67). Finally, it must
be noted that the available input-output tables do not include inter-industry data on
fixed capital stocks and on non-competitive imports. As a result, our investigation is restricted to a closed economy with circulating capital.
Table Al. Product Classification
No

CPA

Nomenclature

Products of agriculture, hunting and related services

1

01

2

02

Products of forestry, logging and related services

305

Fish and other fishing products; services incidental of fishing

4

10

Coal and lignite; peat5

11

Crude petroleum and natural gas; services incidental to oil and gas extraction exclud
ing surveying

6

12

Uranium and thorium ores

7

13

Metal ores

8

14

Other mining and quarrying products

915

Food products and beverages

1016

Tobacco products

11

17

Textiles12

18

Wearing apparel; furs

13

19

Leather and leather products

14

20

Wood and products of wood and cork (except furniture); articles of straw and plaiting
materials

15

21

Pulp, paper and paper products

16

22

Printed matter and recorded media

17

23

Coke, refined petroleum products and nuclear fuels18

24

Chemicals, chemical products and man-made fibres

19

25

Rubber and plastic products

20

26

Other non-metallic mineral products

21

27

Basic metals

22

28

Fabricated metal products, except machinery and equipment

2329

Machinery and equipment n.e.c.

2430

Office machinery and computers

25

31

Electrical machinery and apparatus n.e.c.

32

Journal of Applied Input-Output Analysis, Vol. 15, 200927

33

Radio, television and communication equipment and apparatus
Medical, precision and optical instruments, watches and clocks

28

34

Motor vehicles, trailers and semi-trailers

29

35

Other transport equipment

26

32

30

36

Furniture; other manufactured goods n.e.c.

3137

Secondary raw materials

32

40

Electrical energy, gas, steam and hot water

33

41

Collected and purified water, distribution services of water

34

45

Construction work35

50

Trade, maintenance and repair services of motor vehicles and motorcycles; retail sale36

51

Wholesale trade and commission trade services, except of motor vehicles and motor
cycles37

52

Retail trade services, except of motor vehicles and motorcycles; repair services of
personal and household goods

38

55

Hotel and restaurant services

39

60

Land transport; transport via pipeline services

40

61

Water transport services

41

62

Air transport services

42

63

Supporting and auxiliary transport services; travel agency services

of automotive fuel43

64

Post and telecommunication services

44

65

Financial intermediation services, except insurance and pension funding services
Insurance and pension funding services, except compulsory social security services

45

66

46

67

Services auxiliary to financial intermediation

47

70

Real estate services

48

71

Renting services of machinery and equipment without operator and of personal andhousehold goods

49

72

Computer and related services

50

73

Research and development services

51

74

Other business services

52

75

Public administration and defence services; compulsory social security services

53

80

Education services

54

85

Health and social work services

55

90

Sewage and refuse disposal services, sanitation and similar services

56

91

Membership organisation services n.e.c.

57

92

Recreational, cultural and sporting services

58

93

Other services

59

95

Private households with employed persons

Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy

33

APPENDIX 2: ON THE RELATIONSHIPS BETWEEN PRICESAND VALUES

The system of production prices (see relations (3)-(4)) can be rewritten on the basis of
the complete matrix, C, as follows

7rT = 7TTC + kT

(A.l)

where 7tT = (pT, w) is the 'complete' a la Brody (1970) price vector, kT = 7rTCD is thevector of sectoral profit coefficients, D= (Jand f is an nxn diagonal matrix

formed by the sectoral profit rates. Relation (A.l) may be written asnl = riC{i)+picl + kj

(A.2)

Pi = 7rJc' + piCu + ki

(A.3)

where nT = (pi, pi,..., p,-i, p,-+i,...,p«) (kj = (nlCu)-\-p iCj)D{i)) is the vector derived from
7rT(kT) if we extract its / th element, D(/) is the nxn diagonal matrix derived from D
by extracting its / th row and column, and /?, (fc) is the / th element of nT (kT). Rela
tions (A.2)-(A.3) may be interpreted as the reduction of the 'production costs' (or,more precisely, the prices; see Sraffa, 1960, §7) to the 'production cost' (the price) of
the commodity i (see Dmitriev, 1974, pp. 61-64). From relation (A.2) we obtain

ic7 = pic7(I-C(or1 +k7(I-C(,)r1
or, recalling relation (13),nl = pivl + kl(I-Qi)yl(A.4)

Substituting kj =(7r7C<o+p,-c7)D</) in (A.4) and after rearrangement we obtain
h7=v7T(0(A.5)

where T(/) = p{ I - C<,-)) (I + D(/)) [I - C(/>( I + D(/))]"' is a linear operator 'transforming'commodity / values into prices. If 7c7 = 7rJ, = pT, i.e., prices are reduced to the price oflabour, then we obtain pT= vTT(,n), where T{m)= w(l-A)(I + f)[I-A(I + f)]_1 is thewell known linear operator 'transforming' labour values into prices (see Pasinetti, 1977,
ch. 5, Appendix; Reati, 1986).

When f = 0 and, therefore, kT=0T, relation (A.4) implies thatnl = Pi\J(A.6)

Thus, commodity / values are proportional to prices. Finally, in the special case wherethe vectors of sectoral profit coefficients, kj", and direct input requirements of commod
ity /, cj, are linearly dependent, i.e., kj=zcl, where z is a positive real number, thenfrom relation (A.4) we obtain

nl=(Pi + z)vI
Therefore, commodity / values are proportional to prices.

(A.7)

34

Journal of Applied Input-Output Analysis, Vol. 15, 2009

APPENDIX 3: LABOUR VALUES (LV) AND PRICES OF PRO
DUCTION (POP) OF THE SWEDISH ECONOMY
Table 3.2. POP; 1995

Table 3.1. LV; 1995
CPA

LV

CPA

LV

CPA

POP

CPA

POP

01

0.0096450.0143010.119445

0.1448020.004650051052

0.013202

0.041450051052

0.123605

0.010055

0.012805

0.123255

0.1360100.012460

0.0121100.143660

0.121811013014

0.011161

0.0117

11013014

0.122261

0.159715016

0.011662

0.012615016

0.1585620.1388170.013763

0.0104170.154063

0.112018

0.0145640.012418

0.169064

0.1217190.013565

0.0085190.165565

0.0799200.010166

0.012320

0.111566

0.1088210.008967

0.015621

0.1062670.1407220.0129700.0061220.139170

0.069723

0.011271

0.011323

0.159671

0.1212240.010272

0.014424

0.122472

0.148025

0.012673

0.015025

0.145973

0.147526

0.012374

0.014326

0.1348740.1445270.010875

0.014327

0.151975

0.133328

0.013380

0.016428

0.1527800.134529

0.013485

0.017329

0.155185

0.141030

0.0139900.010930

0.1568900.1118310.013691

0.018431

0.158291

0.153532

0.013592

0.013132

0.171792

0.128133

0.0137930.012533

0.1502930.125934

0.013095

0.0219340.174295

0.147635

0.0140REAL WAGE

0.469335

0.1622REAL WAGE

5.0518360.017336

0.184137

0.011437

0.1458400.006040

0.065941

0.007741

0.0872

Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy
Table 3.4. POP; 2005

Table 3.3. LV; 2005
CPA

LV

CPA

35

LV

CPA

POP

CPA

POP

0.1315010.005750051052

0.0057010.155850051052

02

0.004255

0.005602

0.099955

0.140205

0.004460

0.004905

0.128060

0.1245100.005561

0.0049100.159461

0.157111013014

0.004162

0.005211013014

0.1119620.15730.165763

0.133215016

0.005563

0.004615016

170.0058640.0051170.1499640.134618

0.005265

0.004118

0.1468650.0879190.005466

0.0042190.150466

0.087220

0.005067

0.006820

0.143067

0.141421

0.0048700.0028210.141670

0.0774220.005971

0.0047220.155171

0.116223

0.004172

0.005823

0.143272

0.13430.004173074

0.005724

0.116473074

0.135924
25

0.005575

0.0059250.148275

0.130926

0.005480

0.006926

0.148180

0.13670.139927

0.004985

0.0072270.160085

28

0.0055900.004728

0.1513900.123029

0.005891

0.007529

0.165991

0.152230

0.005992

0.005230

0.1589920.126931032

0.0055930.004331032

0.158893

0.097933

0.005595

0.008933

0.1465950.1505340.0056REAL WAGE

0.503734

0.1880REAL WAGE

12.974935

0.006035

0.163036

0.007136

0.189237

0.0047370.134740

0.002940

0.0784410.004141

0.1057450.0062450.1503

36

Journal of Applied Input-Output Analysis, Vol. 15, 2009

APPENDIX 4: COMMODITY VALUES (CV) OF THE SWEDISHECONOMY
Table 4.1. 'Wholesale and retail trade

Table 4.2. 'Wholesale and retail tradeservices values'; 1995

services values'; 2005

CPA

CV

CPA

CV

01

0.2175450.267202

0.078650®51©52

0.219005

0.202855

0.2454

05

CPA

CV

CPA

CV

01

0.304250051052

0.245002

0.198255

0.27930.255760

0.2597100.2339600.2269100.260361

0.2277

11©13014

0.2146

61

0.199811©13®14

0.216662

0.261715016

0.235662

0.211415016

0.281563

0.2185170.2505630.180417

0.266464

0.223618

0.2591640.2002180.238465

0.16110.1639190.2593650.1309190.254766

200.186566

0.1846200.241667

0.266721

0.188267

0.236021

0.248670

0.1312220.2175700.1105220.254271

0.2227230.224171

0.217423

0.216272

0.242924

0.187672

0.244024

0.191873074

0.2459250.238073

0.256925

0.2651750.243426

0.254274

0.236626

0.273780

0.276827

0.292675

0.233027

0.3048850.290328

0.2722800.250328

0.2782900.256029

0.276785

0.265629

0.297291

0.311830

0.2853900.203330

0.294292

0.2425310.270191

0.290631032

0.263793

0.198632

0.2851920.250233

0.2655950.333533

0.262293

0.237734

0.2986REAL WAGE

37.401634

0.282395

0.306335

0.2916REAL WAGE

14.009535

0.2722360.3337360.3250370.2245370.309140

0.136340

0.107041

0.187641

0.1447450.2930Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy

Table 4.3. 'Construction work

Table 4.4. 'Financial intermediation

values'; 1995
CPA

37

services values'; 2005

CV

CPA

CV

CPA

CV

CPA

CV

0.069701

0.097650051052

0.089501

0.067945020.030350051052

0.0637020.070955

0.091005

0.047655

0.072505

0.080960

0.0762100.067660

0.0623100.089761

0.090411013014

0.070961

0.059211013014

0.065762

0.084615016

0.067162

0.066615016

0.090363

0.075417

0.065763

0.0639170.0895640.085218

0.0685640.083018

0.0827650.100119

0.0689650.0472190.085066

0.120120

0.054766

0.078820

0.083067

0.106521

0.049767

0.081221

0.079770

0.092122

0.064770

0.120922

0.091671

0.074423

0.073171

0.060723

0.070172

0.088724

0.053772

0.068724

0.066673074

0.088125

0.063273

0.075625

0.085175

0.091226

0.065774

0.070426

0.085080

0.096227

27

0.061875

0.08940.082885

0.097228

0.066580

0.087228

0.086490

0.084729

0.064885

0.083429

0.092191

0.111130

0.065090

0.066730

0.095192

0.086031

0.067491

0.097231032

0.088593

0.072532

0.064992

0.075933

0.085395

0.110933

0.064593

0.065034

0.0939REAL WAGE

12.395234

0.062295

0.081435

0.092735

0.0684REAL WAGE

3.724036

0.110936

0.085137

0.076637

0.061140

0.052240

0.050241

0.072041

0.099045

0.0925

38

Journal of Applied Input-Output Analysis, Vol. 15, 2009

References

1. Bidard, C. and Ehrbar, H. G. (2007), "Relative prices in the Classical theory: facts
and figures", Bulletin of Political Economy, Vol.1, pp. 161-211.
2. Brody, A. (1970), Proportions, Prices and Planning. A Mathematical Restatement of
the Labor Theory of Value, Akademiai Kiado, Budapest.
3. Chilcote, E. B. (1997), "Interindustry Structure, Relative Prices, and Productivity: An
Input-Output Study of the U.S. and O.E.C.D. Countries", Ph.D. thesis, The New
School for Social Research, New York.

4. Cockshott, P. and Cottrell, A., Michaelson, G. (1995), "Testing Marx: some new results from UK data", Capital and Class, Vol.55, pp. 103-129.
5. Cockshott, P. and Cottrell, A. (1997), "Labour time versus alternative value bases: aresearch note", Cambridge Journal of Economics, Vol.21, pp.545-549.
6. Diaz, E. and Osuna, R. (2005-2006), "Can we trust in cross-sectional price-value cor
relation measures? Some evidence from the case of Spain", Journal of Post Keynesian Economics, Vol.28, pp.345-363.
7. Diaz, E. and Osuna, R. (2009), "From correlation to dispersion: geometry of theprice-value deviation", Empirical Economics, Vol.36, pp.427-440.
8. Dmitriev, V. K. (1974), Economic Essays on Value, Competition and Utility, Cambridge University Press, London.
9. Eurostat (2008), Eurostat Manual of Supply, Use and Input-Output Tables, Office for
the Official Publications of the European Communities, Luxemburg.
10. Gintis, H. and Bowles, S. (1981), "Structure and practice in the labor theory ofvalue", Review of Radical Political Economics, Vol.12, pp. 1-26.
11. Kurz, H. D. and Salvadori, N. (1995), Theory of Production. A Long-Period Analy
sis, Cambridge University Press, Cambridge.
12. Manresa, A. and Sancho, E, Vegara, J. M. (1998), "Measuring commodities' com
modity content", Economic Systems Research, Vol.10, pp.357-365.
13. Mariolis, T. (2000), "Positive (Non-Positive) Surplus Value with Non-Positive (Positive) Profits" (in Greek), Political Economy. Review of Political Economy and Social
Sciences, Vol.7, pp.81-126.
14. Mariolis, T. (2001), "On V. K. Dmitriev's Contribution to the so-called Transforma
tion Problem' and to the Profit Theory", Political Economy. Review of Political
Economy and Social Sciences, Vol.9, pp.45-60.
15. Mariolis, T. (2010), "Norm Bounds for a Transformed Price Vector in Sraffian Sys
tems", Applied Mathematical Sciences, Vol.4, pp.551-574.
16. Mariolis, T. and Rodousaki, E. (2008), "Total Requirements for Gross Output andIntersectoral Linkages: A Note on Dmitriev's Contribution to the Theory of Profits",
paper presented at the Tenth Conference of Greek Historians of Economic Thought,
30-31 May 2008, University of Thessalia, Greece.
17. Miller, R. and Blair, P. (1985), Input-Output Analysis: Foundations and Extensions,
Prentice Hall, New Jersey.
18. Ochoa, E. (1989), "Value, prices and wage-profit curves in the U.S. economy",
Cambridge Journal of Economics, Vol.13, pp.413-429.
19. Okishio, N. (1963), "A Mathematical Note on Marxian Theorems", Weltwirtschaftliches Archiv, Vol.91, pp.287-299.
20. Okishio, N. and Nakatani, T (1985), "A measurement of the rate of surplus value",in M. Kriiger, P. Flaschel (eds) (1993), Nobuo Okishio-Essays on Political Econ-

Alternative Value Bases and Prices: Evidence from the Input-Output Tables of the Swedish Economy

39

omy, Peter Lang, Frankfurt am Main.
21. Parys, W. (1982), "The deviation of prices from labor values", The American Eco
nomic Review, Vol.72, pp. 1208-1212.
22. Pasinetti, L. (1973), "The notion of vertical integration in economic analysis",
Metroeconomica, Vol.25, pp. 1-29.
23. Pasinetti, L. (1977), Lectures on the Theory of Production, Columbia University
Press, New York.

24. Petrovic, P. (1987), "The deviation of production prices from labour values: somemethodological and empirical evidence", Cambridge Journal of Economics, Vol.11,
pp.197-210.
25. Reati, A. (1986), "La transformation des valeurs en prix non concurrentiels", Economie Appliquee, Vol.39, pp. 157-179.
26. Roemer, J. E. (1986), Value, Exploitation and Class, Harwood Academic Publishers,
Chur.

27. Shaikh, A. (1984), "The transformation from Marx to Sraffa", in A. Freeman and E.
Mandel (eds), Ricardo, Marx and Sraffa, Verso, London.

28. Shaikh, A. (1998), "The empirical strength of the labour theory of value", in R.
Bellofiore (ed.), Marxian Economics. A Reappraisal, vol.2, Macmillan, London.
29. Sraffa, P. (1960), Production of Commodities by Means of Commodities. Prelude toa Critique of Economic Theory, Cambridge University Press, Cambridge.
30. Steedman, I. (1977), Marx after Sraffa, New Left Books, London.
31. Steedman, I. and Tomkins, J. (1998), "On measuring the deviation of prices fromvalues", Cambridge Journal of Economics, Vol.22, pp.379-385.
32. Stigler, G. J. (1958), "Ricardo and the 93% labor theory of value", The American
Economic Review, Vol.48, pp.357-367.
33. ten Raa, T. and Rueda-Cantuche, J. M. (2003), "The construction of input-output
coefficients matrices in an axiomatic context: some further considerations", Economic Systems Research, Vol.15, pp.439-455.
34. Tsoulfidis, L. (2008), "Price-value deviations: further evidence from input-output
data of Japan", International Review of Applied Economics, Vol.22, pp.707-724.
35. Tsoulfidis, L. and Maniatis, T. (2002), "Values, prices of production and market
prices: some more evidence from the Greek economy", Cambridge Journal of Eco
nomics, Vol.26, pp.359-369.
36. Tsoulfidis, L. and Mariolis, T. (2007), "Labour values, prices of production and theeffects of income distribution: evidence from the Greek economy", Economic Sys
tems Research, Vol.19, pp.425-437.
37. United Nations (1999), Handbook of Input-Output Table. Compilation and Analysis.
Studies in Methods. Handbook of National Accounting, United Nations, Department
for Economic and Social Affairs, Statistics Division, Series F, No.74, New York.