Reading “A Note on Ronald Meek‟s „Studies in the Labour Theory of Value‟” is not easy. Therefore I have presented the following „Introductory Remarks‟ at the Conference. The following lines try to outline the logical structure of the problem.
Université Paris X – Nanterre, 8.10.2007
Introductory Remarks to
the Marginal Approach to the Labour Theory of Value
The basic proposition of the labour theory of value is the proportionality of the price to the
labour necessary for the production of a commodity.
A) Prices without a surplus (simple reproduction)
px = wL (1)
p- price, x – quantity, w – wage rate, L – labour
The wage rate
p (2) w?Lx
pwLxLx11111 (3) ??pwLxLx22222
B) Prices with a surplus (capitalistic reproduction)
px = wL + (1+r)K (4)
r – rate of profit, K – value of capital
Define the rate of surplus value s as well as the organic composition of capital o as
rKK s?o? (5) wLwL
Here we are at a point where further complications arrive as orthodox Marxists claim that the
surplus m is independent of capital and the rate of profit. m is a function of labour hours and the wage rate only. Then this s= m/wL has to be transformed into s=rK/wL. This is the
famous Transformation Problem. The problem has not been resolved properly. But see the
works of Gérard Duménil and Duncan Foley on the “New Interpretation”. However if that
problem can be resolved we still arrive at the problem as we discuss it here.
Notice the following relation: r = s/o
rKwLsrK (5a) r???oKwLK
p = wL (1 + s + o) (6)
Relative prices expressed with rates of surplus value and organic compositions of capital
pw(1?s?o)Lx11111 (7) ?pw(1?s?o)Lx22222
B1) Marxian assumption s?s 12
From the assumption follows o = o as the rate of profit r is uniform. 12
pw(1?s?o)LxLx1111111 (8) ??pw(1?s?o)LxLx2222222
Notice that this means that there is a proportionality between paid labour (L and L) and 12
s?sB2) The rates of surplus value are different: 12
??wLxL/xpw(1so)Lxe11e1111111??? (9) ??pw(1so)LxwLxL/x22222e22e22
L – labour embodied in commodity i ei
Here we have replaced the expression (1+s+o)L by L iiiei
The Problem Restated for the Case of Capitalistic Reproduction (see Equations 1 and 2)
Lepx?wL?wx (10) ex
pthen ? (10a) wLxe
L is labour embodied and consists of paid labour, unpaid labour and the labour embodied in e
the used up capital. Here it is obviously equal to the Ricardian concept of labour commanded,
L , which is by definition L = p/w. cc
The solution of the Marginal Revolution and Jevons (see Jevons’ chapter on labour in his ‘Theory of Political Economy)
?1LLe?? (11) x?x?x?Land
pw??p?x?L (12) ?L?x
The wage rate is equal to the ratio of price to the marginal labour value or equivalently the
wage rate is equal to the value of the marginal product (a standard result in microeconomic
theory for the maximization of profits in the case of perfect competition)
The solution substituted into equation (10) gives
??LLpLepx?wL?wx?wx?x (13) exxLxx????
?L?xOne should notice that Jevons proves that is embodied labour.
The Solution of Sraffa
p?wa?p(1?r)A (14) n
p – vector of prices, a– vector of labour coefficients, A – matrix of technical coefficients n
p??I?(1?r)A?wa (15) n
?1 (16) ??p?waI?(1?r)An
?1 (17) ??v?aI?(1?r)An
p = wv (18)
Now the vector v is regarded by the Neo-Ricardians as the vector of vertically integrated
labour coefficients if r = 0. Its elements indicate the labour hours needed for the production of
a commodity summing up all the labour hours used up also in intermediate production. This
can be seen when the vector is expanded to a power series
?12n?1 (19) ??v?aI?A?a?aA?aA?...aAnnnnn
If the rate of profit r is positive then the Neo-Ricardians speak of quantities of dated labour.
?122n?1n?1 (19) ??v?aI?(1?r)A?a?a(1?r)A?a(1?r)A?...a(1?r)Annnnn
iiNotice the surplus elements in it the arA. The Neo-Ricardians do not regard these elements n
as embodied labour and they speak of the vector v as representing labour commanded, L. c
This is because by definition L = p/w = v. c
p?But we follow Jevons and regard w as This is consistent with Sraffa‟s argument. w?L?x
Then v must be
?L?L?Ln12??v?,,... (20) ?x?x?x12n
With other words Jevon’s discovery can justify the position that Sraffian quantities of
dated labour are embodied labour. Sraffa’s solution should be seen as a reinstatement of the labour theory of value.
A Note on Ronald Meek’s 'Studies in the Labour
Theory of Value'
By Klaus Hagendorf
University of Paris X – Nanterre
Postal Address: 20, rue Turgot, 75009 Paris, France,
Email: firstname.lastname@example.org Abstract:
Ronald Meek has (deliberately) ignored a very important discovery of Jevons. When labour is
measured in terms of marginal labour values prices are proportional to these values and
commodities exchange accordingly. This has been rediscovered by Soviet economists and that
has been published in the JEL in the 70ies. Furthermore it is shown that under neoclassical
assumptions the vector of marginal labour values is equal to the Sraffian vector of quantities
of dated labour.
In his "Studies in the Labour Theory of Value" Ronald Meek has overlooked an important
inconsistency in Jevons‟ treatment of labour.
* I owe thanks to John S. Chipman, Stefano Perri and Antoine Rebeyrol for helpful comments
and corrections. I only am responsible for remaining errors.
In the chapter on labour in his "Theory of Political Economy" Jevons attributes 2 dimensions
to labour: time and intensity (Jevons 1871, p. 170). On the other hand he realizes that in
equilibrium utility equals labour and expresses relative prices as the ratio of marginal utilities
or marginal productivities (Jevons 1871, p. 186) .He discusses labour in terms of disutility
and considering the equilibrium situation arrives at the remarkable result "thus we have
proved that commodities will exchange in any market in the ratio of the quantities produced
1by the same quantity of labour” (Jevons, 1871, p. 187).
But surely it is clear that marginal productivity is a function not only of direct labour but also
of capital, the value of which can be expressed in labour units. We may best interpret the
capital intensity of labour as a crude measure of the social integration of labour, the third
2dimension of labour. The deeper the social integration of labour the more productive it can
be as it is assisted by more embodied labour. Under competitive conditions the higher the
capital intensity of labour the more productive must be that labour in order to yield a uniform
rate of return on capital.
1 Ronald Meek does not mention this important remark by Jevons at all in his otherwise so
carefully conducted studies. In fact a reference to this statement seems to be very difficult to
be found indeed in the literature, Marxian or orthodox.
2 Stigler (1941, p.34) criticising Jevons in a footnote suggests also that labour should be
considered having three dimensions: “The essential dimensions would be efficiency of labour,
duration of labour (per working day), and intensity of labour …”
Ronald Meek distinguishes two states of the commodity producing society, the early state of simple commodity production and the state of capitalist commodity production. It seems evident that the third dimension of labour, its social integration measured by its capital intensity is exactly the dimension of labour which distinguishes the capitalist state from the simple state of commodity production. Furthermore, instead of invalidating the law of value according to which prices correspond to labour embodied in the commodities, marginal analysis overcomes the famous contradiction between values and prices, prices equal values.
Jevons, instead of refuting Ricardo has in fact made the labour theory of value more perfect although one may render him justice in pointing out that as soon as substitution is allowed production costs are generally not uniquely determined and demand conditions enter into the determination of prices. But in equilibrium commodities exchange according to the labour embodied, labour understood as three-dimensional efficiency units.
Marx (1867) used a more accurate measure of the social integration of labour, the concept of the organic composition of capital which is precisely the ratio of embodied labour in (constant) capital to paid direct labour (wages). Modern economics does not consider wages as capital anymore and it may be more appropriate to name the organic composition of capital organic
composition of labour instead because that is what it really is. In contrast the capital intensity
is a ratio of some physical quantity of a commodity serving as capital and paid direct labour or if the value of capital is used, the money value of capital to paid direct labour. But although Marx had a more accurate measure of the social integration of labour he could not take advantage of it properly in the context of the theory of value. He dealt with the second
dimension, intensity, by using the concept of socially necessary labour time and using this as
his homogeneous labour unit he had to adapt a unique rate of surplus value.
The Soviet economist A.L. Lur‟e developed “An Abstract Model of an Optimal Economic
1 in which he derives Jevons‟ Process and Objectively Determined Valuations” (Lur‟e, 1966)solution for the optimal allocation of resources in a planned socialist economy: “in the
optimal plan the differential expenditures on various economic resources must be proportional
to their differential useful effect for society” (p. 23). In the optimal plan “optimal valuations
and the prices that correspond to them will be proportional to the socially necessary labor expenditures if by these are meant the marginal increments in labor on the scale of the entire
socialist economy corresponding to a unit increase of one or another resource.” (p. 27). Lur‟e
distinguishes in the following differential socially necessary expenditures of labour from
Marx concept of socially necessary expenditures of labour. His concept of differential socially
necessary expenditures of labour corresponds to the vertically integrated labour inputs:
“differential expenditures of socially necessary labour refer to both direct and indirect
expenditures, reflecting the interrelation of all the links of the national economy that are
This article has been cited in the Journal of Economic Literature by Lettiche (1971). “A comparatively small number of Soviet economists, however, have used mathematical
economics as an instrument for theoretical advance and as a stimulus for revision of dogma
and obsolete concepts … His (Lur‟es) presentation is definitely not representative of the Soviet economic literature in general.” (Letiche, 1971, p. 450).
considered in the preparation and analysis of optimal plans …” (p. 28) (see also the Appendix).
But Lur‟e does not want to interpret his differential socially necessary expenditures of labour
or Kantorovich‟s optimal determined valuations as expressions of Marxian values and refers
to Engels‟ criticism of such interpretations in his preface to the third volume of Capital. It
appears to us that Engels‟ criticism in its theoretical aspects is based on the conviction that one could not derive a logically satisfactory unit of labour values other than in Marx original
approach. But it seems to us that Kantorovich and Lur‟e have exactly achieved this.
Surely as it stands Marx concept was different. He adapted a unique rate of surplus value
independent of the degree of social integration of labour. But is this not a shortcoming of his
analysis? We are well able to explain the law of value and the exploitation of labour on the
basis of the three-dimensional concept of labour. Engels‟ criticism of Stiebeling appears as
less convincing once one has tackled the mathematical problems and in particular Euler‟s
Theorem. It may be justified to ask if Marx was not busy to improve his mathematical skills
after the publication of volume I of Capital in order to search for a proof of his theory in
terms of marginal analysis. We believe that Engels‟ criticism of Julius Wolf, G. C. Stiebeling
and others should be understood first of all as politically motivated. As Ronald Meek puts it:
“Marxists have indeed opposed the numerous suggestions which have been made from both
inside and outside their ranks to purge the labour theory from the body of Marxism, or to
“reconcile” it with the marginal utility theory … They have been encouraged in this view by the fact that many of those within their own ranks who have criticised the labour theory have
eventually shown themselves to be interested not so much in purging the labour theory from
Marxism as in purging Marxism itself from the ideology of the labour movement.” (Meek,
1976, p. 202).
A modern economist who is a case in point is John S. Chipman who has discussed the
problem of the unique rate of surplus value. Chipman (1952) poses the question “whether any
consistent theory of value can be drawn from Marx‟s writings. It will be shown that one
assumption – namely that of equal rates of surplus value among industries – is responsible for nearly all the errors and contradictions in Marx‟s theory; and that this assumption must be
altogether discarded if the theory is to uphold any claim to empirical validity.” (p. 527).
Chipman (referring to Capital, vol. III, ch. X) criticises Marx justification of equal rates of
surplus value: “Marx believed that competition tended to equalize rates of surplus value. The mechanism by which such equality is achieved is not described; apparently it is competition
among workers. There does not seem to be any valid reason why competition among workers,
or among firms, should equalize rates of surplus value.” (Chipman 1952, p. 533 f.). He comes to the conclusion “The rate of surplus value is not independent of the organic composition of
capital, but is, on the contrary, directly related to it. … Prices, then, are everywhere equal to
values, and individual profits are equal to individual surplus values, and the Marxian
contradiction is easily solved.” (p. 540 f.)
One should think that here Chipman has found his way to differential socially necessary expenditures of labour and the marginal labour theory of value. But in his conclusions he scraps it altogether: “[Marx] wished, whenever he thought he could get away with it, to cling
assiduously to the labour theory of value. Even where he had to reject it, he took pains to