I have been considering a case in which a simple Labor Theory of Value (LTV) is a valid theory of prices of production. When, for each technique, all processes have the same organic composition of capital, prices of production are proportional to labor values. Given labor values and direct labor coefficients in each industry, an uncountably infinite number of techniques - as specified by a Leontief input-output specified in terms of physical inputs per physical outputs - satisfies these conditions.

In outlining this mathematics, I start with labor values and derive technical conditions of production as a detour on the way to prices of production. (I have also considered a perturbation of this possibility, as an application of my pattern analysis.)

Has anybody commenting on Marx actually started with labor values, taken as given, in this way? If this is a straw person, I am good company. Ian Steedman (1977) makes something like the same accusation. See the section, "A spurious impression", in Chapter 4, "Value, Price, and Profit Further Considered", of his book.

But I have found examples of other approaching Marx in something like this way. I refer to von Bortkiewicz (1907) and Seton (1957), two authors taken as a precursor to the Sraffian reading of Marx. The fact that Steedman can be read as criticizing such authors complicates the claim that this literature exhibits continuity. I think others have also argued that some novelty arises in Steedman's critique insofar as he argues that labor values are redundant, since prices of production are properly calculated from technical data on production and the physical composition of wage goods.

Perhaps my examples of Bortkiewicz and Seton should not be
read as propounding any large claim that Marx takes labor values
as more fundamental, in some sense, than physical conditions in
production processes. Rather, Bortkiewicz started from
the schemes of simple and expanded reproduction at the end
of Volume 2 of *Capital*.
Since Seton, and other authors, were generalizing and
commenting on Bortkiewicz, they, as a matter of
path dependence, happened to keep the assumption of
given labor values.
One wanting to argue for a
reading of Marx that I seem to be stumbling into, without
any firm commitment, needs to deal with Volume 1.

I have two additional notes on rereading these references. First, I like to talk about Marx' invariants in the transformation problem. I thought I had taken this term from formal modeling in computer science. Edsger Dijkstra and C. A. R. Hoare talk about loop invariants, and I sometimes even comment my code with explicit statements of invariants. But Seton has a section titled "Postulates of Invariance".

Is Steedman disappointed in the reception of his book? Obviously, his points about the transformation problem, including the possibility of negative surplus value being consist with positive profits, under a case of joint production, have been widely discussed. But consider his exposition of simple examples intended to demonstrate that Sraffa's analysis can take into account all sorts of issues that some had argued were ignored. Consider letting how much work capitalists can get out of labor being a variable, heterogeneous types of abstract labor not reducible to one and the possibility of workers of each type exploiting others, wages being paid, say, weekly, during processes that take a year to complete, how wages relate to the rate of exploitation when a choice of technique exists, the treatment depreciation of capital, and the existence of a retail sector for circulating produced commodities. How many of these analyses have been taken up and continued by those building on Sraffa? (I think some have.)

**References**

- Eugen von Bohm-Bawerk (1949).
*Karl Marx and the Close of his System: Bohm-Bawerk's Criticism of Marx*. Edited by P. M. Sweezy. - Ladislaus von Bortkiewicz (1907). On the Correction of Marx's Fundamental Theoretical Construction in Third Volume of
*Capital*, Trans. by P. M. Sweezy. In Bohm-Bawer (1949). - F. Seton (1957). The "Transformation" Problem.
*Review of Economic Studies*, 24 (3): 149-160. - Ian Steedman (1981, first edition 1977).
*Marx After Sraffa*, Verso.

## 10 comments:

As I understand it, Marx takes as given labour values. With that he is able to compute aggregate output and aggregate input. Then he gets the ratio aggregate output to aggregate input which is R. With R he is able to get production prices, being those the ones at the extreme, when all the output goes to capitalist ( w=0 ). At the extreme (w=0) he can establish that when the industry has the same organic composition as the average then labour value (w=1) and price of production ( w=0) is connected by an horizontal line. When the organic composition is higher (lower) than the average, the labour value (w=1) and price of production (w=0) of each commodity are connected by straight lines of positive (negative) slopes. Between these extremes prices of productions aren't in these lines ( only by a fluke) by they could be taken as a good approximations if we are considering aggregates and deviations from the straight lines cancel each other approximately.

Following Schefold if the technology is really big and squared ( the Matrix of inputs An with n-> infinity) and the industry coefficients are random then the deviations of prices of productions from the straight lines in between the extremes continue but at the aggregate the cancel each other exactly.

Starting from the postulate that in big aggregates (like total output, total input, total product and the division of the product in two parts of equal compositions being Wages and Profits) deviations cancel exactly (in Shefold's case with Big Random Matrices) or approximately ( in Marx's one where I think we could say he is considering the technology of an Empire like UK so maybe not random or squared but actually a good approximation). He continues saying we can take the ratio R as constant and unaffected by distribution. These being the three well known invariant conditions.

I made a mistake...R is the ratio (Aggregate Output - Aggregate Input)/ Aggregate Input or Aggregate Product/ Aggregate Input. There is another special case where even with prices of production deviating from the straight lines connecting the extremes (w=1 and w=0) we can get an exact cancellation of deviations in Big Aggregates being it the Sraffian Standard System. So in the Standard System the three invariant conditions are also met. There are hints in Volume 3 to the Standard System.

This is more o less what as just a stur (dy) socialist aficionado I think i got.

PS: It would be interesting if considering a matrix L of heterogenous labour input coefficients would reduce the uncountable infinite technologies satifying the LTV. Also the discrete nature of some inputs like 1 pig and not 3.14159 pigs or 0.5 pigs could reduce the space.

What i mean in the last comment is that it is said since Steedman that labour values are redundant because we don't need them to get prices of production and that we can compute them by setting w=1. It is not negated that they can be useful for some analysis focusing on productivity. What I'm thinking is that in your examples with the simple LTV you get the result that for a given vector of labour values and labour coefficients (If I understand it properly) assuming identical organic compositions of capital in each industry we can get an uncountable infinite number of technologies that go. I guess that the same happens if instead of a vector of labour values we use a vector of production prices. But maybe if we go for a matrix of labour coefficients and a matrix of labour values given I think the door can be closed and we can go just in one direction from labour values to prices of production but not the other way around without indeterminacy or at least more indeterminacy than in the "from labour values" case.

Multiple Matrices of labour values with a Matrix of labour coefficients will give the same vector of production prices or a matrix of production prices consisting in the vector of production prices

p*I (the identity matrix) but starting with a vector of production prices orp*I will give just a vector of labour valuesvor V=v*I.Perhaps you would like to comment on my work respecting both P. Sraffa and Karl Marx:

"Production Prices Systems as derived from Labour Values Systems."

Abstract

Slightly changing Karl Marx procedure to calculate his production prices by keeping surplus value in the price cost of commodities, allows us to envisage a labour values system as a production prices system. The current industry rates of profit, in labour terms, are used in the calculation of these production prices which will be equalized afterwards. This work presents an alternative approach to calculate production prices and the rate of profit based in the eigenvalue and the eigenvector of the Leontief matrix. This allows us to see production prices systems as derived from labour values systems and keeping them proportional. Only after the industry rates of profit equalization occurs, i.e., when a similar remuneration to all capitals has to be assured, will prices differ necessarily from values. Prices and labour values initially form a unique system from which prices become autonomous.

https://mpra.ub.uni-muenchen.de/id/eprint/83908

I think neither of you may be taking labor values as given, in my sense. Sturai is outlining Marx's procedure for deriving prices of production from labor values and cases in which it works, or at least, cases in which Marx's invariants hold. Vicenc Melendez-Plumed, presumably anonymous, is doing the same, albeit he is interested in the general case when not all invariants hold.

But is it not the case that both of you think of labor values, if an outsider wants to calculate them for some reason, as being derived from conditions of production expressed in physical terms?

I think interesting the case where one assumes certain aggregates are of average organic composition of capital. Eatwell offered, in the 1970s, a reading of Sraffa related to Marx through the standard commodity. I don't understand Schefold's recent work to relate to it to this, though I appreciate the point about linear wage curves.

Vicenc, I have not absorbed your paper. I found the paragraph around footnote 1 confusing. The use of "standard" in the previous paragraph suggests the Sraffa's standard commodity to me. And even though Sraffa does not mention eigenvalues, he does seem to be calculating eigenvectors in his definition of the standard commodity. But I don't think that is what you are referring to here. I think you want the sum of a Leontief matrix and commodities consumed by workers' for advanced wages.

I think Section 6 needs a qualification the Steedman (1977) presents special cases where labour intensity and the working day vary.

I am vulnerable to this criticism myself, but I wish the number in the Annex were presented with dimensional units (e.g., tons, person-years per ton, person-years, etc.).

I wish I was able to read references in other languages.

Thank you.

Vicenc Melendez

Post a Comment