Capital Theory

These two books are at about the level of maths I already have and I intend to do a close reading of them both, to write papers comparing Maksakovsky to them for academic journals at a similar level.

[CTDI] Got hardcopy (not long after first published in 1975). In Library Genesis and in Google Books.

[CTD] Got hardcopy (not long after first published in 1980). Not in Library Gensis but is in Google Books.

Bliss [CTDI] clearly demonstrates superiority of “neoclassical” understanding that choice of technologies actually used depends on wage and profit rates even with purely linear production functions in Table 9.1, p210. This is central to understanding both Marx and Maksakovsky, who both simply take it for granted and do not attempt to explain what should be obvious to anyone and is indeed obvious to most “vulgar economists”, but not apparently to “neo-Ricardian” charlatans like Steedman waving linear algebra as a magic wand. The charlatans even ended up accepting the reduction to absurdity of their whole approach by “Okishio’s Theorem” as though it was a vindication against Marx.

The outline of totally incoherent “Marxist responses” at that wikipedia page provides a vivid illustration of the extinction of Marxist economic theory. Maksakovsky explains clearly how the contradictions Okishio tries to analyse statically with a static “real wage” consumption basket in fact drive the dynamic cyclic accumulation of capital with higher real wages and a higher organic composition of capital.

I did lots of runs of a linear programming package on a university mainframe (together with Julian Shaw) to show shifts to higher organic composition with accumulation using technologies like Table 9.1 around the same time [CTDI] was published. Mentioned Bliss to Geoff Harcourt (at an Australian Political Economy Movement conference in 1976) when discussing why I found the Cambridge M.I.T. made more sense to me than the Cambridge U.K. side in the “Cambridge capital controversy”. He asked who in particular, I said Bliss and he said that Bliss showed “good taste”.

In that discussion I also mentioned that it was unlikely that convex sets could cease to be separable by hyperplanes under socialism and that efficient prices were consistent with Marx’s theory of value as demonstrated in linear programming. This resulted in mention to me of “Pontryagin’s Principle” which is indeed a more general statement of the duality between prices and efficient quantities required by the proportional distribution of labor for a given technology and demand preferences and corresponding duality of commodities as use values and exchange values. This goes back to Lagrange, D’Alembert and Euler whose “variational” principles were imported into economics from mechanics, but it was apparently seen as something very recent around 1980.

BTW I recall seeing a paper by Geoff Harcourt (possibly unpublished) that mentioned as an oddity of intellectual history of value theory that I had first drawn attention to the impossibility of evaluating joint products in terms of embodied crystallized labor and the necessity to instead compare the total industry input and output together with consumer preferences for use values as reflected in demand in the discussions at that conference. I’m sure I was not the first to point that out, but would like to find the quote.

Bliss sums up his position in opposition to Harcourt’s side of the “Cambridge capital controversy” in his concluding Chapter 15, “Disputations” as follows:

As has been noted many of those who feel that neoclassical theory is apologetics for capitalism are not themselves Marxists. However, since many people are influenced by Marxist ideas who are not themselves Marxists it is not clear that this point invalidates what has been claimed.

The model that has figured in the foregoing chapters is not the ‘neoclassical’ model as many people will understand that term. Outside ch. 8, and a brief example or two, the notion of a production function with aggregate capital as one of its arguments, to some the hallmark of neoclassical theory, has not figured at all. Moreover, marginal ideas feature in the model as quite subsidiary to the important properties of that model. The equilibrium theory of capital would be a more natural title – but let it not be forgotten that we have examined more than one kind of equilibrium. Nevertheless, the model is much closer to neoclassical theory than it is to one version at least of Marxist theory in the following regard. It does not show the distribution of income to be the outcome of a uni-directional chain of causes starting from the rate of exploitation. It shows the distribution of income to be the outcome of the balancing of a large number of mutually interacting forces. In so depicting the determination of the distribution of income the model may be accurate or misleading. The reader will have to make up his own mind which, and he would be ill-advised to do so without reading other works than this one.

It is a serious disadvantage of the equilibrium theory that it is a complicated model devoid of simple general results. As such it is perhaps not very practical and even its adherents may have recourse to simpler models (such as the partial equilibrium model) to assist with answering concrete questions. Its advantage, on the other hand, is that it is flexible and can be adapted to answer all kinds of questions and to take into account institutional factors of many kinds. Where the justification of the distribution of income is concerned it is, of course, impotent, although it can be employed by people with all kinds of different values, and even to choose policies to improve the distribution of income. It is apologetic only if all alternatives to the Marxian system are apologetic – for it is an alternative to the Marxian system.

Marx’s analysis was a “disequilibrium theory” so any “equilibrium theory” is certainly not Marxist. But Bliss correctly describes both sides of the “Cambridge Controversies” as believing that determination of distribution of incomes by the rate of exploitation prior to the determination of prices rather than as the outcome of a large number of mutually interacting forces is a reflection of the influence of classical ideas that lived on in the tradition of Marxism.

That shared, sincerely believed, delusion as to what “Marxism” accepted reflects the complete extinction of Marx’s critique of classical political economy in modern economic theory.

Marx’s critique cannot merely be revived by reaffirmation. It must be renewed by development. Maksakovsky provides a good starting point for that renewal and development which must not be allowed to get lost again.
Burmeister [CTD] comes after and goes beyond Bliss.

Along with Maksakovsky’s dialectical presentation in semi-quantiative language it is necessary to re-state Marx’s value theory in modern mathematical language (dual variables, control theory etc as above).

I started doing this in 1976 with “Notes on ‘Activity Analysis in the Theory of Growth and Planning’ Edited by E. Malinvaud and M.O.L. Bacharachi”

(International Economic Association Series) E. Malinvaud, M. O. L. Bacharach (eds.)-Activity Analysis in the Theory of Growth and Planning_ Proceedings of a Conference held by the International Econom.pdf

title = {Activity Analysis in the Theory of Growth and Planning: Proceedings of a Conference held by the International Economic Association},
author = {E. Malinvaud, M. O. L. Bacharach (eds.)},
publisher = {Palgrave Macmillan UK},
isbn = {978-1-349-08463-0,978-1-349-08461-6,978-0-333-40626-7},
year = {1967},
series = {International Economic Association Series},
edition = {},
volume = {},
url = {}

Table of contents :
Front Matter….Pages i-xv
Front Matter….Pages 1-1
Economic Growth at a Maximal Rate….Pages 3-42
Maximal Paths in the von Neumann Model….Pages 43-63
Some Analytical and Practical Aspects on the Theory of Capital….Pages 64-107
Front Matter….Pages 109-109
Dynamic Programming of Economic Growth….Pages 111-141
Programming Involving Infinitely Many Variables and Constraints….Pages 142-149
Alternative Preference Functions in Problems of Investment Planning on the National Level….Pages 150-169
Decentralized Procedures for Planning….Pages 170-208
Front Matter….Pages 209-209
Mathematical Programming of Long-Term Plans in Hungary….Pages 211-231
Consistent Projections in Multi-Sector Models….Pages 232-244
Programming Models of Interregional Efficiency and Land Use in Agriculture….Pages 245-268
An Experimental Model for Investment Planning….Pages 269-278
Front Matter….Pages 279-279
Summary Record of the Debate….Pages 281-329
Back Matter….Pages 331-334

Got as far as some half-baked “Notes on Economic Models” dated 21 September 1981.


These referred to Heesterman (1971) p72 as well as Bliss (1975) Ch 10 with errors at p236:

(International Studies in Economics and Econometrics 3) A. R. G. Heesterman (auth.)-Allocation Models and their Use in Economic Planning-Springer Netherlands (1971).pdf

title = {Allocation Models and their Use in Economic Planning},

author = {A. R. G. Heesterman (auth.)},

publisher = {Springer Netherlands},

isbn = {978-94-010-3086-1,978-94-010-3084-7},

year = {1971},

series = {International Studies in Economics and Econometrics 3},

edition = {1},

volume = {},

url = {}


Table of contents :
Front Matter….Pages I-XIV
Front Matter….Pages 1-1
What is Efficiency?….Pages 3-8
The Generalized Input-Output Model….Pages 9-66
Inter-Temporal Allocation in the Generalized Model….Pages 67-91
The Balanced Growth Frontier….Pages 92-104
The Dynamized Leontief Model….Pages 105-115
Foreign Trade in the National Economy Model….Pages 116-123
Front Matter….Pages 125-125
The Costing Problem….Pages 127-135
Discounted Cash Flow in the Standard Case….Pages 136-155
Increasing Returns to Scale….Pages 156-161
Some Special Evaluation Problems in Particular Sectors….Pages 162-164
Front Matter….Pages 165-165
The Distribution of Outputs….Pages 167-175
Opportunity Cost and Exchange Price….Pages 176-183
Back Matter….Pages 184-203

Those references convey the essence.

I recently came across my above notes again after deciding to resume studying and writing on this stuff and establish this web site. I am astonished that I still haven’t got around to proving the conjectures or explaining anything clearly after 35 years!

I intend to refresh and catch up on basic maths as above and get something along those lines into publishable form as soon as I have done the minimum necessary to ensure Maksakovsky does not get forgotten again.

Unfortunately that will take quite a while so in case I again don’t get around to it I am putting what is already there online by above links and references.


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