Online Economic Papers

Value Theory

Did Marx have a Labour Theory of Value,

It seems absurd that one has to answer this question.

It was so thoroughly answered by previous generations of economists in the affirmative, that it would seem unnecessary even to examine the issue. But David Harvey has recently posted a short article claiming that Marx was an opponent of the labour theory


A Critique of the Patnaik’s theory of Imperialism  A critical review of the book on Imperialism by the Patnaiks, focussing on their analysis of tropical product prices and the theory of international value. Backed up by :Analysis of Patnaik claims, spreadsheets to support my critical review of the Patnaik’s book.

On the a-priori probability of Marxian labour values and prices of production.
I argue two main points. The first is that although Marx is conventionally taken to have formulated two different theories of price in the three volumes of Capital, labour values in volume I and prices of production in volume III, there is actually a third theory, hidden inside the reproduction schemes of volume II. This theory is not explicit but can be logically deduced from the constraints that he presents on simple reproduction. It is not a theory of individual prices, but a theory of relative sectoral prices.

Laws of motion of Capitalism – this is a presentation developed by Dave Zachariah out of material that the two of us have discussed. It is in many ways a presentation of the key ideas of our Conservation Laws paper which is next in the list.

Defence of Empirical Evidence: draft reply to Shimshon Bichler and Jonathan Nitzan in response to their criticisms of our previous work in their book Capital as Power. It summarises the reasons why the observed empirical data tend to validate the theory that labour time is the source of exchange value.


Testing the labour theory of value : an exchange An exchange with Shimshon Bichler and Jonathan Nitzan stemming from an open letter originally posted by Stefanos Kourkoulakos regarding the conference Crisis of Capital, Crisis of Theory held at York University Canada.


What is at stake in the debate on value.   html version. Paper outlines the empirical data on correlations between labour values and prices and discusses various objections that have been raised in the literature to these.


Hilbert Space Models Commodity Exchanges Abstract. It is argued that the vector space measures used to mea- sure closeness of market prices to predictors for market prices are invalid because of the observed metric of commodity space. An alternative representation in Hilbert space within which such measures do apply is proposed. It is shown that commodity exchanges can be modeled by the application of unitary operators to this space.


A Note on the Significance of the Standard Commodity in Sraffa’s System, a joint paper with Ajit Sinha. The paper discusses the role of the Standard Commodity as a numeraire. We argue that the heart of Sraffas motivation for introducing the Standard Commodity was the dependence of relative prices on technical conditions in the basic sector. We show, by constructing a large class of worked examples that the direction of price movements under technical change will be dependent on the numeraire. If the choice of numeraire is arbitrary then so are the relative movement directions of prices under technical change. Joint.pdf, Pretty print output of a program to evaluate the hypothesis that the direction of movement of a commodities price under technical change can be dependent on the numeraire. This is the program used to evaluate the hypothesis discussed above. The Vector Pascal source of the program is available as Joint.pas


Symmetries and exchange relations, Exploration of how to use metric space theory to develop the chartalist theory of money.


Vector Space Metrics in Economics. Argues that capitalist economic activity can be modeled by rotation operators acting on a Hilbert space.


Value price transformation as a real process :rr-167-94 Published as “Does Marx Need to Transform?”, by Allin Cottrell and Paul Cockshott for a conference on the centenary of the publication of Volume 3 of Marx’s Capital, which took place in Bergamo in December 1994. The paper argues, on an empirical basis, that actual prices fall somewhere between the untransformed labor values of Capital, Volume 1, and the prices of production discussed by Marx in Volume 3.


Hunting productive work. The paper, jointly with Dave Zacharaih summarises the definitions of productive labour derived from Smith and Marx. It attempts to develop a more general definition deriving from Sraffa’s standard commodity and the theory of relative surplus value. The implications of the new definition for the examination of highly socialised capitalist economies like Sweden are examined.


The Scientific Status of the Labour Theory of Value , a paper which uses Chaitin Kolmogorov complexity theory to evaluate the accuracy of the predictions of different economic theories of value.

Value’s Law Value’s Metric: RR-94-168 An investigation into the metric space generated by commodity exchange. Provides empirical data comparing labour and electricity as the possible supports for this metric space.


Notes on Dynamic Value An attempt to come up with a simultaneist value theory that handles fixed capital and technical change.





Monetary theory

This is a review of a proposal raised by the New Economics foundation for the establishment of a digital currency to run in parallel with Sterling in Scotland. I would characterise the proposal as a form of utopian capitalism. I will argue that the proposal has several flaws, and should be assessed in a sober and realistic fashion.

Conservation laws, finanial entropy and the Eurozone crisis, with Dave Zachariah, The report attempts of apply econophysics concepts to the Eurozone crisis. It starts by examining the idea of conservation laws as applied to market economies. It formulates a measure of financial entropy and gives numerical simulations indicating that this tends to rise. We discuss an analogue for free energy released during this process.

The concepts of real and symbolic appropriation are introduced as a means to analyse debt and taxation. We then examine the conflict between the conservation laws that apply to commodity exchange with the exponential growth implied by capital accumulation and how these have necessitated a sequence of evolutionary forms for money, and go on to present a simple stochastic model for the formation of rates of interest and a model for the time evolution of the rate of profit.

Finally we apply the conservation law model to examining the Euro Crisis and the European Stability pact, arguing that if the laws we hypothesise actually hold, then the goals of the stability pact are unobtainable.


CREDIT CRUNCH: ORIGINS AND ORIENTATION PAUL COCKSHOTT AND DAVE ZACHARIAH , an article which looks at the causes of the credit crisis and how  economic policy should respond to it.


Bitcoin is not what socialism needs. Polemic against the fashionable idea that socialism should use the blockchain.

Statistical Marxism

Methods of modelling in the light of information theory and entropy, a paper prepared for the conference Nuevos paradigmas en la economa y cienciassociales del Siglo XXI , to be held in Mexico City, October 2010 ( link disabled whilst paper is reviewed). Power point presentation slides here.


Information and mass production Babbage to Boltzman Information theory whilst it grew out of the needs of the telecoms industry, was built on foundations provided by 19th century thermodynamics. Its domain of application has over the years been seen to widen. This talk shows how information theory helps us understand the key processes that made the industrial revolution possible, by examining the close connection between entropy,  information and the technologies of mass production.


Information, Work, and Meaning an introduction to information theory by me and Greg Michaelson, it relationship to thermodynamics and to classical political economy with particular emphasis on how it applies to industrial mass production.


Information and economics A critique of Hayek :rr-166-94 Written jointly with Allin Cottrell, looks at the concept of information as presented by Hayek and compares it with that used in modern information theory. It questions the extent to which Hayeks economic conclusions are sustainable on information theoretic grounds. Russian edition     Information and economics, ( Информация и экономика: критика Хайека) An extended and updated version of this paper was produced in 2007 that  reinforced the original conclusions with recent results in economic computability theory.

Socialist Economy


“Socialism” in the Economic Report of the President,

Something unusual has just happened. The current Economic Report of the President (March 2019; henceforth Economic Report) has devoted one full chapter to attacking socialism, under the title “Markets versus Socialism.”. Tonak and I wrote a reply to Trump’s economists. Backup spreadsheet : Deaths in Ukraine, this spreadsheet calculates excess deaths in Ukraine following the restoration of capitalism, about 3.4 million by 2010. Turkish translation, Serbian translation.

Venezuela and New SocialismIn 1989 Paul Cockshot and Allin Cottrell wrote a book on socialism which was published three years later in English as Towards a New Socialism. This book was addressed at an audience in the USSR and East European countries because it dealt with the problems that socialism was then facing in these countries. It had been the intention to have it translated and published in Russian. The book presented a model of how to run a socialist economy based on clear economic and moral principles and re-asserted the basic values of socialism against the pro-capitalist measures being introduced under Gorbachov. Events moved to fast to allow the to come out in Russian before the USSR fell, but since then what it says has been recognised to be sufficiently important that publishers in Sweden, Germany, Czechoslovakia and Venezuela have published translations under a variety of national titles.

In June 2007 at a workshop in Venezuela to launch the Spanish translation entitled Hacia el socialismo del siglo XXI, Paul was asked how the principles in the book could be applied to the process of establishing socialism in that country. This report tries to answer that question.

Ambedcar, Baudrillard, Buddhism and Socialism An extended introduction to a proposed Indian edition of Towards a New Socialism that attempts to situate our work with respect to the Buddhist Socialism of the famous Dalit leader and intellectual Ambedcar.


Supplementary chapters for the draft French edition of Towards a New Socialism. These chapters were written in 2008 for a proposed French edition, but the French publisher withdrew after we had written the chapters. Since the chapters relate to general updateing of the work, and as such may be of interest to English language readers, I have made them available here.

Mises, Kantorovich and Economic Computation An article that reviews the work of Kantorovich in the light of von Mises claim that rational calculations were impossible without markets. It gives a tutorial introduction to the use of Kantorovich’s methods, compares his approach to that of Dantzig. An assesment is given of the extent to which new interior point methods of linear programming strengthen or weaken Kantorovich’s claims.Russian edition available as In Natura Calculation from Neurath to Kantorovich ( Расчёт в натуральной форме, от Нейрата до Канторовича ).


Reflections on economic democracy, paper that is appearing in Research in Political Economy


21st Century Marxism it was written for Junge Welt, a German left daily, in advance of a Berlin conference on Marxism for the 21st Century


Cantor Diagonalisation and Planning,Murphy (2006) recently argued that one could use the diagonal argument of the number theorist Cantor to elucidate issues that arose in the socialist calculation debate of the 1930s. We will here argue that Murphy’s argument has certain problems, both at the number theoretic level and from the standpoint of economic realism.


Boettke Syntax and the Turing Test, a reply by Greg Michaelson, Allin Cottrell and I to a paper on Methodology by Boettke which he published in Cahiers DEpistemolgie. Boettke is a prominent economist of the Austrian school.


Computers and the Economic Calculation Debate, talk given in Jan 2006 in Berlin.


Application of Artificial Intelligence Techniques to Economic Planning (pdf) Paper dates from the early 1990s but was recently OCRed by Helmut Dunkhase to make it accessible over the web.


Value, markets and socialism Examine the very limited role for markets in a socialist economy and the different form of appearance that value ( abstract labour ) has in such an economy.


Economic planning, computers and labor values Since the collapse of the Soviet Union it has seemed to many that the socialist calculation debate is essentially over, with a decisive verdict in favor of the market. Recent instabilities in the world market are again prompting the question whether some form of conscious regulation of economies may be appropriate. We argue that the increasing power of modern computer technology along with the use of Ricardian-Marxian labor values opens up new possibilities for economic planning. In particular we criticise the notion put forward by Samuelson that ‘bourgeois prices’ are the appropriate measure for socialist economic calculation.


Against Mises Von Mises was the first prominent economist to argue the impossibility of a socialist economy. His ideas continue to be recycled by opponents of socialism.


“Calculation, Complexity and Planning: The Socialist Calculation Debate Once Again,” by Allin Cottrell and Paul Cockshott, published in ROPE, summer 1993. We present a counter-argument against Mises’ charge that rational economic calculation is impossible under socialism (a charge recently revived by Don Lavoie). The paper also considers other contributors to the Socialist Calculation Debate, such as Oskar Lange.


“Socialist Planning after the Collapse of the Soviet Union”, by Allin Cottrell and Paul Cockshott, published in Revue Europeene des Sciences Sociales, 1993. We make the argument that what failed in the USSR was not socialist planning as such, but a particular and definitely flawed variant of same, and suggest the outlines of an alternative system of planning. The paper is complementary to our 1993 book, “Towards a New Socialism.”

Profits and Crisis

Demography and long term profit rates We discuss the original formulation of the theory of the falling rate of profit by Marx and the criticisms of the theorys micro-foundations by Roemer. We then counterpose to this an alternative macroeconomic interpretation in which the falling rate of profit is driven by demographic factors. We follow this up with an examination of why the assumptions made in Roemers analysis are empirically unjustified. In particular we criticize his use of the average rate of profit rather than the monetary interest rate as the regulator of investment decisions. We conclude with an examination of the social implications of a declining rate of profit.


The organic composition of capital and profit rates, Appeared 2003 in Cambridge Journal of Economics. Shows that industries with high organic composition have low profit rates. The source data for this is available to others as a spreadsheet,that shows the rates of profit by industry for the USA in 1987, against the organic composition of capital for these industries. It shows, that counter to expectation, industries with a high organic composition of capital have a low rate of profit and vice versa. The spreadsheet is an excel one.


The declining rate of profit and technical change an examination of the effect of moral depreciation on profit rates. A version in postscript is also available.


Testing Marx: Some new results from UK data This paper was published in the Spring 1995 edition of Capital and Class. It covers among other topics the degree to which industrial output prices in the UK correspond to those predicted by labour values. Corrections to the data originally published.

Realisation Crises and the Polarisation of Capital:  cse-02-93 pdf version


Paper given at 1978 CSE conference that pioneers the methods of empirical marxian political economy and attempts to draw up a transition programme for the UK at that point.

Online Spreadsheets

These are Google Sheets documents used in preparing material for various papers. They are shareable in view only mode but you should be able to download them as Excel format for further work.


Kalecki Model, a spreadsheet showing how the Kalecki business cycle model works. Explained in this video.
Deaths in Ukraine, this spreadsheet calculates excess deaths in Ukraine following the restoration of capitalism, about 3.4 million by 2010.
Analysis of Patnaik claims, spreadsheets to support my critical review of the Patnaik’s book.
Gender pay gap in the USA,  Spreadsheet analysing gender pay gap 1979 to 2017
UK Pensions without exploitation, calculations to show that the UK pension system would run at a surplus just on contributions alone. Backup for video on ending exploitation.
Costings for citizens income scheme in the UK.  Backup for this video.

Reproduction and transformation problem examples

Reproduction Scheme, a Capital vol II style reproduction scheme showing the functional dependencies ( you have to look at the formulae in the cells to understand these ).
Effect of profit Equalisation, takes the previous reproduction scheme and applies profit equalisation. It shows that simply doing this results in imbalances of supply and demand that would block reproduction.

Kliman Transform  This spreadsheet illustrates how application of the Kliman transformation process which overcomes the above problem but requires a reduction in money wages to allow reproduction to proceed. The spreadsheet was generated by a programme kliman.pas a pretty print of which is kliman.pdf. Compiled and run using Vector Pascal. The topic is discussed in this Video.

Capital movement, It is hypothesised by Kliman and others that capital moving from Dept I to dept II can lead to profit equalisation. This shows that a transfer of £12 capital from dept 1 to dept 2 will exacerbate the inequality since it will cause the demand to fall for dept I further reducing its profit rate and also blocking reproduction