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Monday, December 6, 2010

MARX'S ECONOMICS IN MODERN DRESS

Noumena asked about books on the modern mathematical reinterpretation of Marx's economics, in addition to Morishima, and Robert Vienneau was spot on with his mention of Sraffa and Roemer. Let me attempt a more systematic answer.

Marx's economic theories are a critique of, and also a continuation of, the classic tradition of political economy in which the two great names before Marx are Smith and Ricardo. It was Marx's great misfortune that in the decade after he published volume one of CAPITAL, a theoretical revolution took place in mainstream economic theory, usually referred to as the marginalist revolution, led by three theorists working simultaneously and independently of one another: Jevons, Menger, and Walras. The result was to change fundamentally the nature of the questions asked by economists, and to sweep into the dustbin of history not only Marx but also Mill, Ricardo, Smith, and the rest of the classical school. Marx's disciples continued to write and talk as he had done, making them look, over the years, more and more quirky, cranky, sectarian, and, dare I say it, marginal. Eventually, Paul Samuelson could get away with describing Marx as a "minor post-Ricardian autodidact." [I have always thought that for Samuelson, the author of the most successful college economics text ever written, the autodidact part was what particularly ticked him off.]

This was pretty much the state of play until 1960, when Piero Sraffa, an Italian economist living and working in Cambridge, England, published a little book not quite one hundred pages long, called PRODUCTION OF COMMODITIES BY MEANS OF COMMODITIES. Sraffa was the editor of the magisterial multi-volume edition of the works of David Ricardo, and his work might easily be viewed as a resurrection and justification of Ricardian theory, but lest one have any doubt about where Sraffa's sympathies lay, we should recall that it was he who brought the paper, ink, and pen to Antonio Gramsci with which Gramsci wrote his PRISON NOTEBOOKS. Although Sraffa makes use only of the most elementary mathematical operations, and writes in a spare, monastic style, his work really builds on the linear programming work of Wassily Leontieff.

In the thirty years or so after Sraffa's little book appeared, an extraordinary world-wide theoretical discussion arose among well-trained theoretical economists who were sympathetic to the classical and Marxian programme, and were disenchanted with the General Equilibrium models then all the rage. This was no small mathematical quibble. What was at issue was nothing less than what economics ought to be talking about. The classical school asked two great questions: How does the annual social product get divided up among the three classes in society [landowners, entrepreneurs, workers]? And, What are the conditions for stable continuous economic growth? These questions focused attention on class conflict and class division, which Smith and Ricardo, as well as Marx, thought was central to capitalism. They also focused on issues of growth versus stagnation. The neo-classical school asked totally different questions: What is the rational way to allocate scarce resources with alternative uses? How does subjective desire or preference determine market price? It was, of course, possible for them to ask about distribution and growth, but since those questions did not lie at the heart of their theories, their answers were ad hoc and rather unsatisfactory ["each factor in production is paid its marginal product" etc.]

Marx said many things in his economic writings, of course, but central to them were a series of theoretical claims, about the relationship between exploitation and profits, about the inner contradictions of a capitalist economy, about the falling rate of profit, and so forth. Following Sraffa, the new mathematical Marxists, as I may call them, undertook to translate Marx's theoretical claims into modern dress, using essentially linear algebra rather than differential calculus. This involved making a different set of simplifying assumptions than those underlying neo-classical theory. [So, for example, in the neo-classical marginalist models, it is assumed that there is a contunuously infinite number of alternative production techniques combining inputs in varying quantities. The mathemtatical Marxists make the opposite simplfying assumption that at any one time, there is a single dominant production technique, that can be represented by a vector of quantities of inputs per unit output. The mathematical result is that instead of twice differentiating a continuous production function, you invert a matrix of input coefficiants.]

Speaking very broadly and generally [and revealing my own prejudices], these theoreticians demonstrated that Marx had a full-blown mathematically quite respectable theory that was in fact correct about a good many things, wrong about some others [the falling rate of profit had to go -- thanks to a theorem by Okishio, later re-proved more simply by Bowles]. I myself made a small contribution to this literature [in a paper, online now, I believe, called "A Critique and Reinterpretation of Marx's Labor Theory of Value"], although John Roemer, bless him, noted that a year before I published. a very similar result had been proved by an Spanish economist writing in Spanish. [sigh. This never happens in philosophy.]

So, here is a short list of some of the best books in this large and excciting literature. I have actually read all of these, believe it or not. It cost me a good deal of effort, but was well worth it.

Morishima, MARX'S ECONOMICS, 1973
Luigi Pasinetti, GROWTH AND INCOME DISTRIBUTION, 1974
Andras Brody, PROPORTIONS, PRICES AND PLANNING 1974
Abraham-Frois and Berrebi, THEORY OF VALUE, PRICES AND ACCUMULATION 1976
Luigi Pasinetti, LECTURES ON THE THEORY OF PRODUCTION 1977
Ian Steedman, MARX AFTER SRAFFA, 1977
Walsh and Gram, CLASSICAL AND NEOCLASSICAL THEORIES OF GENERAL EQUILIBRIUM
Luigi Pasinetti, STRUCTURAL CHANGE AND ECONOMIC GROWTH 1981
John Roemer, ANALYTICAL FOUNDATIONS OF MARXIAN ECONOMIC THEORY 1981
Stephen Marglin, GROWTH, DISTRIBUTION, AND PRICES 1984

If anyone is interested, I can say a bit about what each of these has to offer, but sufficient unto the day.

19 comments:

Matthew J. Brown said...

Would you lump Joan Robinson in as an earlier contributor to this group?

Robert Paul Wolff said...

That is a complicated question. The Cambridge capital controversy pitted her against the neo-classicals, but they were not enraptured with Marx [whom Robinson rejected dismissively with a quote from Voltaire.] There are a number of collections of essays on this subject, which you can hunt down.

Matthew J. Brown said...

I wasn't thinking of her role in the capital controversy (which I'm not sure I understand), but her earlier book, An Essay on Marxian Economics (1942), which I remember reading and enjoying as an undergrad after trying and failing to puzzle through Sraffa. I recall her as being sympathetic to Marx, but perhaps I misremember (or didn't understand it at the time!).

Noumena said...

Thanks very much!

Robert Paul Wolff said...

I have not read the 1942 book, I am afraid. I should take a look at it.

wallyverr said...

Robinson's 1942 book is the first edition of the 1966 second edition quoted on pp14-15 of Moneybags Must Be So Lucky. The comment in Moneybags is not very complimentary ("Joan Robinson says, echoing the vulgar empiricism of the Viennese positivists..."), but I found her short book helpful when I read it many years ago.

Any views of three other books I enjoyed reading around the same time?: Sweezy Theory of Capitalist Development, Mandel Marxist Economic Theory, and Baran Political Economy of Growth.

I'm interested in hearing more about the other books.

Robert Paul Wolff said...

Oh dear. That is not very scholarly of me! So I guess I have read the Robinson book. [Small gossip tidbit -- in 1954, when I was a traveling scholar from Harvard, age twenty, and disenchanted with Oxford, I read three books while I was in Oxford -- Samuelson's economics text, and books by Chamberlin and Robinson on imperfect competition. Then I bought a tiny motorcycle and drove to Rome.]

I will gather my energies and try to say something about the books I listed, as a sort of reader's guide. There is a great deal of overlap in them, of course, but they are also distinctive in their different ways.

Chris said...

Professor,
I noticed the absence of David Harvey, and Chris Harman; both people who I believe have expounded and expanded Marxist economics. I recently read Chris Harman's book, ZOMBIE CAPITALISM, which carried Marxist economics from Marx hitherto the financial bubble.

Robert Paul Wolff said...

It just shows the limits of my knowledge. I was unaware of their work. I will take a look at Zombia Capitalism. It sounds interesting.

Robert Vienneau said...

I haven't read all of those. Two more closely related - lots of math:

Christian Bidard, Prices, Reproduction, Scarcity

Kurz and Salvadori, Theory of Production

What do you think of the idea that the success of the marginal revolution was a reaction to Marx? Commentators on my blog have agreed that the success was politically inspired, but talk about it as a reaction to either the Ricardian socialists or Henry George.

Robert Paul Wolff said...

I think the success was a combination of political considerations and a sheer fascination with the math, but I am almost certain its success was not a reaction to Marx. Remember, Marx wrote in German, and his work was virtually unknown in academic circles for quite some time. He was really quite obscure. Looking backwards, in the aftermath of the Bolshevik revolution and all, we tend to forget that.

What do you think?

I will say that the total lack of interest in the economics profession in the elegant mathematical reinterpretations of Marx is patently political. This stuff is as elegant as theirs, and they claim to be all about formal elegance, and yet the four decades long outpouring of work seems to have had no impact whatsoever on the profession.

Chris said...

What about the imperialist Marxist? I'm thinking about Wallerstein, Lenin, Luxemborg, etc.

Robert Paul Wolff said...

Let us just say that I am, to Marx, as a primitive Christian is to Jesus. I do not feel the need to defend, or explain away, Stalin or Lenin or Luxembourg or anyone. I just read CAPITAL and think about what it means. I do not blame Jesus for Father Coughlin or Pat Robertson, and I do not blame Mohammed for Usama bin Laden.

Chris said...

Oh you misunderstood me, I was asking about them in regards to their economic work, not their political careers.


Although tongue best of my knowledge luxemborg
Was more of a saint than a monster...

Chris said...

*to the best
not tongue
damn IPhone auto-correct.

john c. halasz said...

So what then do you make of the "temporal single system" interpretation of Marx' economics? In particular, they claim that the "transformation problem" doesn't exist, or, at least, not in the form that has long been attributed to him, based on neo-classical criticism. Supposedly, in order to account for the equilibriating equalization of the rate of profit in the light of differing capital intensities between sectors of production, Marx would have to transform labor-values into cost-prices of production, in which case a) labor values are declared to be redundant, and b) Marx theory is demonstrated to be inconsistent, since he can't provide such a procedure without double-counting. (It's not considered that the neo-classicals themselves are doing the double-counting by projecting their equilibrium assumptions upon him). But to the contrary, that's an inversion of Marx' actual claim, (unsurpisingly, since the inversion of essence and appearance is a dialectical feature of ideology), which is that cost-prices of production can't be determined without first determining the distributions of surplus-value. The transformation problem then becomes a complex account of the formation and movements of prices, (which Marx is not eager to exactly solve, since changing technical conditions are constantly changing the formation of cost-prices of production, the equivalent of Ricardan "natural prices"). But one of the upshots is that capital intensive sectors are drawing labor-value off of labor intensive sectors, which not only obviates crude objections to labor-value and exploitation, but accords with the rents accruing to market-dominant, capital-intensive oligopolies.

john c. halasz said...

Alan Freeman of the TSS school has a punchy, quite readable paper called "If They're So Rich, Why Ain't They Smart?", which addresses some remarks to Sraffa's account as reproducing the neo-classical "dual system" interpretation.

Here's a link to some of his papers:

http://ideas.repec.org/e/pfr102.html

His confederate Andrew Kliman has a paper addressing Okishio's theorem, the upshot of which is that there's nothing wrong with the fancy math, only it just doesn't apply. (Kinda like that "too bad for the facts" remark: i.e. the claimed empirical objection just misconstrues the point at which the facts meet up with their formal-systematic context.) At any rate, the "tendential law of the falling rate of profit" is just that, a tendency, not a deterministic covering, and the thesis is largely a complex one about the increasing technical productivity and correspondingly, increasing concentration of capital stocks.

Robert Paul Wolff said...

I am afraid I am totally unaware of the TSS system [this just shows the limits of my knowledge]. I am delighted that smart economists are continuing to work on Marxian themes in modern dress.

wayne said...

I think you have to include some of the recent works on this subject - most notably David Harvey's work.