My Stuff

Coming Soon:

Now Available: Volumes I, II, III, and IV of the Collected Published and Unpublished Papers.

NOW AVAILABLE ON YOUTUBE: LECTURES ON KANT'S CRITIQUE OF PURE REASON. To view the lectures, go to YouTube and search for "Robert Paul Wolff Kant." There they will be.

NOW AVAILABLE ON YOUTUBE: LECTURES ON THE THOUGHT OF KARL MARX. To view the lectures, go to YouTube and search for Robert Paul Wolff Marx."

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Thursday, April 29, 2021


T.J. asks the following question:  “when I (the capitalist) buy 8 hours of labor, I get more labor than is required to produce 8 hours of labor. So I get more than I pay for. But when I buy 8 bushels of corn, I only get 8 bushels of corn. Is it just that the algebra (which again, I don't understand) shows that when I buy 8 bushels of corn, I get more corn than is required to produce 8 bushels of corn? Maybe my hangup is that it just seems obvious that when I work for 8 hours, my boss makes more money from my labor than I'm going to spend housing and feeding myself, but it doesn't seem at all obvious that when I buy 8 bushels of corn, I could reproduce more than 8 bushels of corn from that input.”


The simple answer, T.J., is yes, exactly so.

Leaving aside the algebra, which I realize is for some people an obstacle, not an aid, to understanding, let us just ask this question: if it takes more than 8 bushels of corn somewhere in the economy directly or indirectly to produce 8 bushels of corn, how can the system possibly survive? In the next cycle of production, the system will have to be reduced in size and after several such reductions the system will go out of business entirely.


Intuitively, if you are measuring things in some commodity directly or indirectly required rather than in labor directly or indirectly required, the same truth is going to have to hold, namely that it will take less than one unit of any commodity required in the production process directly and indirectly to produce that unit if the system is to survive and flourish. In fact, with a little of that dreaded algebra, we can show that so long as in each cycle of production there is some physical surplus over and above what is required to run the system again at the same level of output for another cycle, then all of the labor values or corn values or iron values or X – values for any input X will have to be positive and for any X, the X – value of X will be less than one, meaning that there will be surplus X value generated in the system. What is more, and should be intuitively obvious, the X value of this physical surplus appropriated by the capitalists will exactly equal the surplus X value extracted from the direct X inputs into the system. All of those propositions that Marx intuitively grasped as true for labor turn out to be true for every input into the production process.

Wednesday, April 28, 2021


Prompted by a comment from Jerry Brown, I should like to return to the subject of the Labor Theory of Value. To many people who identify themselves as Marxists, the Labor Theory of Value plays somewhat the same role in their belief structure as is played by the doctrine of the Incarnation for Christians – if you give it up, you can no longer really claim to be one of the faithful. It is obvious from what I said in my recent series of posts on Marx that I do not share this view and although I have written about this before, I think it is important enough to return to the subject and spell out my views at greater length.


As I explained in my series of posts, what came to be called the Labor Theory of Value started life in the writings of Adam Smith as his attempt to explain what determined the customary or usual prices at which commodities sold in the marketplace. Smith was well aware that fluctuations in supply and demand would cause daily prices in the market to vary, but he noted that experienced buyers and sellers would learn that there was a usual or customary price for corn or cloth on which they could rely. He called this price the natural price of the commodity, or, using an 18th-century synonym, its value. He was here introducing an idea that much later on came to be called the equilibrium price for a commodity. Smith then offered a very primitive explanation for the determination of the natural price or value of a commodity, namely the amount of labor it cost its producer. Smith had thus given birth to the idea of a labor theory of equilibrium price or, as he referred to it, a Labor Theory of Value.


Smith was aware of, but not able to come up with a solution for, several serious problems with this primitive theory. It fell to David Ricardo to solve the problem of rent or the price paid for the use of land and also to propose a brilliant solution for the problem of the accumulation of stock, what today we call capital. His notion of embodied labor enabled him for the first time to put forward a full-scale labor theory of equilibrium price or Labor Theory of Value. But there was a problem with this idea, brilliant as it was, and Ricardo knew it. The problem was that if different lines of industry exhibited varying proportions of capital and labor, then equilibrium prices would deviate from the quantities of labor embodied in the outputs.


It was at this point that Marx began his theoretical work. He believed he had a solution tgo Ricardo’s problem, but he chose to postpone discussion of it until volume 3 of Capital because he believed he had found a deeper problem in the traditional theory whose solution would reveal the mystified and ideologically concealed truth that capitalism rests on exploitation, not on free and equal exchange in the marketplace.  The problem, to put it quite simply, was that the classical political economists had no explanation for the emergence of profit. The key to Marx’s solution of this problem was his distinction between labor and labor – power, and with it the introduction of the category of surplus labor value, which, Marx claimed, is the real source of profit and the demonstration of the fundamental fact that capitalism rests on the exploitation of the working class.


No sooner had Marx put forward this dramatic critique and transformation of the classical theory of the political economists than economics as a discipline underwent a triple revolution. More or less simultaneously but independently of one another, Stanley Jevons in England, Carl Menger in Switzerland, and Leon Walras in France introduced the notion of marginal productivity, on the basis of which they undertook to explain equilibrium prices solely by referring to the relationship between demand and supply, putting entirely to one side any question of the quantity of labor directly or indirectly required for the production of commodities.


Smith and Ricardo became, in effect, curiosities put in a museum of outmoded ideas. Marx did not suffer the same fate. Quite to the contrary, he developed an intellectual following and then, mirabile dictu, a political following of revolutionaries who succeeded in taking over two of the largest countries in the world. The Labor Theory of Value ceased to be a brilliant but problematic explanation of the determination of equilibrium price in a capitalist market system, and became the esoteric doctrine of the Priesthood of the Temple. In some parts of the world, questioning the Labor Theory of Value got you stigmatized as a heretic, an unbeliever, even – God forbid – a liberal. In other places, it could get you killed.


Now I am, as I observed on the front page of this blog, an atheist. I do not believe in the Jewish God. I do not believe in the Christian God. I do not believe in the Muslim God. And I also do not believe in the divine revelation of the Labor Theory of Value. I do believe that capitalism rests on the exploitation of the working class, not as an article of faith but as the conclusion of a lifetime of study and consideration. I call myself a Marxist simply to express in a single word my admiration for the student of society who first articulated and defended this simple but fundamental fact of the modern world.


One might be tempted to say dismissively or disparagingly, “oh well, if that is all you mean when you call yourself a Marxist, all manner of people could say that without calling themselves Marxists.” They could, I suppose, but they don’t. It is quite remarkable how hard the world’s greatest Nobel laureate economists work to avoid acknowledging that capitalism rests on the exploitation of the working class, and if I were an old-fashioned Marxist, I might even say that it is no accident that the same people cannot bring themselves in their writings to utter the word “Marx.”


Yesterday evening, a string quartet composed of members of the North Carolina Symphony came to the retirement community in which I live to give a free concert to us old folks. For the first time in 15 months, Susie and I entered the auditorium, suitably masked and appropriately distanced, and enjoyed an hour of first-rate live classical music. The principal offering was the last of Beethoven’s middle quartets, Opus 95. I could not recall whether I had played that quartet back in the day when I was the violist of an amateur quartet that met weekly in Amherst, Massachusetts. But when the ensemble played the dramatic opening phrase I recalled it quite well. As they continued on through the quartet, I began to have doubts whether I could ever actually have played the viola part in so demanding a work, so when I got back to our apartment I pulled out the music from my shelves and took a look. Sure enough, the viola part was covered with a blizzard of pencil markings that I had put in to guide me through the music. Needless to say, we did not play it as they did nor quite up to speed, but we did play it.


It is always nice to recall that chamber music was originally designed to be played in a chamber – a private gathering room or salon – not  in a concert hall. The cellist in our little amateur quartet was a woman who played with a rich full tone. She sat to my right in the traditional quartet arrangement and one of my greatest pleasures, as I worked my way through my part, was hearing her in my right ear.  It has always been a source of sadness to me that when I moved down to Chapel Hill I was unable to find a quartet to play with.

Monday, April 26, 2021


Sidney Morgenbesser’s classic put down having been quoted, I will reproduce here two great stories from the Sidney legend which I tell in my autobiography, one of which, the second one, is not widely known.

Some months after the Spring of '68, Sidney was called for jury duty, and as luck would have it, he was tapped for a case involving alleged police brutality.  During the voir dire, the Assistant District Attorney assigned to try the case asked Sidney whether he had ever been treated brutally or unfairly by the police.  Sidney thought for a moment and said, "Brutally, yes.  Unfairly, no."  The ADA asked him to explain, and Sidney told the story of the attack by the TPF.  "And you didn't think they were acting unfairly?"  "No," Sidney said, "they were hitting everybody."  Sidney was a genuinely great man.

            While I am telling Sidney stories, let me tell one more that may not have made its way into the blogosphere.  A few words of explanation are required.  One of Columbia's best known professors at that time was the literary scholar Lionel Trilling.  Trilling was a New York Jewish boy who, before spending his entire career at Columbia, actually went to the high school [De Witt Clinton] at which my father taught for a while.  Despite his origins, he affected a cultivated WASP manner that, I imagine, he thought would be appropriate in an Oxford Senior Common Room.  Trilling was one of a number of Columbia professors who chose to focus their energies in the College rather than the Graduate School.  [That was an old rivalry for which I do not have time or space in these memoirs.]  One day, Sidney went to a cocktail party, at which he spotted Trilling holding forth in his best Oxonian style.  Sidney walked up and said, in a loud voice, "Ah, Lionel.  Incognito ergo sum, eh?"

            Now, this was pretty clearly a prepared bon mot.  Sidney, like Samuel Johnson, was not above lying in bed at night crafting a witticism that he would carry about with him until an occasion arose for delivering it.  As an author who does most of his writing in his head, I do not deprecate the practice.  Indeed, my favorite Oscar Wilde line is one that he never actually published, and that has come down to us only because someone present on the occasion had the good sense to record it.  I am referring, of course, to Wilde's immortal judgment on Dickens' Old Curiosity Shop -- "One must have a heart of stone to read the death of Little Nell without laughing."

Sunday, April 25, 2021


It is a lovely spring day here in North Carolina and I have finished my morning walk. I diverted myself during the long slog by recalling some lovely one-liners from the philosophical literature and I thought I might amuse myself and perhaps even amuse you as well by putting  them down in a blog post. Before I do that, however, I should like to offer my heartfelt thanks to those of you who have written truly generous compliments in response to my sometimes rather pathetic musing about the lifecycle and my current place in it. I do not think I could find words to tell you how much these comments meant to me. As I struggle, in Dylan Thomas’s beautiful words, not to go gentle into that good night but to rage, rage against the dying of the light, the thought that I have reached out and touched some of you warms me against the cold.


Now onto happier thoughts. Philosophers are by and large not known for their brevity but from time to time one of them gets off a line that stays in the mind, capturing in a few words a powerful and complex thought. I have some favorites, some of which I have quoted before but the very most favorite of all I think I have never actually quoted here. So let me get started.


I begin, as all philosophers must, with Plato. All of you will I am sure recall his great dialogue, the Gorgias, whose structure interestingly enough is exactly that of Book 1 of the Republic.  After disposing easily enough of Gorgias and Polus, Socrates confronts Callicles, to whom Plato gives some of his strongest arguments and most telling lines. Here is my favorite, delivered by Callicles shortly after he enters the dialogue:


“When I perceive philosophical activity in a young lad, I am pleased; it suits him, I think, and shows that he has good breeding. A boy who does not play with philosophy I regard as illiberal, the chap will never raise himself to any fine or noble action. Whereas, when I see an older man still at his philosophy and showing no sign of giving it up, that one seems to me, Socrates, to need a whipping!… Such a fellow must spend the rest of his life skulking in corners, whispering with two or three little lads, never pronouncing any large, liberal, or meaningful utterance.”


Skulking in corners, whispering with two or three little lads, is surely the greatest description ever given of the profession to which I have devoted my life. Only a philosopher as great as Plato would have the courage to put those words in the mouth of the character who is defending everything that Plato hates.


My second example comes from a text that I have frequently made reference to, the Preface to Kierkegaard’s brilliant short work, Philosophical Fragments. Virtually every line of the brief Preface is worth quoting but I shall restrict myself simply to this passage in which Kierkegaard gives voice to the intense seriousness with which he approaches philosophy:


“But if anyone were to be so polite as to assume that I have an opinion, and if he were to carry his gallantry to the extreme of adopting this opinion because he believed it to be mine, I should have to be very sorry for his politeness, in that it was bestowed upon so unworthy an object, and for his opinion, if he has no other opinion than mine.”


To lighten this post a bit after that desperately serious text, let me just mention a delicious question that appeared many decades ago on the Moral Sciences Tripos at Cambridge University. A few words are required for those of you too young to remember what epistemologists were fussing about 70 years ago. The centuries – long debate between the rationalists and the empiricists had at long last come down to a question of the role in empirical knowledge of something called sense data reports, which were supposed to be descriptions of the sensory perceptions on which, according to the epistemologists, all knowledge is based. Because it was widely believed at that time that each of us is unable actually to know what is in another’s mind, a good deal of ink was spilled (this was before computers) on the question whether there could be a private language in which sense experience would be described by the person who actually had that experience but who could not successfully communicate the experience to others. Wittgenstein blew up that debate with the argument that there could not be a private language and so theorists of knowledge moved on to other questions. Roughly at that time, some wit making up the final examination for Cambridge University undergraduate philosophy students came up with an examination question that captured the whole complicated kerfuffle in four words. His question was: “What were sense data?”


That is the ultimate inside joke.


Now on to my all-time favorite. It comes from a work published 370 years ago, the Leviathan by Thomas Hobbes. Chapter VI of Part One has the rather elaborate title “Of the Interior Beginnings of Voluntary Motions; Commonly Called the Passions; And the Speeches by Which They Are Expressed.” The entire nine page chapter is well worth quoting but I shall restrict myself to my favorite nineteen words, which in scarcely more than two lines dispose for all time of the endless debates about what should be considered genuine faith and what a mere cult. I conclude this post with these words, which I have loved since reading them almost 70 years ago:


“Fear of power invisible, feigned by the mind, or imagined from tales publicly allowed, RELIGION; not allowed, SUPERSTITION.”



Wednesday, April 21, 2021


 David Palmeter observes that America paid a price for going to an all volunteer army, and he is quite right. Recall that the transition from the draft was in the first instance a consequence of the disaster of the Vietnam War which almost destroyed the discipline and effectiveness of the draft Army. The Defense Department ended the draft, improved the pay for the ranks, offered career opportunities to those who enlisted, and in that way enabled America finally to create the one thing it was missing on its way to becoming a full-scale imperial power: a professional army. America was now free to deploy troops endlessly for extended periods of time around the world without triggering the kind of social unrest and political turmoil that characterized the Vietnam era. With the adoption of that smarmy phrase, "thank you for your service," Americans could go about their business untroubled by the threat of actually having to serve in the military if they chose not to.  

If Americans want to impose their will on the world, they should have to belly up to the bar, put on the uniform, and take the risks themselves. I am sure it will strike most readers of this blog as odd that I am in favor of a conscript army but I really do not see any other way to get America to retreat from its imperial ambitions.

As tthey used to say in the part of Queens where I grew up, tuchas auf tisch.


Deep breath. Guilty on all counts. A victory? No, but anything less would have been a great defeat and in this world at this time we need whatever we can get. I will not live to see it, but the next 20 or 30 years in this country are going to be very, very difficult. Military men and women have joined the right wing militia groups and the right wing militia groups have infiltrated the military. White anxiety is growing apace and voter suppression threatens to undermine the progressive tendencies of demographic change.  Can we once and for all time put to rest the myth of American exceptionalism? 

Monday, April 19, 2021


In my haste to bring my short series of posts on Marx’s economic theory to an end, I am afraid I dropped the ball and forgot to complete one part of the argument. You will recall that Ricardo got stuck at the end of his life on the problem of explaining the very common situation in which different lines of production exhibited different proportions of labor indirectly and labor directly required in production. Marx believed that he had a solution to this problem but, as I explained, chose to wait until volume 3 before presenting it. Only after he had posed and solved the problem that the classical political economists had not even seen, namely explaining the origin of profit itself, could Marx returned to the question of what to do with Ricardo’s puzzle.


Marx’s solution was quite interesting. He argued that in a mature capitalist system it is the system as a whole and not simply individual lines of production or even individual factories that must be examined. In the general case in which different lines of production exhibit varying organic compositions of capital, to use Marx’s term, it is the entire capitalist system to which we must turn to identify the relationship between profit and surplus labor. In any particular line of production these two quantities may not be equal (or, to be more precise, proportional) but in the system as a whole they are equal, thereby establishing that capitalism as a system rests on the exploitation – which is to say the extraction of surplus value from – the working class.


Marc seems simply to have assumed that this was true; how could it be otherwise! But the modern mathematical economists who returned to Marx and Ricardo and brought their analytical tools to bear on those theories did attempt to prove Marx’s claim and they came up with a quite fascinating result. As Piero Sraffa had made clear in his foundational monograph, it is essential to distinguish between those commodities that are required directly or indirectly in the production of all other commodities – commodities which he called basics – and luxury commodities which may be required in their own production or even in the production of other luxury commodities but which are not required directly or indirectly in the production of all the commodities in the system. In the little model that I created in my book, Understanding Marx, I included a luxury sector which somewhat facetiously I identified as a sector devoted to the production of theology books – this is a nod to the religious pretensions of the early English capitalists.


Now, it seems that if there are no luxury goods being produced in an economy – or, what is pretty much the same thing, if the luxury goods sector is only a tiny part of the entire economy – then Marx is actually correct! Total profits in the system as a whole will indeed be equal to total surplus labor, for a suitable choice of numeraire.  This means that all of the profits are being poured back into the economy to expand the scale of production. “Accumulate! Accumulate! That is Moses and the prophets to the capitalists,” as Marx sardonically remarks at one point in Capital.


But how do we know that there is some balance in the size of the different lines of production that will, when the capitalists do their very best to reinvest, correctly use all of the physical surplus that is produced in each cycle of production? Well, Sraffa demonstrated that that is necessarily true. Indeed, things get a little bit more delicious than that. In the 20th century, the great Hungarian – American mathematician John Von Neumann, proved an important theorem in growth economics concerning the maximum growth path for a capitalist economy and it is precisely when an economy is on that maximum growth path that Marx’s solution to Ricardo’s problem is correct.


I do not suppose many people find this as delightful a fact as I do, but it is one more way of seeing that despite using only, as Stalin said, addition, subtraction, multiplication, division, and the taking of averages, Marx was in fact a brilliant intuitive mathematical economist.


Several very recent comments have raised questions about game theory and about Analytical Marxism.   Since I have written online an entire short book on the use of formal methods in political philosophy in which I talk at some length about game theory, I will simply point those who are interested to that book, which is archived at, accessible via the link at the top of this page.  As for Analytical Marxism, I will refer those who are interested to the review I wrote of a book by the smartest and most interesting of that crew, Jon Elster, also available at

I feel a little bit like the over the hill lounge pianist noodling away at the piano and saying, every so often, "and then I wrote," before going into some old tune.


 I have written before about what we old folks call a senior moment and in particular about my strange inability to remember the name of the great soprano Kathleen Battle. Last night, I lay in bed tossing and turning for more than an hour trying to remember a name that I simply could not come up with.  I could see the person in my mind. I knew that the person was a man. I knew he was American, that he was white, that he was pretty old, that he was short and funny looking, that he was a Harvard professor of law, that he spent summers on Martha's Vineyard, that he got bent out of shape when the folks on the Vineyard stopped inviting him to dinner parties after he came out for Trump, and I even remembered that he had been one of Trump's lawyers during the first impeachment. I knew his name was not Leo Durocher although I thought it was not too far off that but I just could not remember the name. Finally, I got up, went to my computer, and very quickly established that I was thinking of Alan Dershowitz.

Why on earth is it that I can remember all these things about a person and yet simply not be able to come up with his name? What special link in the brain is failing just for the name but not for everything else about him? That, I must confess, does not keep me up at night, but trying to remember "Alan Dershowitz" really did.

Sunday, April 18, 2021


Two responses to my previous post require some extended discussion, but before I undertake that I do want to call attention to my extraordinary and unexpected influence over national affairs. No sooner do I put up a scathing comment on Paul Kosar and the idea of an Anglo-Saxon Caucus in the Republican party than Marjorie Taylor Greene announces that she is taking the idea down. Of course, skeptics may suppose that Kevin McCarthy's attack on the idea had some role to play in Greene's decision, but those who understand the power of the deep state will reject such superficial explanations.

Saturday, April 17, 2021


All right, at long last let me try to address some of many intelligent comments provoked by my multipart series on Marx. I have gone back in the comments section and collected up some of them, but by no means all. Even so, I want to try to respond to some of these.


Let me begin with a comment I was unable to locate but which, if my memory serves, was posted by LFC. He (is that correct?) notes that if at an early stage in the development of capitalism the ratio of embodied labor to direct labor is 100 to 1, at a later stage it may have grown to 1000 to 1, and that would seem to keep driving the profit rate down if profit really is the money form of the surplus value extracted from the direct labor inputs. This is exactly the inference Marx drew, which led him to postulate that there would be a tendency for the rate of profit to fall in capitalism. As it happens, Marx was wrong. My colleague at the University of Massachusetts, Sam Bowles, proved rather elegantly that in the sort of economy Marx was analyzing if a new more capital-intensive process of production were introduced by an innovative capitalist resulting in a momentary rise in that capitalist’s profit rate, the consequence when the system settle down into equilibrium would be a rise, not a fall, in the profit rate globally. He announced this result triumphantly to a class he was teaching, only to have one of the students point out that a Japanese economist named Okishio had proved it 10 years earlier. Sam was consequently reduced to publishing an article In the Cambridge Journal of Economics with the title “A New Proof of Okishio’s Theorem.”


The second comment came in the form of an email from Jerry Fresia.  He wrote:  "You write that by means of a long historical process workers who produce commodities are deprived of control over their work, their tools, and skills. What is interesting to me is that this exploitation (the correct term here?) is parallel to the alienation that will take place once the farmer, let us say, enters the factory. So apart from alienation in the factory, a farmer who produces corn as a commodity also suffers a type of market dehumanization.  Would it be correct to say that?"


This is a little complicated but the essential answer is yes. Under the pressure of market competition, the natural rhythms of farm work must give way to a sort of industrial farm production that one sees most clearly in the raising of chickens or pigs for market. It is my impression that some independent farmers to this day successfully resist the market pressures sufficiently to gain a genuine satisfaction from the activity of farming but I think they are rare as compared with the industrialization of food production that is characteristic of advanced capitalism.


Jamie Kelly, a philosophy professor at Vassar College, poses several questions into lengthy email messages.  Let me take up the first of them.  The second is too complicated for me to try to deal with in this post. Kelly first writes:  “If you abandon the centrality of the labor/labor-power distinction, does that mean you also give up on Marx's account of surplus value (i.e., it is the difference between the value labor produces, and the value of labour-power)? That would surrender a lot of the theoretical apparatus of Capital (e.g., his account of the working day, and maybe even his account of automation), but I don't see how surplus value can be cashed-out without relying on the labour theory of value.


To my mind, the key historical claim that Marx makes about the transition from feudalism to capitalism is the doctrine of double freedom: workers under capitalism are free in the sense of having the right to sell their labour power, and 'free' in the sense of having nothing to sell but their labour power. This undergirds both his claims about the exploitation of workers, and his explanation of the enormous productivity of capitalism. Do you think double freedom can be made sense of without the labour theory of value?


Marx leverages the labor/labor-power distinction so much throughout Capital, that I am having a hard time seeing how the working day, machinery and modern industry, or even primitive accumulation (i.e., the best parts of the book) can be salvaged without it.” 


There are several questions in this message, all turning on my rejection of The Labor Theory of Value. First, recall what I said early in my essay about the 19th century meaning of the phrase “theory of value.” To Smith or Ricardo or Marx a theory of value was a theory of natural or long-term or equilibrium price, as we would say today. Marx’s theory of capitalism without The Labor Theory of Value is, many would say, like Hamlet without the Prince. Certainly that is the view of most contemporary writers who identify themselves as Marxists. But I think this is wrong. I do not think there is a single important and valuable element of Marx’s analysis and critique of capitalism that cannot survive scuttling a theory of natural price that turns out to be analytically incorrect. You can see this quite clearly in Kelly’s second paragraph where he talks about the “doctrine of double freedom.” The exploitation of the workers is grounded in their having lost everything but their bare ability to sell their labor and the mystification of capitalism that serves to rationalize it and justify it in the eyes of those who live within it is nicely captured by this notion of double freedom. Marx’s account of the working day, of machinery and modern industry, of primitive accumulation and much else, grounded in his extensive historical studies, nowhere makes essential use of The Labor Theory of Value. Whether you take to my rudimentary effort to develop an alternative analytical framework or not, I think that effort makes clear that one can talk meaningfully about the ways in which capitalism exploits labor quite independently of the particular analytical framework that Marx introduced to explain this phenomenon, which he correctly believed lay at the root of the structure of capitalism. When I hear Marxists insisting that there cannot be Marxism without The Labor Theory of Value, I sometimes think I am listening to Catholics saying it cannot be Christianity without the virgin birth or Shiite Muslims saying there cannot be Islam without the hidden Imam or Jews saying  you cannot be Jewish if you do not keep kosher. I am willing like Spinoza to be driven from the congregation if that is what it takes to follow what I believe to be the truth.


The frequent commentator who uses the nom de blog Marcel Proust, writes as follows:  “So far as I am aware, all economic systems more technologically advanced than that of hunters and gatherers -- perhaps excepting pastoralism -- depend fundamentally on the exploitation of someone. The only reason that I can understand for taking this to be Marx's key insight is that capitalism has successfully mystified itself, if I may engage in a huge bit of anthropomorphism and attribute agency to the system itself. Nearly everyone who is part of the system believes that one way or another, they are making free choices and therefore cannot possibly be exploited.” To which I need only say Amen. Marx could not agree more. What distinguishes capitalism from slavery or feudalism, the two earlier forms of economic organization about which Marx writes, is not the fact but the manner of exploitation as well as the accompanying mystification that is typical of capitalism.


Well, that is enough for today. I will go back and look again to see whether I can surface some other interesting comments.






 Paul Gosar, a Republican member of the House of Representatives from Arizona, whose paternal grandparents were Slovenian and whose maternal grandparents were Basque, is one of a number of Republicans who have formed a new political organization devoted to preserving the Anglo-Saxon heritage of the American Republic.

Friday, April 16, 2021


Before finally replying to some of the many interesting comments on my multipart Marx essay, I should like to say just a few words about why I find blogging an odd and in some ways unsatisfactory mode of communication. One of the criticisms of classical social contract theory, advanced by many commentators, is its treatment of the political community as a timeless assembly of mature and independent adults. There is some feeble effort to take account of subsequent generations, but they tend to be treated as no different from immigrants who enter the community and sign on to the commitments made in the original contract. But the truth, of course, is completely other. All of us live through a lifecycle starting with birth, moving from childhood to adulthood, then if we are fortunate to old age, and finally to death.


Everyone knows, even if the theory takes no account of it, that we are different as children from what we are as young adults, different as young adults from what we are in our maturity, and different again in old age. Readers of this blog have all noticed that I increasingly often make reference to my age, of which I am extremely aware, indeed in some ways obsessively so. I have spent the last 71 years in the classroom, as it were, first for five years as a student, then for 53 years as a teacher, and then for the past 13 years as a blogger, part-time teacher, YouTube lecturer, and always throughout my life as a writer.


As I have often remarked, I have spent most of my life in my head, but inevitably, properly, humanly, my relationship to the world around me has changed as the decades have gone by. As a young man I was energetic, enthusiastic, confrontational to authority wherever I could find it, forward-looking, and utterly wrapped up in the ideas in my head. As the years went by, and especially after I had children, I became supportive, generative, quasi-parental toward my students, for all that my published work continued to announce me as a radical, a man of the left, a critic of established authority.


When I was young, I scarcely noticed what was said about the books I published. I read very few of the reviews and did not have a strong sense of myself as a member of and participant in a scholarly community. My decision to resign from my Columbia professorship and move to the University of Massachusetts was, I finally came to realize, very strongly motivated by a desire to withdraw from the bustle of the Academy to a retreat where I could pursue my ideas untroubled.


Now that I am in my late 80s and compelled to acknowledge that my life is nearing its end, I think a great deal about those who have read my writings and have found something of value in them. It is important to me, in a way it never was before, to believe that something of what I have written will live after me.  I am eager to receive, as I do, confirmations that out there in the world somewhere are readers who have enjoyed my books, my articles, or even these blog posts. I am not quite like the Ancient Mariner who stoppeth one in three, but I am not too far off either.


But blogging by its structure and nature is almost completely insensitive to the natural rhythms of a human life. The posts appear as if by magic and linger on in cyberspace presumably forever. I cannot see the people to whom I imagine myself to be talking nor can they see me and, strangest of all, I cannot really tell where they are, how old they are, whether they are male or female, and who they are as people. I do not find this liberating, I find it unsettling. I would rather be sitting around a table teaching a class of 15 than posting little essays that are read perhaps by a thousand. That is why I have gone to such lengths, even taking weekly flights, to find a place where I can sit around that table yet again as I have so often in the past 66 years.


Well, if I am not the Ancient Mariner I am most certainly Mr. Chips.



Thursday, April 15, 2021


Marc Susselman is a lawyer in his early 70s who, 53 years ago, was my student during the year that I visited at Rutgers. For some while he commented on this blog as MS, but when his logorrhea got out of control and he became querulous and dyspeptic besides, I tried to limit him to one post and one riposte a day. When that failed, I deleted a great number of his seemingly endless comments and told him to go elsewhere. After a bit, he resurfaced as Samuel Chase and the same habits reappeared. I deleted some of those comments, but he is now apparently returned as John Doe.


Marc is intelligent, accomplished, and knowledgeable but he has one characteristic that he seems not to share with anyone else who ever comments on this blog: he makes me want to stop blogging. When he is in full bray, I cringe from checking the comments section. I thought about simply continuing to blog without ever reading the comments, but that destroys much of the purpose of blogging and besides, many of the comments are thoughtful, intelligent, provocative, responsive to what I have actually posted, and deserving of some reply.


So I am just going to say it straight up. Marc, go away. You are younger than I was when I started blogging. Start your own blog, build your own audience, and have at it, but not here. Those of you who enjoy your interactions with Marc can migrate to his blog and exchange views with them to your heart’s content. Just not here.

Wednesday, April 14, 2021


As one black man after another is murdered by police, and impotent rage wells up in me, I ask myself what, if anything, I can contribute to the public response save my cries of anguish. A veteran of more than 20 years in the police force shoots and kills a 20-year-old man who has been pulled over for a routine traffic stop, and by way, I suppose, of exculpation she says that it was a mistake, she meant to use a Taser rather than her service revolver. Why in God’s name even think of using a Taser on someone who has been pulled over for an expired registration tag!


Long ago I learned the terrible meaning of the phrase “the conversation” as it is used in American black families. The number of black men killed by police each year is tiny in comparison to the total black population in America, but that says nothing about the experience of being black in this terrible country.


As I was walking this morning, I recalled a passage in my last and least read published book, Autobiography of an Ex White Man, in which I tried a thought experiment to communicate something of what it must have been like to be a slave on a pre-Civil War plantation. I was reacting to an important and widely read book by the Nobel laureate Robert Fogel and his younger colleague William Engerman, Time on the Cross. Here is what I wrote 16 years ago. Nothing has changed.


“Needless to say, any individual slave was not likely to be whipped very often.  Robert Fogel and Stanley Engerman, in a widely discussed and much criticized book, report that on one plantation whose owner, Bennet Barrow, kept careful records of his two hundred slaves, about half the slaves were not whipped at all during a two year period, and overall there were 0.7 whippings per slave per year.  Since a number of readers have actually concluded from this bit of data that things weren’t so bad in the Old South, I tried a little thought experiment in an effort to imagine what effect whippings might have had on a slave.


Down the road from the University of Massachusetts is Amherst College, a famous private liberal arts institution that has on several occasions been ranked the best college in America.  It has a faculty of two hundred  --  just about as large as the slave population on Barrow’s plantation.  Suppose a whipping post were set up in front of the Robert Frost Library in the central college common.  And suppose that on an average of once every four or five days, an Amherst College professor were stripped to the waist, man or woman, and whipped at that post until the blood ran for some infraction of college rules or simply for failing to grade papers on time.  Now, as a member of the faculty, I would presumably be intelligent enough and educated enough to be able to calculate that my chances of being whipped were only 0.7 per year, and I would also have noticed that if I was extremely careful, and never talked back to the Dean or the President, I might never be whipped at all.  Nevertheless, I think it is reasonable to suppose that the steady progression of brutal public whippings would have, how shall we say, a chilling effect on me.

Such a fantasy seems absurd, of course, but that is just another way of saying that we White people don’t really think of the slaves as people like ourselves, regardless of the political correctness of our sentiments.  Whipping slaves is terrible, cruel, inhuman, but it is something that happens to other people, whereas whipping professors, bizarre though that may sound, is something that might happen to me.”


Monday, April 12, 2021


I am so sickened by the endless killing of black men and women by police officers that it is difficult for me to offer thoughtful, high – toned commentary on theoretical issues. 

Sunday, April 11, 2021


A number of readers have raised important questions that I need to address, but before turning my attention to that I have decided to finish my exposition. I am sure it is clear that I have vastly more to say than I am putting into this little multipart essay – I mean, I have published two books and a number of lengthy articles on the subject. My purpose here has been simply to highlight my claim that it is possible to bring the literary criticism and the mathematical economics together in a fruitful fashion.


I am fond of saying that Karl Marx was the greatest student of society who ever lived and I genuinely believe that, but I do not think he was a prophet or messenger from God. He was a student of society, which means that he looked at the world around them, studied it as deeply as he could, analyzed it as best he could, got a great many things – important things – right, and of course got a number of things wrong. Today, I want to talk about what he got wrong or more broadly what he failed to foresee, because understanding those failures or inadequacies can help us to understand a good deal about the world in which we live.


As I see it, Karl Marx got four big things wrong or failed to foresee them. The first of these concerned how the capitalist class would evolve; the second concerned how the consciousness of the working class would evolve; the third concerned what would happen to capital; and the fourth concerned what would happen to labor. That is a lot of big things. Before I turn to them one by one, let me repeat that Marx got the very biggest thing dead right. He was right about it when he wrote and he is still right about it. One can express that one big thing in a simple sentence only nine words long and those nine words remain the most difficult nine words for the greatest economists in the world to comprehend. Here they are:


Capitalism rests on the exploitation of the working class.


The first thing Marx failed to foresee was that the capitalists, despite their vicious leave no prisoners competition with one another, would manage in a crisis to band together sufficiently to save capitalism itself. Marx was correct that the booms and busts characteristic of early capitalism would get worse and worse until there was a worldwide economic crash. But to put the matter simply in a phrase, Marx failed to foresee Keynes. He understood that the state was the executive committee of the capitalist class but he did not see that the committee would prove capable of pulling capitalism back from the brink each time its own self-destructive expansion and competition threatened its survival.


The second thing Marx failed to foresee or to appreciate was the power and permanence of the national, racial, and religious identifications that in the early days tended to set German workers against French workers, white workers against black workers, Catholic workers against Protestant workers, and all Christian workers against Muslim workers. In the second decade of the 20th century, socialists like my grandfather confidently predicted that German and French workingmen would not willingly go into the trenches and kill one another for their capitalist masters. Indeed, at the beginning of the first world war, many socialists were pacifists, not out of religious conviction but out of a belief that workers would and ought to be united across national boundaries by their class position in the ever more international capitalist economy. One hundred years later, we are compelled to face the bitter truth that in the lives and passions of hundreds of millions of men and women worldwide, class solidarity is trumped by patriotic nationalism, religious fervor, or racial animosity.


The third thing Marx failed to foresee was that capitalism, as it grew in the way that he anticipated it would, would morph into shareholder ownership of capitalist enterprises. I have talked about this before on this blog and I will not go into any detail about something that is, after all, familiar to us all because it is the world in which we live. Since Marx insisted that the functioning of capitalism could not be traced to the personalities or desires or greed of individual capitalists but had to be understood systematically and structurally, his theory was well positioned to adapt to the new form that capitalism took, but he himself did not, so far as I know, anticipate the rise of the limited liability joint stock enterprise. The complete divorce in the general case (Jeff Bezos to the contrary notwithstanding) of ownership from managerial control is, looked at one way, the perfection and logical conclusion of the tendencies that Marx perceived in the earliest days of the development of capitalism, but of course he did not foresee how it would play out in detail.


And fourth – perhaps most important, to my way of thinking – Marx completely failed to see that a permanent steeply pyramidal structure of jobs, wages, and salaries would become the seemingly unalterable face of mature capitalism. When Marx was writing, capitalism was systematically destroying traditional crafts and guilds and breaking down structures of job knowledge and performance that had characterized the pre-capitalist era. The world that Marx was looking at seemed to be reducing the workers to an undifferentiated mass of semiskilled machine operatives who lacked both tools and skills in particular historical crafts. Indeed, it was this development which encouraged him to believe that class consciousness would grow as workers first in one factory, then in one industry, then in many industries, then in one nation, and finally worldwide would come to understand their common interest in uniting and confronting capital. But what happened in the 20th century was the emergence of a steep pyramid of jobs and compensations. A manual worker making a barely survivable wage might, from an analytical perspective, occupy the same position in the structure of a capitalist economy as a middle manager of a large corporation making perhaps 40 or 50 times as much money, wearing a suit, getting fringe benefits, and so forth, but there was no likelihood whatsoever that the two of them would make common cause against their common exploiter. Indeed, as my two old University of Massachusetts friends and colleagues Sam Bowles and Herb Gintis demonstrated in a lovely mathematical essay, one could show that in the modern capitalist world relative exploitation had replaced absolute exploitation, so that not only did capital exploit its high paid employees, but they in turn relatively exploited employees further down in the pyramid of wages and salaries.


It follows from all of this that there is a very serious need not to reject Marx’s fundamental insight concerning the exploitative character of capitalism but rather to continue developing modern understandings of contemporary capitalism grounded in that fundamental insight and completely attendant to the realities of 21st-century international capitalism.


This analysis, which echoes somewhat the analysis I offered in my essay “The Future of Socialism,” goes some way toward explaining to those of us still in mourning why socialism has not succeeded capitalism.


Before I continue  mydiscussion of the thought of Karl Marx, let me offer a little expression of praise for the online version of the New York Times crossword puzzle. For about 13 months now I have been doing the puzzle online rather than on paper, as had been my custom for 20 years or more. The great virtue of doing the puzzle online is that the app keeps track of how you do day by day, week by week, month by month. As everybody knows who is addicted to the Times puzzle, it starts very easy on Monday, gets progressively harder until Thursday, which always has a special tricky gimmick in it, and then continues getting harder until Saturday. The Sunday puzzle is not harder, it is just longer – in difficulty it is roughly equal to the Wednesday puzzle. Today the app told me that I completed the puzzle in less than my average time but not as quickly as my best time. The app also purports to keep track of my global average of successful solutions but there is a flaw in the app which makes its calculation incorrect. I think I have successfully solved the puzzle roughly 95 or 96% of the time in the past 13 months but the app claims that my success rate is 99.5%. The problem is that when I fail and ask to see the completed puzzle so that I can find where I made my mistake, the app records that my streak of successful solutions is ended but then incorrectly treats the revealed puzzle as a successful solution. Oh well, nothing is perfect, but the New York Times puzzle online comes close.  On to Marx.

Friday, April 9, 2021


I took a day off from the extended comments I have been making about Marx because this morning I appeared as a guest in a freshman writing course at Cornell University where the students just got finished reading my little book In Defense of Anarchism.  It was a lovely experience and seeing them all on my computer on gallery view cheered me up no end. I have spent the last two weeks binge watching the trial of Derek Chauvin.  That has been somewhat depressing, I must confess

It is hard to be 87 years old and see what this country is becoming, but then Prince Philip just passed away at 99 so perhaps I will get to see a little bit more of what the better half of my fellow Americans can make of this place.

Tomorrow, I want to try to respond to some of the responses I have received both on this blog and in email messages to what I have been writing. 

Thursday, April 8, 2021



My Interpretation of the Thought of Karl Marx


Part Seven: The Irony Hits the Math


So Marx was wrong. The distinction between labor and labor power is not the key to understanding both the exploitation that lies at the heart of capitalism. But he is clearly right that the workers are exploited. Furthermore, he is clearly right when he claims that capitalism misrepresents itself as a system founded upon freedom for all including the workers. And he is right that capitalism manages both the mystify itself and, unlike the church, even to conceal the fact of this mystification so that both workers and capitalists and the economists who analyze their doings imagine wrongly that what goes on in the capitalist marketplace is free of the clouds of mystery that surround the altar and the throne.


It was also clear to me that the sophisticated mathematical reinterpretations of the classical school of Political Economy, while they were an enormous analytical advance on the arguments of Marx or Ricardo, completely failed to capture the mystifications of capitalism or the irony in the description of capitalism as a system of “free markets.” So I put to myself a question: is there some way of revising the mathematical analysis so that it preserves the power and clarity that had been achieved by the modern reinterpreters of the classical school while at the same time, in some manner of speaking, introducing the irony into the equations? No one had ever asked this question before, so far as I could tell. Indeed, no one had ever conceived it to be a question one could ask. But I had an idea.


Let us for a moment clear away the equations and ask what Marx is telling us about the situation in which 19th-century English workers found themselves. He is telling us that by a long historical process the workers have been deprived of control over their own labor, they have been deprived of the tools of their labor, they have been deprived even of the skills which they use in their labor.  As part of what Marx memorably called “the reserve army of the unemployed,” the workers are compelled to accept the wages that the capitalists offer and to labor in the factories in the manner and under the conditions dictated by their employers. They do not have land on which they can grow their own food if they choose not to accept employment in the factories. They do not have looms or forges, spinning jennies or lathes. They have only their own bodies which day after day they apply to the tools and raw materials presented to them by their employers.


Now, in a free market, a competitive market, a capitalist market – so all the classical Political Economists agreed -- there is a single ruling rate of profit which is adjusted and regulated by the free choices that capitalists make to move their capital from sector to sector in pursuit of the largest return on their investment. If a capitalist who owns a factory that weaves woolen cloth observes that capitalists in the furniture business make a higher rate of return (and, let us recall, that in the classical school perfect information is assumed), then over time and with some adjustment that capitalist can cash in his investment in the woolen factory and shift it with to a furniture factory. To be sure, this is not a switch that can be made overnight for there is a problem with what is called “fixed capital,” but over time and more or less bumpily, the capital gets transferred to the new sphere of production. This has the double effect of increasing the amount of woolen cloth available in the market and decreasing the amount of furniture available for sale. Changes in the relative size of demand and supply alter the prices at which these goods sell which in turn reduces somewhat the rate of return in the cloth industry and increases it in the furniture industry. So by an unceasing series of such individual capitalist decisions and actions the profit rate is perpetually equilibrated. This is the familiar picture painted by Ricardo and his lesser contemporaries. The system of price equations representing the operations of a capitalist economy provides a mathematical model for this story of what goes on in the normal functioning of capitalism.


Now, since capitalism represents itself – or, more precisely, misrepresents itself – as a system in which the workers must be understood as producers of a commodity, labor, on a par with the furniture producer and the woolen cloth producer, a mathematical model of this economy must include an equation for the labor producing sector. Like all the other equations, this equation must include a profit markup.


Thus far the mystification. Ah, but the labor producers, unlike the furniture producers and the cloth producers, cannot shift their capital to a different line of production when they observe that it pays a higher rate of return, for their capital is nothing other than their bodies and the only way they can cash in their investment in their bodies is by… cashing it in, which is to say dying. This is nothing against capitalism, of course. Capitalism places no legal or other constraint on the choices of the workers. It is just an unfortunate metaphysical accident, perhaps laid at the door of Descartes if someone must be blamed, that the workers’ body and soul are inseparable this side of the grave.


Suppose we were to write a system of equations for an economy in which the workers genuinely are treated as free petty commodity producers of the commodity labor. And suppose we were to express mathematically this unfortunate constraint on the workers’ ability to move their capital into other lines of production, thus in a manner of speaking – and only in a manner of speaking – building the ironic treatment of capitalism as a free market system into the equations.  Well, because of the unfreedom of those condemned to produce labor, the rate of return in that sector may not be equal to the rate of return in the other sectors and so it must be represented by a different variable, which in my new system of equations I arbitrarily decided would be ρ or rho. What mathematical conclusions could we then draw?


Without troubling you overly with the mathematics, and, I might say, hardly surprisingly, it turns out that the total profit appropriated in the system by all of the capitalists exactly equals the profit forgone by the workers on their capital – their bodies – by the fact that they cannot shift that capital about in pursuit of a better rate of return and hence are forced to sell their output below what would otherwise be its equilibrium price. (Those who wish to see all of this demonstrated mathematically can take a look at my essay A Critique and Reinterpretation of Marxist Labor Theory of Value, archived and accessible by the link at the top of this page.)  In the world Marx was looking at rho was effectively zero.


And there you have it. In a simple model that abstracts for the moment from any number of complications that in a fully developed theory would of course have to be taken care of, you can see transparently the real root of capitalism’s exploitation of workers, an exploitation, Marx makes clear over hundreds of pages, that was grounded in a long historical process leading from late feudalism to the capitalism of 19th century England.


This is just a beginning, quite obviously, but it is I think a good beginning for it places center stage in all of its complexity Marxist conception of the essence of capitalism and of the combination of theoretical and literary devices required to capture that complexity. Tomorrow I will say just a bit about how to develop this theory in order to make it come closer to fitting the reality of the capitalism we know today.

Wednesday, April 7, 2021


When I referred in my last episode to linear algebra, I did not have in mind the little corn/iron price and labor value equations that I offered by way of illustration. I had in mind rather the Perron Frobenius theorems concerning the maximal eigenvalues of square nonnegative matrices. This material may very well be taught overseas in grade school, but I do not think it is covered that early in American schools. However, when I decided that I would present my little equations to my UNC Chapel Hill philosophy department graduate course in the spring of 2020, I was apprehensive about going through the real mathematics so I went online and googled around for a while. I came upon the official website of the North Carolina State Department of Education. There I found an elaborate table specifying what the State Department Of Education requires to be taught in every grade from kindergarten to 12th grade in North Carolina public schools, in the areas of reading, spelling, writing, American history, biology, chemistry, physics, and also mathematics. With a little effort, I determined that the simple version of my mathematical analysis used only mathematics that is required to be taught in North Carolina schools in the ninth grade, and I told my graduate students that in a desperate effort to keep them in the course.


So, if you went to an American high school and made it through your freshman year mathematics course, you should not have any trouble with this part of my exposition. Those of you who want the full monte can consult my essay entitled A Critique and Reinterpretation of Marx’s Labor Theory of Value, accessible by clicking on the link to at the top of this blog.


                                                 My Interpretation of the Thought of Karl Marx


Part Six: Enter the Mathematics


(Several of the comments call for a response but I will postpone that in order to get on with my exposition.)


There is, of course, vastly more to be said about Marx’s views in volume 1, but I wish at this point to turn to the modern mathematical interpretation of classical Political Economy which I mentioned at the very beginning of this exposition. Unlike their modern descendants, the classical economists made almost no use at all of formal mathematics. Marx had a go at working out some numerical examples but mostly he botched it and it added very little to his explanation of his theories. When the modern mathematical re-interpreters of Ricardo and Marx undertook to translate their theories into equations, they had to formalize a decision that Ricardo and the others had made more or less without explicitly stating it.


In order to reduce the complexity of real economic activity to equations, economists must in effect choose between supposing that there is one dominant technique for the production of each distinct commodity and supposing that there are an infinite number of techniques for the production of each distinct commodity. To put this point as simply and formulaically as I can, they have to decide whether they are going to use linear algebra or calculus. The neoclassical assumption of an infinity of alternative ways of combining inputs to produce an output lends itself to analysis using calculus and the classical assumption of a single dominant technique of production for each commodity finds its most natural expression in systems of linear equations.


Linear algebra makes it possible to handle formally any finite number of commodities, each one represented by a single vector of inputs per unit of output. One can then manipulate what is called the unit input matrix to derive a variety of powerful conclusions. Since I may have lost many of you at this point, let me give a very simple example which will serve quite adequately to illustrate what I want to say. All this is laid out precisely and at length in my book, Understanding Marx.


Suppose we are talking about an elementary economy in which there are only two commodities, corn and iron. (What we call corn does not grow in England, of course, but the term “corn” was used by the English to mean “the dominant grain of a region,” hence the great debate in the early 19th century in parliament as well as in the writings of the political economists over the so-called “corn laws” regulating the importation of grain from abroad.)  I have invented the following little corn/iron economy to illustrate what I want to say. Since I am now doing economics, there is no need for me to worry about the real-world relevance of what I am saying.


Suppose it takes 100 units of labor, 2 units of seed corn, and 10 units of iron to produce 300 units of corn. If we use the Greek letter l for labor value or quantity of embodied labor with subscripts indicating whether we are talking about the labor value of corn or the labor value of iron, and if we recall, what is essential, that direct labor must be entered at par since it is labor directly, not indirectly, contributed to the production of the output, then we can write the labor value equation for the corn sector in the following way:


                        100 + 2lc+ 10li  =   300lc


In words, this equation says that when producing 300 units of corn, the 100 units of labor directly applied in production and thus embodied in the corn output, added to the amount of labor embodied in the two units of corn used in production and the amount of labor embodied in the 10 units of iron used in production taken altogether equally amount of labor embodied in the 300 units of corn that are the output of the production process.


Using the letter p with appropriate subscripts to stand for the prices of corn and iron, the letter w to stand for the wage paid for the labor, and the Greek letter π to stand for the rate of profit, we can write the corresponding price equations for this little corn/iron model. The price equation in the corn industry looks like this:


                        (100w + 2pc+ 10pi)(1 + π)  =  300pc


If I choose the appropriate input quantities for the iron sector and carry out a series of mathematical manipulations with which I shall not trouble you, I can demonstrate that the prices of corn and iron are proportional to their labor values, as Ricardo claimed, and also, what is really quite interesting, that these prices and labor values are independent of the wage and the profit rate, which vary inversely to one another, thereby also demonstrating the class conflict between labor and capital. All very impressive.


I spent a very great deal of time plowing through 10 or more thick difficult mathematical economics texts in each of which the theories of Ricardo and Marx were explored in excruciating detail. The big take away from all these books was that both Ricardo and Marx had been, contrary to the conventional wisdom, brilliant intuitive mathematical economists, much of whose theoretical work was sustained by this sophisticated 20th century analysis.


But as I toiled away at my studies I noticed something curious and eventually troubling. There were symbols in the equations in these books for just about everything that Ricardo and Marx had talked about – symbols for quantities of inputs, symbols for quantities of outputs, symbols for prices of commodities, symbols for quantities of labor, and also the wages of labor, symbols for profit rates earned by capitalists. But nowhere in the equations could I find a symbol for Marx’s signature concept, labor power. Since in Capital Marx had made the distinction between labor and labor power the key to his solution to the central problem of the origin of profit, it seemed to me that any modern mathematical rendering of his theories should have somewhere a symbol for that central concept, but it was nowhere to be found. In effect, the mathematical economists I was reading, all of whom were extremely sympathetic to Marx’s theories, seemed to be saying that his story about the distinction between labor and labor power was simply, in Pooh Bah’s immortal phrase from the Mikado, merely “corroborative detail designed to lend an air of verisimilitude to an otherwise bald and unconvincing narrative.”


At this point a thought occurred to me. (Now, this is a sad tale but I feel compelled to tell it nonetheless.) Since there is no symbol for labor power, the distinction between labor and labor power plays no role at all in the formal analysis of Marx’s theories. To be sure, in the labor value equations the labor inputs are valued at par and in the price equations the price of labor has a letter, w, all its own, but the first is an assumption, not a conclusion, and the second is simply a notational convention. Could one write a set of equations that permitted us to calculate the iron value of labor and corn, rather than the labor value of corn and iron?


Iron value!? What on earth would an iron value be? Nobody ever talks about iron values or corn values but only about labor values. There might in fact be a distinction between labor power and labor and no corresponding distinction between corn power and corn or iron power and iron but if the distinction between labor power and labor did not enter into the equations then that would make no difference.


So I had a go at setting up some corn value and iron value equations and seeing what I would get. The first question – quite important – was whether one could always be sure in calculating iron values or corn values that when the equations were solved those values would be positive. After all, it would not make much sense to say that the amount of corn directly or indirectly required for the production of a unit of iron was negative! Well, a little mathematical manipulation (with some help from friends in the UMass economics department) revealed that so long as there was any surplus of any commodity anywhere in the system, all the corn values, or iron values, or labor values, or x-values in the system would necessarily be positive.


One of Marx’s most striking claims, demonstrated to be correct by the modern mathematical reinterpretations, was that the labor value of the physical surplus is exactly equal to the surplus labor extracted in the production process from the workers – a lovely mathematical demonstration of the fact of exploitation. But a little more manipulation with the equations demonstrated that this was also true for corn values or iron values. The corn value of the physical surplus was exactly equal to the surplus corn value extracted from the corn inputs in the system, and so forth.


In fact every single theoretical claim made by Marx in Volume 1 of Capital (all the claims in volumes two and three, for that matter) could be replicated using these nutty notions of corn value and iron value.


I was remarkably pleased with myself when I had reached these conclusions for I thought that I was the first person in the entire history of the discussion and commentary on the theories of Karl Marx to have even thought of this, let alone to have demonstrated it mathematically.  I told this story on my blog 10 years ago. Let me close this episode in my exposition by reproducing what I wrote there:


In 1981, I published an essay entitled "A Critique and Reinterpretation of Marx's Labor Theory of Value," in a journal called PHILOSOPHY AND PUBLIC AFFAIRS. [I believe it is available on-line.] In that essay, I proved an extremely important theorem that shows that Marx was wrong to impute the exploitative capacity of capitalism to the labor/labor power distinction. I was, I firmly believed, the first person ever to realize the underlying logical flaw in Marx's argument, and to demonstrate it mathematically. The proof was not much from a mathematical point of view. Indeed, when I had first actually proved the theorem several years earlier, I was ignorant of linear algebra, and had used nothing but elementary algebra and some ingenious labeling moves. After the essay appeared [since I made the mistake of publishing it in a philosophy journal, almost no one read it who was capable of appreciating it], the brilliant, mathematically extremely sophisticated Marxist John Roemer published a reply and criticism in the journal in which, in passing, he pointed out that the same theorem had been published two years earlier by Josep M. Vegara in a monograph entitled ECONOMIA POLITICA Y MODELOS MULTISECTORIALES.


Sic transit gloria mundi



Tuesday, April 6, 2021


LFC makes the following comment: “Prof. Wolff has said that one of his aims is to "put the irony into the equations," but where is the irony here? I get the mocking language ("moneybags") and the element of mystification, but mockery and mystification aren't the same as irony. So where is it?” Once again, I am afraid that by rushing through my ideas too quickly I have neglected to include essential points, so instead of the next episode in this soap opera I will directly address LFC’s question. That will actually set things up for what I wanted to say next.


The central ironic utterance whose true meaning Marx seeks to expose is the phrase “free market.” In the era preceding the development of capitalism there was a complex network of constraints on economic activity. Guilds controlled the actions of master artisans and of the apprentices and journeymen in their establishments. Where a cabinetmaker could ply his trade, what prices he could charge for what he produced, what he paid to those working under him, these and many more aspects of economic activity were regulated by a mesh of laws, customs, and guild regulations. It was the elimination of these constraints that unleashed the enormous productivity of capitalism.


Thus the actions of entrepreneurs were free in the sense of being freed from traditional and other constraints. The workers too were free, or at least so it was said by the theorists and apologists of the new economic order. The workers were free to travel wherever they wished in search of work. They were free to bargain for wages in any way they wished, demanding more, refusing to accept the job that paid less, moving from city to city and from employer to employer without legal or other constraint. So it was that Marx described the marketplace as “an Eden of the innate rights of man… (where) alone rule Freedom, Equality, Property and Bentham.”


Thus far the apparent or superficial meaning of the phrase “free market.” But although the superficial meaning applied truly to the capitalists it was for the workers bitterly ironic. The deeper meaning was that the workers were indeed free – they were freed of the land on which they grew their food or tended their sheep. They were indeed free – they were freed of the tools of their labor. They were indeed free – they were freed even of the skills which they had acquired over long years of practice, for those skills were now built into the machines that they or their children tended. The workers were freed of everything save their capacity for labor and having nothing else with which to get their food, clothing, and shelter they were thus compelled to accept the wages offered by entrepreneurs or starve.  Their “freedom” was in fact slavery – wage slavery as it came to be called.


But Political Economy perpetuated the myth that workers, like their employers, were free men and women engaging freely in the production of commodities which they then freely brought to market and freely offered at any price they freely chose. Indeed, this myth was endorsed by the legal system, for just as the law forbade entrepreneurs to join together forming a “combination (of entrepreneurs) in restraint of trade,” so the workers were forbidden to join together into unions which the law construed also as “combinations (of entrepreneurs) in restraint of trade.”


There are other ironies in the standard descriptions of capitalism, including one that will play a central role in my mathematical analysis of the situation but it is this characterization of capitalism as a Free Market system that is the central unconsciously ironic utterance of all classical and neoclassical economic theory. In Capital, especially in the early chapters, Marx struggles first to give voice to and then to expose as meretricious the myth of the free market.  


I hope that these remarks begin to respond to the question posed by LFC. In the next one or two chapters of this saga I hope to enrich and deepen these insights and connect them up with the modern mathematical reinterpretation of the classical and Marxian Political Economy.