Friday, 10 October 2025

TOWARDS AN APPROACH TO THE PROBLEM OF THE TRANSFORMATION OF VALUES INTO PRICES

 «Il n'est de richesses que d'hommes»

                                                                                       «Humans are the only wealth»

Jean Bodin 1529-1596


1. Some Preliminary Considerations  - The Context

The infamous "transformation problem" reminds me of an old elementary school song that applied to dividing fractions: "Invert the terms of the broken divisor and apply the multiplication rule." The "transformation problem" is a perfect example of how to transform an explanatory demonstration of a given phenomenon—a demonstration that was (and continues to be) logically consistent and coherent with the empirical reality to which it applies—into a pseudo-demonstration of how its author was ultimately completely wrong. As explained later in the text, if we consider that Marx was certainly perfectly aware that the overall equality between "values" and "prices" is nothing more than a tautology and that therefore the important thing was to explain deviations from an average, by definition always a theoretical abstraction, we find ourselves in an unusual situation in which the mathematical proof (albeit indirect and unintentional) that Marx's explanation regarding the transformation of "values" into "prices" was correct is, through magic or intellectual juggling, transformed into proof that the entire Marxist theory about the functioning of the capitalist system is ultimately wrong.

Even at the level of common language, the word "value" ends up representing an idea replete with distinct meanings and significances, most often depending on the circumstances in which it is used. From "respect values" to "cultural values," including "moral values," to the "fiduciary values" of financial managers and the "added value" of accountants, we have plenty to choose from. For the purposes of this article, we'll focus primarily on "economic value," of which "fiduciary values" and "added value" are simply two expressions of today's business world.

For many decades now, Karl Marx's ideas have been generally considered dangerous and subversive, particularly by well-thinking and usually refined people. And yet, Karl Marx himself was a man of good family. Then, after the fall of the infamous Berlin Wall, the implosion of the former Soviet Union, and the alleged "conversion to capitalism" by the People's Republic of China, Karl Marx's ideas were considered by all creators of ideas and opinions as definitively wrong and, preferably, buried forever in the archives of erroneous ideas and to be forgotten. At most, a kind of archaeological curiosity to enliven some academic debates about what could have been, but ultimately was not. A strange thing that would later come to be called Socialism. Now, it turns out that Karl Marx wrote above all and especially about the social and economic system in which we all live: Capitalism. About what an eventual socialist society would be or could become, Marx wrote very, very little indeed. In a total of approximately 5,000 to 6,000 pages (depending on the edition) already inventoried from all of Marx's writings, our author wrote around twenty or thirty pages on possible hypotheses for the functioning of a possible, but necessary, socialist society. A first question to ask here would be to know for what purpose, or why, Karl Marx considered the future advent of a socialist society necessary. The answer typically given to us by those who persist in studying capitalism following Marx's ideas is relatively simple: the "holy prophet" discovered, through analysis and reflection on the facts observed at his time, a whole series of logical and de facto contradictions inherent in the regular functioning of the capitalist system. From social crises and recurring wars to the deepening of social inequalities, including concentrations of companies and financial crises, there is a little bit of everything in the contradictions identified and explained by Karl Marx.

And yet, the economic analysis studied in universities, schools, and institutes around the world almost always overlooks the ideas and concepts developed by Marx. On the one hand, many economists consider him a sociologist (a mortal sin...), but on the other, he is also often considered a philosopher and historian, rather than an economist. If it were possible to summarize the vastness of Karl Marx's writings on the social and economic system we call capitalism, the "half dozen" basic concepts and another "half dozen" theorems, we would say that Marx's thought boils down to, or rather, is based on, two fundamental pillars: the theory of value and the law of the tendency of the rate of profit to fall. The so-called law of the tendency of the rate of profit to fall could be said to be to the capitalist system what the law of gravity is to physical science applied to a planetary system. But we will address that in another paper. There is also much to say about the theory of value. It should be noted from the outset that the idea or concept of value is usually poorly treated in the overwhelming majority of economics textbooks used in our universities, schools, and institutes. Economics students (and, naturally, their professors) reason and work in terms of "prices." For them, the idea of "value" has metaphysical overtones, more or less "subjective," and of little operational interest to the study of economics. If the reader is curious, try opening one of those tome-de-sacs on introductory economic analysis and see what it says about "value." A dozen or so occurrences, a few more or less ironic comments about the concept's irrelevance, some gross distortions of the ideas of the classics of political economy (from Adam Smith to Karl Marx), and that's all.

Thus, the concept of "value" remains, despite the fact that all taxpayers in virtually every industrialized country (and beyond) around the world pay a tax called VAT or "value added tax." Despite this, the concept of value is typically relegated to the metaphysical curiosities surrounding the hard core of scientific knowledge in economics. If we were to conduct a process of inquiry with all those who propagate and defend this state of affairs in the world of teaching and reflection on the state of the capitalist economy, we would say that they seem afraid to view this world, the capitalist world, through the analytical framework of the set of concepts and theorems developed by Karl Marx. Imagine, the reader, the study and analysis of Biology without resorting to a now-common instrument like the microscope, and you can get an idea of what can be lost in terms of understanding the reality that surrounds us, simply because we set aside certain ways of seeing the world. Well, for Marx, the value of a commodity is determined by the amount of "living labor" plus the amount of "stored labor" (or labor derived from the previous labor in the form of machines and materials) consumed in its production. This value always ends up being measured by the social validation that is given, whether of "living" labor or of "stored" labor, which was expended in the expectation of being sold. In other words, "value" always ends up being measured in "prices." In other words, in a way, it is society itself that ends up carrying out the infamous "transformation of values into prices," through its collective and dynamic assessment—in the market—of what is "socially necessary labor" to (re)produce anything. It is worth noting in this regard that some economists specializing in econometrics have compared the market system to a kind of computer system that seeks "à tâtonnements" (through successive iterations...) the solution to this problem. "Socially necessary labor" is understood by any neighbourhood shopkeeper or factory production engineer: it is simply the labor time required under normal working conditions and according to the prevailing social conditions of technology and labor productivity. From Adam Smith, over 200 years ago, to Frederick Taylor over 100 years ago, this whole "normal working conditions and labor productivity" thing has been studied and widely discussed. But even so, there are still economists who believe otherwise. That it makes no sense to speak of labor as the primary source of commodity value.

A company, any company, must always purchase all sorts of materials that, as stated above, are nothing more than objectifications of "stored labor." Even conventional economists recognize that it is not at this stage of the production process that companies can aspire to make a profit. It is one of the fundamental postulates found in every economic analysis manual: "in perfect competition, economic profit is zero." It is important to highlight here, especially because the cases are well-known and widely publicized, that there are many situations in which the "heads of purchasing" of large companies are materially incentivized to obtain ever lower prices from their suppliers. Any argument that arises from this is unfounded. This is because if all "heads of purchasing" are equally effective—the so-called theoretical model of perfect competition—then we will always end up in a situation where upstream suppliers not only cannot lower their own prices any further, but will have to charge equivalent prices to all their customer companies. Therefore, let's assume here that it's reasonable to assert that—ultimately—a company can't aspire to profit from "stored labor." This leaves what's left is so-called "living labor" (the same as the "added value" of the ICMS tax). This "living labor" has the unique and very human characteristic of being "profoundly elastic." This means that people—humans—are capable of producing (transforming Nature) more than they consume to stay alive, well, and raise a family. On the other hand, any and all business leaders involved in the management of so-called "human resources" understand the material, concrete, and tangible value of a motivated workforce, in contrast to the (negative) value of an unmotivated, hostile workforce, even prepared to boycott, even if hidden or silent. But while it's clear that a committed workforce can produce much more than an unmotivated workforce, that's not even what Marx was talking about when he spoke of the creation of "surplus value." Once again, under the general average conditions prevailing in capitalist society at a given stage of its continuous evolution, there will always be a difference between, on the one hand, the "socially necessary labor" required to maintain society as it was, and, on the other hand, the "surplus labor" that will allow that society to accumulate and grow. This, of course, provided that the product of this "surplus labor" is reinvested and not entirely spent on ostentatious consumption.

It is this "surplus labor" that generates "surplus value" that in its turn is the source of "profit" and gives rise to the idea of "labor exploitation”. In a way, just as the peasant exploited the land, so the industrial entrepreneur exploits labor. In the discussion of the "problem of transforming value into prices," the profit rate is considered the ratio between "surplus value" and "total capital invested." In the entrepreneur's accounts, before the investment is made or at the beginning of the annual production cycle, for example, or in the so-called budget plan, this is, as is evident, a potential (systemic) profit rate. By the way, and in a word, it should be added that the ratio between, on the one hand, the "surplus value (of labor)" and, on the other, the "value of (labor) socially necessary for the (re)production of labor power" is in turn called the "surplus value rate." Something more commonly referred to as the "exploitation rate".

 There are thus good reasons to believe that when it comes to science of economic analysis, all of us, citizens with a minimal interest in the affairs of the world, as well as, and especially, those who don't even care much about it, are all lulled into a gigantic ideological deception, very well-constructed and managed, with multiple and diverse dimensions. From preconceived notions like "immigrants are taking jobs from national workers" to the very common idea that unemployment is the fault of very high wage costs, there's a bit of everything. On the other hand, and to further compound the conceptual confusion that the smartest people thrive on, we have the definition of the cynic as someone who knows the price of everything and the value of nothing. This is how what should probably be the most important and central issue in teaching, analysis, and research in economics  - the idea that most directly affects the lives of all of us collectively and each of us individually - this basic and elementary notion of "value" - is, more often than not, simply ostracized, vilified, distorted, and dismissed as irrelevant or even potentially pernicious and subversive. Who knows what conclusions students around the world would reach if they were to perceive the workings of the capitalist system differently.

The great difference, the fundamental fault line that divides economic analysts and thinkers, lies precisely in the way some approach this fundamental concept of economic science: value. Both Adam Smith and Karl Marx, having also studied classical Greek thought, point out that Aristotle had already outlined an analysis of the value of things and the emergence of a universal means of measurement and exchange. In more recent times, at the dawn of the Renaissance, we find Saint Antoninus, Bishop of Florence who lived between 1384 and 1459, known for his works on value, production, and distribution of wealth. What must be emphasized is the predominance of the concept of value, a predominance that persists until the classics of the 18th and 19th centuries. Without delving into spurious conspiracy theories here, it is worth noting the coincidence that it was precisely following the detailed explanation of the workings of the capitalist system, based on a specific theory of value, that an alternative explanation emerged, one that has diligently sought to consign the concept of value to the dustbin of the history of ideas. However, as is natural and because there is no conspiracy theory here, the fact that the aforementioned detailed explanation of the workings of the capitalist system leads to consequences already in the realm of social engineering that were of little interest to some social classes certainly has nothing to do with the emergence of an alternative explanation and the attempt to forget the other. For many authors who have participated in the debate, the "transformation problem" seems to consist of finding a kind of general rule, an algorithm or set of equations that allows for the transformation of the ratios between, on the one hand, the amounts of living labor and the amounts of capital, embodied in the various commodities, and, on the other, their respective relative prices.

It is a futile and irrelevant exercise for an explanatory theory of the functioning of the truly existing capitalist economy. But despite being a futile and irrelevant exercise, it has served to fuel an extensive and prolonged debate surrounding the very original validity of Marx's entire labor theory of value and, consequently, his entire theory of the functioning of the capitalist system. We say that this is a futile and irrelevant exercise, insofar as it is, mutatis mutandis, equivalent to trying to find some algorithm or set of equations that would allow us to determine, at any given moment, the intensity of rainfall in any given location, as well as the average size of the raindrops, their respective falling speed, and their angle of approach to the ground surface. Taking into account the very slope of the soil... As if all of this were crucially important for determining the next wine harvest, considering the impact of rain on the grapes on the vines... We said above that the overwhelming majority of studies on the capitalist economy are conducted with reference to a basic and fundamental concept: price. It is in relation to price that interesting, useful, and necessary things are studied, such as supply and demand curves and the constant search for equilibrium in various markets. The idea of price is as common and normal to economists as the ideas of atoms and molecules are to the physicists and chemists of this world. There's no way around it; economists think of "prices," not "values." "Values" will be things that belong to the world of ethics and culture, or at most to sociology, but strictly speaking, they will have very little or nothing to do with the scientific study of economics. This is the unofficial position of economics education, and the matter is closed. Now it turns out that all the authors of Classical Economics, from Adam Smith, the "patron saint" of our conventional economists worldwide, to Karl Marx, a sort of cursed and ominous prophet of the end of capitalism, all thought and reflected on the capitalist world, then in full ascendance, in terms of "value." Thus, and in this context, the issue or problem of how "values" (of things) would be transformed into "prices" arose.

However, for many good people—and as always, in these matters, there are people of all kinds—the infamous "problem" of the transformation (of values into prices) constitutes nothing more nor less than the Achilles' heel of Karl Marx's entire work. It is like the "feet of clay" of an intellectual giant, to whom even some adversaries allow themselves the generous luxury of paying homage despite everything. In any case, in fact, and as Ernest Mandel points out, "from Böhm-Bawerk writing a century ago to the recent contributions of Sraffa (1960) and Steedman (1977), the way Marx dealt with the transformation of values into 'prices of production' in Volume III of Capital has been considered by many of his critics as the main problem of his 'system,' as well as constituting a reason to reject the labor theory of value altogether." As will become evident, if this is the central question of Marx's economic analysis, then if we demonstrate «by “a”, plus “b”»  that Marx was wrong on this point, then everything else in his work goes down the drain, into the dustbin of ideas, or, at most, comes to be seen as a mere and unnecessary deviation from the classical thought of David Ricardo. As a careful reading of literature aimed at the general public, particularly supposedly economic and management magazines, reveals that it has already been demonstrated «by “a´” plus “b”» that Marx was indeed wrong. In the same way that some more playful math students demonstrate that «one equals two». It's simple, and in running text, it goes like this: «one plus infinity equals infinity; two plus infinity equals infinity; then we have that infinity equals infinity; then infinity intersects with infinity, so we have that one equals two».

 

2. A Brief History of a Debate Made of Ambiguities

As the story goes, when, after the death of his friend Karl Marx, Engels published Volume II of «Capital», he challenged the economists of his time to try to "guess" how Marx explained  - in the third volume that he, Engels, was then preparing  - the transformation of "values" into "prices."

 It's important to remember that throughout the first volume of «Capital», Marx had consistently reasoned and presented his thinking in terms of "values," which would seem to underlie the pragmatic reality of everyday business, but which would be as if invisible, even to a more careful observation limited to the surface of things. Naturally, people conduct their business in terms of prices, even though they may be (and usually are...) always thinking in terms of values. We're all familiar with expressions like "this is worth more than..." or "this isn't worth that"... According to the Labor Theory of Value and its corresponding "law of value," the only original source of capitalist profit is the surplus product generated in the production process. This "capitalist profit" is, in turn, the source from which subspecies or subcategories of profit arise, such as commercial profit, interest, property and monopoly rents, taxes, etc. On the other hand, and this is the crucial point, this surplus product has its sole and exclusive source or origin in human labor. Machines only "transfer" their own value. Only people create new value (the so-called value-added VAT can be a good practical illustration of this phenomenon...). Also according to the Labor Theory of Value and its corresponding "law of value," the various capitals invested in different sectors of activity should give rise to different rates of profit, as they all have different organic compositions. In other words, all capitals are different from one another in their respective proportions of "constant capital" (machines, energy, buildings, and materials used) and "variable capital" (human labor). But it turns out that in the real world of capitalist enterprises, the process of competition leads to a permanent, tendential equalization of profit rates. So, how can this contradiction be explained? On the one hand, the different organic compositions of each capital should give rise to different profit rates. On the other hand, observed reality shows us that profit rates are all tendentially equal. For Bohm-Bawerk (and all who followed), this contradiction would be the irrefutable and definitive proof that Karl Marx's entire theory was simply wrong.

Almost immediately after the release of Volume III, apparently eagerly awaited by most economists of its time, several works appeared, two of which marked the controversy that followed for decades. These were "Karl Marx and the Closure of His System," by the Austrian economist Eugen von Bohm-Bawerk, published in 1896, and «On the Correction of Marx's Fundamental Theoretical Construction in the Third Volume of Capital», published in 1907 by Ladislaus von Bortkiewicz, a Russian economist and statistician of Polish descent.

In response to this challenge, the first author to believe he had discovered a fundamental error in Marx's work, precisely on this crucial issue of the transformation of so-called "embodied values" into "prices of production," was Eugen von Böhm-Bawerk, an economist of the neoclassical school (today better known by its political expression, neoliberalism). In the aforementioned essay «Karl Marx and the Closure of His System», Bohm-Bawerk accused Marx of logical inconsistency.

For this critic, it made no sense for Marx to have written thousands of pages constantly talking about "values," only to now explain the functioning of the capitalist system based on the concept of "prices." In the typical non-dialectical dichotomy, one either speaks of one set of referents or another set of alternative referents. For proponents of dichotomous thinking, one cannot mix "apples" with "apples," even if one may eventually transform into the other. The question of one "set of referents" transforming, with the evolution that may be inherent to them, into another "set of referents" seems not to be on the horizon of their ideas. And yet, as the Poet[1] would say, "the whole world is composed of change, always taking on new qualities..." Underlying Bohm-Bawerk's critique is a static view of the world, when every vision and explanation that Karl Marx offers us about the functioning of the capitalist system, is based on the dynamics inherent in living things and in constant transformation. It would seem, therefore, that Bohm-Bawerk was simply missing the mark. Or, in more mundane terms, one author (Marx) was talking about "garlic" and another author (Bohm-Bawerk) responded with "oak galls[2]".

Be that as it may, this "conclusive" and "definitive" critique proposed to close the matter, and the argument of logical incoherence, formulated by Bohm-Bawerk, is still used today by mainstream economists (the so-called neoclassicals) whenever it is necessary to dismiss the entirety of Marx's ideas as incorrect from a scientific standpoint and irrelevant from a political perspective.

Attention should be drawn, here and now, to two or three fundamental aspects of this entire issue. First, it is necessary to point out a possibly honest (or not malicious) distortion of Marx's thought. To say of Marx, for example, that he was trying to solve a problem of transforming one system of measuring value (units of labor time) into another system of measuring value (the prevailing prices in any given market). As if both systems of measurement were commensurable, somewhat like converting centimetres into inches or even converting gas tension into available energy—all physical quantities with different configurations. It is a case of saying, nothing could be further from the truth. For Marx, labor (time) is like an immanent characteristic that, being embedded in, and part of, everything and anything that can be bought and sold, ultimately determines its value. Moreover, this value manifests itself, in the pockets and wallets of each of us, in the form of purchase and sale "prices." We are therefore faced with three distinct analytical categories: "labor time," "value," and "price."

For Marx, the idea of a "transformation of values into prices" (or vice versa...) in the sense of two distinct, albeit parallel, measurement systems would be simply absurd precisely to the extent that for him prices are merely the external and visible manifestation of something that, through human labor, has come to permeate the goods and services actually traded in markets.

But if this is so, then why did Marx even pose the problem of any transformation, and why did his friend and editor Friedrich Engels issue the aforementioned challenge? The explanation may seem complicated, but it is not. Marx was simply trying to explain (and resolve) an apparent paradox of David Ricardo's labor theory of value. In other words, Marx was explaining where he, Ricardo, had erred in his (Ricardo's) version of the labor theory of value. In other words, the only "problem of transformation" was, strictly speaking, a Ricardo problem, not a Marx problem.

But what, then, was Ricardo's problem? Ricardo's problem consisted of trying to explain how, in the capitalist system, there would be a tendency toward equalization of profit rates, an equality that should ultimately prevail, in a regime of free competition among all economic agents. On the other hand, if in various and distinct sectors of activity there were  - and there always are - different degrees or indices of capital intensity relative to labor, and therefore - or even - different rates of exploitation, how could all of this ever result in a more or less (or tendentially) uniform rate of profit across all sectors of activity? If this were not the case, then one would have to admit that, beyond labor (living, current, etc.), there would be some other source of value that could explain the different profit rates across sectors. In other words, and to conclude this question, if one could not explain the «transformation»" (of “values” into “prices”), one would have to conclude that the labor theory of value (Ricardian or Marxian, it doesn't matter...) had no explanatory value. Hence the claim that "this" would be the Achilles' heel of Marx's entire theory.

Another issue worth mentioning is the objective Marx proposed with his elaboration or discussion of the aforementioned "(Ricardian) problem of transformation"... - the division of the spoils. In this regard, it should be noted that while Volume I of Capital is fundamentally a discussion of the societal process of the system of value (and surplus value) production, Volume III of Karl Marx's opus magna is fundamentally devoted to the "division of the spoils" (as it is often said) of the surplus value created in capitalist society. We say "division of the spoils" because Volume III contains an explanation of how the various social groups involved in the production process, namely industrial capitalists, bankers, and landowners, appropriate the surplus value produced in the meantime. This entire process of "sharing the spoils" follows a fundamental rule expressed through the aforementioned (tendential) equalization of the rate of profit. It has been written, somewhat sarcastically, that while the banner or slogan of socialism would be something like "from each according to his ability to each according to his contributions," the banner or slogan of capitalism would be something like «from each capitalist according to his capacity to exploit living labor, to each capitalist according to his control of inherited capital.»

Another aspect still to be considered is the question of capital movements or flows between different sectors of activity in search of more attractive applications or, in other words, those with a "higher rate of profit." Marx's critics seem to believe that any movement of capital from one sector of activity to another occurs instantaneously, establishing an average profit rate that is the same everywhere. Interestingly, the examples used to prove Marx wrong - and that his labor theory of value is therefore irrelevant—are always examples that demonstrate significant differences in profit rates, both due to and due to postulated and distinct organic compositions of capital and, consequently, different rates of exploitation of the labor factor. The problem with this approach is that the reality of actually existing capitalist society is far more complex than these examples should represent. Therefore, the differences between the different sectors of activity do not manifest themselves abruptly and radically. Whether regarding the organic compositions of capital prevailing in each sector of activity or the corresponding operating rates, what we have in practical economic life is a continuum of rates that vary over the years, whether among the various sectors of activity or among the various companies within each of the distinct sectors. When attention is sometimes drawn to a possible contrast between a steel mill and a hypermarket, with regard to their respective organic compositions of capital, this call is made merely for the purpose of illustrating the issue at hand. Nothing guarantees that there cannot be a hypermarket whose organic composition of capital is not similar to that of a given steel mill. In other words, the multiple and diverse activities of production of goods and services end up having organic compositions of capital that are not as disparate from one another as it may seem when discussing the infamous problem of transformation.

On the other hand, and in any case, the transition or shift from one line of business to another that is "more profitable" is not, in itself, a cost-free process. The idea or concept of "transaction costs" has long been part of economics and management textbooks and has even reached popular literature and magazines. Today, every "square-minded person" in the executive suite of any medium-sized or large company talks about "transaction costs," if only to explain to us why they want to charge consumers certain expenses that are supposed to be part of their operating costs. Transposing the idea underlying the concept of "transaction costs" to a concept of "transition costs," any capitalist company cannot change its activity "from one day to the next" without first carefully calculating all the costs involved, simply because another particular activity is presenting higher, or much higher, profit rates. This is the concrete reality of the business world in the capitalist system, and it is this world that, apparently, Karl Marx explains better than many of our conventional economists. However, the critical response to Engels's challenge took on new dimensions when, in 1906/07, the economist Ladislau Bortkiewicz published his work on the relationship between values and prices in the Marxian system. In this work, he recognized that Marx's proposed solution to explain the infamous "transformation" was incomplete and proposed his own. Bortkiewicz's proposed solution, however, also represented a return to David Ricardo's theses regarding the determination of value. In other words, Bortkiewicz's proposed solution ignored Marx's theoretical innovations on "value" and its determination. And what innovations had these been?

 

Until the synthesis of classical political economy, developed by John Stuart Mill in 1848, all thinkers addressing these problems more or less agreed that the source of commodity value would always be human labor. This was the so-called "labor theory of value." This remained to be explained, even to escape the trap of circular reasoning or, in more straightforward terms, the chicken-and-egg dilemma. Indeed, if it was human labor that determined value, it remained to explain how the value of labor was determined. Marx began the resolution of the problem by establishing a crucial, basic, and fundamental difference between, on the one hand, "labor" (that which happens, something that results from human effort), and, on the other hand, "labor power" (the potential capacity to do things, to work, or to produce results). In a way, it's a distinction similar to that which might be said to exist between a battery (the "labor power") and electricity (the "labor"). It's that simple. Considering the radical nature of this distinction, affirmed by some and, more often than not, rejected and ignored by others, between "values" and "prices," as well as its relevance for a better understanding of the functioning of the capitalist system, we might be tempted to conclude that, after all, perhaps we all live, all of us without exception, in an endless forest of deception or, if you prefer, in a gigantic deception in which we are lulled. While conventional economists, from which our ministers of economy and finance almost always emerge, here and in all countries, of the OECD, teach us that "value" is a metaphysical concept with no operational relevance in the world of objective things, tax inspectors and tax collectors continue, gradually and without any connection to these philosophical questions, to levy taxes on "value added." For it is precisely this fundamental distinction that continues to be rejected by conventional economists of various persuasions, or even by the so-called neo-Ricardians. And yet it never occurs to engineers and electricians, or even to any consumer of home appliances, for that matter, not to make this kind of distinction between "battery" and "electricity." It also happens that in the first volume of Capital, Marx had outlined his perspective on how the capitalist system works, from a global, theoretical, and abstract perspective. And above all, considering the "production process" phase. How a capitalist system would or would not function, regardless of whether it began in England in the mid-to-late 18th century or is currently operating in China at the beginning of the 21st century. Capitalism itself, in its intrinsic logic and underlying the palpable reality of every day and of all of us.

Already in Volume III, published by his friend Frederick Engels after Marx's death, the analysis of the system's functioning was relatively limited to the observable surface of "prices." Scholars of these matters then say that, whereas in Volume I, Marx was discussing the "value system," in Volume III, Marx was turned to discussing the "price system”.  Some authors speak earlier of "space of values" and "space of prices," somewhat as if the "mathematical space of values" were – so to speak  - underlying the "mathematical space of prices." On the other hand, in the aforementioned Volume I, Karl Marx set out to explain the source or origin of profit, an explanation he provided through the concepts of exploitation and surplus value ("mehrwert," commonly translated as "surplus" or "surplus value"). Whereas in Volume III, Marx set out to explain how the aggregate profit of the entire system ended up being distributed, or shared, among the various categories of social actors entitled to it. A conventional Marxist would simply say "the distribution of profits among the various groups of capitalists."

 

3. The Problem's Dormancy and Slow Reawakening

After the publication of Bohm-Bawerk's work and the responses, one by Bortkiewicz proposing a ("dualist") solution and another by Rudolf Hilferding severely criticizing Bohm-Bawerk's failure to understand the fundamental problem, the "transformation problem" seemed to have dropped into hibernation. In the case of Marxist currents, there was, on the one hand, its (more or less dogmatic) "operationalization" with the attempt to "build socialism in one country" and, on the other, a general decline in the amount of its study in so-called Western countries. This is a good example of how, also (and above all) in the social sciences, their development depends on the historical circumstances in which they occur. With the end of World War II and a relative calm in ideological tensions and the rise of the intervening state in economic development, the renewed study of Marx's ideas became "politically acceptable" in Western countries as well. Thus, in 1948, J. Winternitz published an article in "The Economic Journal" with the significant title "Values and Prices: A Solution to the So-Called Transformation Problem." Soon after, Paul Sweezy, an American economist known as a Marxist and founder of the "Monthly Review," presented as "editor," analyst, and part-translator a book containing the three works that originated the debate: "Karl Marx and the Close of his System" by Eugene Böhm-Bawerk; "Böhm-Bawerk's Criticism of Marx" by Rudolf Hilferding; and "On the Correction of Marx's Fundamental Theoretical Construction in the Third Volume of Capital" by Ladislaus von Bortkiewicz. In 1942, he had already published "The Theory of Capitalist Development," a book in which he summarized Marx's ideas, which he helped disseminate among North American scholars. In that same book, he explicitly referred to the "problem of transformation."

However, the renewed interest among scholars in the "problem" and the search for a possible "solution" took time. It was only in 1960 that Piero Sraffa's book, «Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory», appeared, specifically addressing this issue. This book revisits and updates Bortkiewicz's approach within the framework of a linear production model. As the title of his book indicates, the Sraffian interpretation means, first, that the fundamental data of Marx's theory should be assumed and expressed in terms of physical quantities, whether with regard to the technical coefficients of production or with regard to "real wages," seen as a kind of "shopping basket" of consumer goods for the working classes. Second, that the rate of profit should be determined simultaneously with the determination of the prices of production, and, finally, that both the rate of profit and the prices of production are derived from the physical quantities of the commodities produced. Thus, we have the birth of so-called "physicalism" in the approach to the "problem of transformation." In other words, not only was the interpretation proposed by Bortkiewicz sound and recommended, but it also gained new adherents and broadened the field of possible solutions to a problem originally raised by David Ricardo back in 1817. This approach has since become the best-known "interpretation" of the problem. The names most commonly associated with this current today are Ronald Meek, Maurice Dobb, Michio Morishima, and Ian Steedman. However, the authors of the mainstream of conventional economic analysis - the school of utilitarian marginalism—were (as they seem to remain today) relatively oblivious to this issue. Bohm-Bawerk had already demonstrated that Marx was wrong, and the matter was therefore closed. Even so, an author with the academic stature of Paul Samuelson decided to take the plunge and, in 1971, published in the Journal of Economic Literature an article that has gone down in history: «Understanding the Marxian Notion of Exploitation: A Summary of the So-Called Transformation Problem Between Marxian Values and Competitive Prices.»

In it, he concluded, among other things, that the problem would have no solution - perhaps it would be more appropriate to say that the "problem made no sense" - for the simple reason that it involved two incompatible and incommensurable approaches: the marginalist approach to "prices" and the (for Samuelson) Ricardian-Marxist approach to "values." With a strong dose of irony or sarcasm, he then suggests his infamous eraser algorithm:

«Consider the two mutually exclusive alternatives of 'values' and 'prices'. Write one. Then perform the transformation using an eraser, erasing what you wrote. Then write the other. Voilà! You have just completed your transformation algorithm».

From the perspective of conventional economists, the matter was thus closed (and for them, "once and for all"). At the turn of the 1960s and 1970s, the period of expansion of Western economies, once called the "glorious thirty years" of post-war reconstruction, came to an end. The end of this period was heralded by the occurrence of several phenomena, such as the end of the gold standard (strictly speaking, the guaranteed conversion of dollars into gold), decreed by President Nixon in August 1971, or the occurrence of the first oil crisis in October 1973. The ensuing crisis of relative stagnation, mitigated though it was by the existence of the welfare state in almost all the most developed countries, revived interest in the work of Karl Marx in many academic circles, and elsewhere. This interest was naturally motivated by the search for coherent and logical explanations for the crisis. Around the same time, works were even published announcing the crisis and even the end of conventional economics, as it proved incapable of explaining the crisis. The reaction of the defenders of the established order was immediate, and since there was no way to achieve the desired "dynamic equilibrium" in which everyone would live happily ever after, the blame for the crisis was placed on state intervention. Thus was born the neoliberal monetarism of Ronald Reagan and Margaret Thatcher.

Returning to what most directly concerns us here—the "problem" of transformation—it was in the early 1980s that the first writings appeared questioning the "interpretation" of the problem that had prevailed until then: that of Bortkiewicz, later made known by Paul Sweezy and further elaborated by Piero Sraffa in the 1960s. Between 1980 and 1983, separately and independently, Gérard Duménil and Alain Liepitz in France and Duncan Foley in the United States published four essays that relaunched the debate—this time, continuing to this day. The articles in question are, respectively, "De la Valeur aux Prix de Production Une Reinterpretation de la Transformation" (1980 in the journal Economica) and "Beyond the Transformation Riddle: A Labor Theory of Value" (1983 in the journal Science and Society) by Gérard Duménil, "The ‘So-Called Transformation Problem’ Revisited" (1982 in the Journal of Economic Theory) by Alain Lipietz, and "The Value of Money, the Value of Labor Power, and the Marxian Transformation Problem" (1982 in the "Review of Radical Political Economy") by Duncan Foley. These authors are joined by a myriad of other researchers, each proposing a new perspective on the various variables involved in the problem: the rate of profit, the rate of exploitation, the organic composition of capital, as well as the various options regarding the technical and organic compositions of capital, the consideration (or not) of different rates of exploitation, and the consideration (or not) of the invariance of a particular variable, particularly the rate of profit. Significantly, the "transformation problem" also becomes the subject of master's and doctoral theses and dissertations in socioeconomic sciences.

The works of Duménil, Liepitz, and Foley thus gave rise to a current that came to be known as the "new solution," sometimes also referred to in the literature as the "Duménil-Foley-Lipietz" solution. With varying degrees of nuance and some differences that are sometimes more inflated than real, all of these authors continue to claim the Marxist legacy in their interpretation of how the capitalist economy works. But they all seem to "suffer from a common problem": interpreting Marx to the point of distorting him. This, at least, is the criticism levelled against them by another current that has since emerged, which we might call "renewed orthodox Marxism." The term "renewed orthodox Marxism" is used to describe the fact that the most well-known authors of this current claim to interpret Karl Marx's work according to the interpretation of the classics of Marxism from a century ago, and in particular, in the case of the problem of transformation, Rudolf Hilferding's interpretation and his critique of Bohm-Bawerk's analysis and interpretation. In other words, while the aforementioned "new interpretation" considers that Marx actually proposed the existence of two distinct, albeit parallel, accounting systems—one based on "values" and the other on "prices," this other current considers that the problem of transformation, strictly speaking, does not even arise. Since prices are nothing more than the visible expression of a substance that is immanent to all commodities (labor value), the problem does not arise of finding a general rule of conversion or "transformation," but rather the problem of how the form of "visible expression" of values (prices) affects the distribution among the various groups of capitalists of the amount of the total global surplus, from which profits, rents, and interest derive... This current has since come to be known as the "TSSI approach" (Temporal Single-System Interpretation). It is called "temporal" insofar as this approach views the problem and content of value (and its expression in the form of prices) as evolving over time, in particular between the moment of the "purchase of the means of production," the actual manufacture, and their subsequent sale, so that capital returns to its initial form of "money capital."

It is called a "singular system" because, unlike the approach of the aforementioned "new solution," it considers a single "accounting" system: that of prices, with value "merely" its underlying substance and labor its immanent measure. The authors who, among others, have stood out most in this current and who, in fact, seem to have "invented" the term, are Guglielmo Carchedi, Alan Freeman, Andrew Kliman, Eduardo Maldonado-Filho, and Alejandro Ramos Martinez. Naturally, various works have since emerged that seek to bridge or establish a bridge, if not a synthesis, between these two approaches. The fundamental difference, however, seems to be the contrast (radical, crucial...) between a dynamic approach and a static one.

 

4. How Things Stand

So we have that "mainline" economics (the kind routinely studied in schools) continues to blatantly ignore—or, strictly speaking, "overlook"—this "problem." For their part, the neo-Ricardian and "Marxian" currents continue to diligently try to solve the (Ricardian) "problem" of the transformation of values into prices within a framework of static general equilibrium. Finally, with regard to authors who claim to be original Marxists (albeit occasionally revised and "updated"), they also diligently try to explain to others how, in fact, there is no problem of transformation in the original Marxist analysis and how the theory of value continues to be not only relevant but, above all, fundamental, for understanding and explaining how the capitalist system works. The "transformation problem" is typically presented in the form of tables and sets of equations that are supposed to represent the relationships between various quantities such as capital and its composition, whether of firms or of sectors of activity, the surplus values resulting from productive activities, the amortization values of the various capitals, the resulting values of the goods produced, the cost of production of these same goods, the rates of exploitation (if they are assumed to be distinct), the rates of profit, and the deviations between "prices" and "values." In some interpretations, these deviations are supposed to occur only at the detailed or individual level, since at the global level of the system there will be equality "by definition" (the total surplus value produced will necessarily equal the total profit available for distribution).

Judging by the tenor of some criticisms found in the literature, it's reasonable to get the feeling that reading Marx's examples is likely to lead some readers to believe that in the real world of the economy of his time (or today, 2007), there would be a sharp distinction in the organic composition of the various sectors of activity, inspiring the idea that only foolish capitalists would venture to invest in the least profitable sectors or branches of activity. In the real world we all live in, industrial entrepreneurs are already there, in the sectors they currently operate in. While it's true that they seek to leave, whenever possible, for more profitable activities, it's also true that this exit has costs, with or without labor legislation, by the way. It is therefore for this reason alone—merely illustrative—that we present a table based on Marx's tables, with no intention of correcting anything in the original tables. The idea is simply to convey an image of greater variety and less discontinuity between the different branches of activity, with regard to the respective organic compositions of the capital invested in the different branches of activity.

The simplifying assumptions of a uniform surplus value rate of 100% are considered, that is, uniformity in factor productivity is assumed. To calculate the column for the selling price of goods, it is assumed that each sector applies (because that is what each and every manager is ultimately led to expect...) an average prevailing profit rate, in this example, of 20%.

 

 

 

Table developed from «Capital» Volume 3, Chapter 9 pages 255 and 256

Total Capital

Surplus Value

Rate of Profit

Constant Capital Consumed

Value of Goods


 Cost Price of  Goods

 

Sales Price of  Goods

 

Deviations Prices Values

80c + 20v

20

20%

50

90

70

90

0

78c + 22v

22

22%

45

89

67

87

- 2

82 + 18v

18

18%

35

71

53

73

+ 2

76c + 24v

24

24%

30

78

54

74

- 4

84c + 16v

16

16%

40

72

56

76

+ 4

74c + 26v

26

26%

50

102

76

96

- 6

86c + 14v

14

14%

40

68

54

74

+ 6

72c + 28v

28

28%

45

101

73

93

- 8

88c + 12v

12

12%

25

49

37

57

+ 8

70c + 30v

30

30%

30

90

60

80

- 10

90c + 10v

10

10%

20

40

30

50

+ 10

1.100

220

20%

410

850

630

850

0

 

What those tables and respective equations implicitly tell us is that if the world of companies across the planet were rigorously uniform, particularly with regard to the proportions of expenses or expenditures on the various fractions of capital, namely from the perspective of "constant" and "variable" capital, or even from the perspective of "fixed" and "circulating" capital, if all companies in the world, again, were rigorously uniform in this regard, as well as (by the way...) also equivalent in the effectiveness and efficiency of the use of all their resources, then the profit rate would be exactly the same everywhere. The most basic common sense tells us that this is not the case. That, as the Poet said, the whole world is made of change, "always gaining new qualities"  and always in motion. The most common, current, and elementary observation also tells us that, since the world of business is multiple, varied, and complex, any effort to understand its workings must be naturally reductionist. It is therefore necessary to reduce all that variety and complexity to a feasible number of interdependent variables. In the case of the problem of transformation, this complexity is typically reduced to a small number of variables: the value of the wealth produced, the social validation of that wealth in the form of market prices, the relationship between the wealth produced and the resources used in that production, and the social system of appropriation, whether of previously existing wealth or of the surplus or new wealth created from the labor of active generations.

 

 

5. The Problem of Measurement

In his major work - «Capital» - Marx necessarily had to present numerous examples of his observation and reflection on the concrete world. This should not prevent us from understanding that Marx's reflection was also necessarily in terms of abstraction. Underlying the question or problem of the "transformation" of values into prices is another problem: that of measurement. More specifically, that of the measurement of the "value of labor time." Some contemporary authors dismiss the theory of value "for the simple reason" that "value is not amenable to measurement." Others tell us that value was only a relevant analytical category in a historical period in which artisanal production predominated. These same authors even suggest that Marx himself recognized that, with the complexity of the capitalist production system, it would no longer be possible to "evaluate" or "measure" value, as had been possible when each artisan could, with relative ease, estimate how much it would cost to produce the articles offered in exchange. In other words, for some authors, the complexity of measurement makes it simply impossible or even useless. Here we are faced with a confusion between two distinct conceptual levels: one, the idea of developing any measurement criterion and its operationalization; the other, its practical application. Physicists and engineers have always struggled with this problem and have been gradually resolving it. For some Marxist authors, the question doesn't even strictly arise, since value, being an "immanent" measure of labor, is, by definition, not susceptible to quantitative measurement. However, on the one hand, and as Hilferding already pointed out in his critique of Bohm-Bawerk, Marx's labor theory of value allows us to recognize the principles according to which social processes lead to the determination of an average capacity for labor productivity. In other words, they lead to the measurement of value being theoretically possible. Hilferding already accused Bohm-Bawerk of confusing theoretical or conceptual possibility with possible practical feasibility,  in his critique of Marx.

On the other hand, a pragmatic attempt to assess the "value of things," and in particular, manufacturing processes, an attempt routinely carried out by hundreds of engineers around the world, is one thing; the effective objectification of these "values" into "market prices" is another. But, in any case, and for the sake of argument, let us briefly examine the relative complexity of the measurement process in the social sciences. Imagine that someone told you that it was impossible to accurately calculate the average height of adult Portuguese men. You would probably be sceptical about this impossibility. At first, the reader might think, "just set a date, measure the heights of all Portuguese men over the age of 16 (for example), add up all the heights, and divide by the number of men whose heights were measured. It seems simple. But, in fact, to be able to make statements of this nature, it would be necessary to indicate things like the date the data was collected, the size of the population that was measured, and how that population was defined. For example, "who are the Portuguese adults"... (everyone with a Portuguese passport?... Only those living in Portugal?... How was it determined who was measured, how, and when...). On the other hand, since the population of any country is a reality in constant flux, how is the subcategory "adult" defined?... Is the height of all "adults" measured or just that of a sample considered representative?... And how is this "representativeness" determined? This is how we all accept, with a certain naturalness, statements like "on average the Swedes are taller than the Portuguese". Or they were taller than they will be now (...) because in the meantime, over the last few decades and as a result of better diets and healthier lifestyles, it seems reasonably proven that there has been an increase in the average height of Portuguese adult men.

Based on all these questions, things that statisticians deal with routinely, a statement like "it will be impossible to accurately calculate the average height of Portuguese adult men" might seem reasonable. Indeed, it will. But in these social sciences - and economic analysis is a social science (it's always worth emphasizing this - it might be a good idea to adopt an aphorism from Keynes, generally considered (by many good people) to be the greatest economist of the 20th century, who said something like "I'd rather be vaguely right than exactly wrong." Indeed, one of the basic problems in the social sciences is that of measurement. Among other considerations, for example, "how to measure" and "measure what." But it's not only in the social sciences that the problem of measurement arises. This problem also exists in the physical sciences, and there is even a technical discipline (metrology) that aims to study the diverse and multiple measurement techniques and the problems of the varying degrees of accuracy that one seeks to achieve with the measurement process (of whatever it may be). On the other hand, it should be noted that the very idea of "average" is an abstraction. For example, when one says that the average height of Portuguese adults is 172 cm, one is not thinking of any specific citizen. This number may indeed be the exact height of a large number of Portuguese adult men, but it may also not be. In reality, that 172 cm average could correspond to a concrete reality in which 25% of adult men were all 170 cm tall, another 25% were 171 cm, the next 25% were 173 cm, and the remaining 25% were 174 cm. The final average was 172 cm...

The important point to emphasize here is that the difficulty or enormous complexity of any measurement process cannot (should not) be used as a logical or scientific argument to simply dismiss the very idea of measurement. One might comment, "Here we are, we are leading to a kind of Heisenberg Uncertainty Principle in the field of social sciences." But, just as the aforementioned "Principle" does not prevent or disqualify the countless processes of measuring physical reality common to all engineering disciplines and more, it should also not prevent or disqualify the multiple measurement processes in social sciences. All of this concerns the logical relationship between the analytical category "values" and the analytical category "prices," and this logical relationship underlies some of the greatest and most forceful criticisms formulated against Marx's analysis of the functioning, or internal logic, of the capitalist system. There are even authors who simply state that "since value cannot be measured, this concept has become irrelevant." As if it ever had been, insofar as, strictly speaking, "it will never have been possible to 'measure value'." In fact, and with regard to the complexity of the process of measuring or evaluating the impact of the law of value on the formation of commodity prices in their respective markets, Marx tells us at a certain point this significant thing: In capitalist production the general law (of value) acts as a prevailing tendency only in a very complicated and approximate way, as a never-calculable average of endless fluctuations." (Marx, 1981, 261)

It should be noted that the expression "very complicated" may suggest that it is something "very vague" or "impossible to calculate." In a way, this is true. It would be a bit like trying to calculate the overall average velocity from the individual average velocities of all molecules and their respective collision points, in any gas in a permanent movement of expansion and contraction, according to changes in ambient temperature. However, none of this prevents physicists from "measuring" all these quantities, probably even taking into account Heisenberg's so-called "Uncertainty Principle." Physicists would never consider discarding the notion of kinetic energy associated with the motion of molecules, simply because of the complexity of the measurement process.

 

6. In Search of the Holy Grail of Equilibrium

Almost all authors consulted on this subject sooner or later end up referring to the problem of equilibrium. Whether it's the equilibrium between Supply and Demand, the equilibrium between Department I (production of production goods or "machines to produce machines") and Department II (production of consumer goods), or even the equilibrium between Savings and Investment. This equilibrium (in its various manifestations) is most often presented as the ideal (or utopian, something that would be good to achieve...) situation toward which the system would permanently tend, constantly "moving" (gropingly, "blindly," in a market economy...), toward this miraculous but never-attainable state. According to conventional criticism, the (Marxist) labor theory of value can only be compatible with the same prevailing profit rate throughout the economy, solely and solely, on the condition that the organic composition of capital is identical or exactly the same in all branches of productive activity. According to this same criticism, the incompatibility of the (Marxist) labor theory of value with an equality in the profit rate across all branches of productive activity could be demonstrated through a numerical example. Consider two commodities that incorporate the same amount of expenditure in "capital" and "labor" and with the same "rate of exploitation of surplus value" (for this case, let's assume 100%) but with different "organic composition of capital." Let us therefore have a commodity that represents 60c + 20v + 20s = 100 and another commodity that represents 20c + 40v + 40s = 100. According to Marx and Engels, these two commodities will exchange according to the relative content of the labor embodied in them. In this case, labor values will tend to be equivalent to each other, also in terms of money, since constant capital, for the purposes of determining the value embodied in commodities, is nothing more than "stored labor."

The problem, then, lies in the fact that the capitalist producing the first commodity would have a profit rate of only 25% (i.e., 20s divided by 60c + 20v), while the capitalist producing the second commodity would have a much higher rate of 66.6% (i.e., 40s divided by 20c + 40v). Obviously, from the perspective of our conventional critics, such a conclusion is far from the condition supposedly prevailing in an economy in competitive equilibrium.

It is worth asking where this so-called "competitive equilibrium" economy will be or will exist, especially since we will always encounter the problem of the methodological approach of "static" and "dynamic." Sometimes, one gets the feeling that some critics seem to confuse a "snapshot" of any reality with a representation of the dynamics inherent to it. The major problem with this type of analysis and critique is that it ignores the dynamic, ever-changing, and never-stabilized nature of the truly existing economy (in the nature of things, as Heraclitus already observed).

 Another aspect to consider is that when this critique is formulated (with examples and citations that Marx himself would have recognized this difficulty), numerical examples are always presented that leave the idea that the real differences in profit rates effectively prevailing in the truly existing economy are of that order of magnitude. Like it or not, subtly, the idea of an alleged absurdity in Marx's analysis may always linger, since it is clear that no pragmatic capitalist would invest in any productive activity that yielded less than half the rate of profit that could be obtained in other activities.

 

Guilherme da Fonseca-Statter

Oeiras, January 2008



[1] A reference to a famous sentence by the Portuese national poet Luís de Camões.

[2] Literal translation from a Portuguese common expression that means, «muddling things together» or «mixing apples with oranges»


No comments:

Post a Comment