A BRIEF PRIMER ON VALUE THEORY, PART 2.2: The Transformation Problem


Two Critiques

Of Equilibrium and Inconsistency

In von Helmholtz’s explication of the first law of thermodynamics, delivered at the Physical Society of Berlin in July of 1847, it is suggested that all energy in the universe is held at a constant level. Energy may change forms, moving from one state to another, with more energy accumulating in one state at time and more in another state at another – but the aggregate amount remains. The introduction of entropy, of course, altered this picture, leading to the scenario we described at the end of the previous post.

Marx’s value theory follows closely in these footsteps. Just as energy, in the framework of the first law of thermodynamics, remains at a cosmological constant, so does the amount of value in the economy. It might asymmetrically exist in different forms, Marx says, but there is an overall consistency when the system is viewed as a totality. This leads Marx to three suppositions concerning the capitalist system:

  • The total amount of value is equal to the total amount of prices
  • The total amount of profit is equal to the total amount of surplus value
  • The total amount of rate of profit in money is equal to the total rate of profit in value

It has been argued that Marx failed in properly demonstrating these conclusions, which arises we look the way the ““the transformation of values into prices of production” is handled. This itself requires just a bit of unpacking, so let us return to the example of our two table-making firms from the previous section. When we left off, Firm 1 had decided to follow in Firm 2’s steps by adopting labor-saving technology. Assuming that these firms are the two major ‘sinks’ for the production of value in this economy, the rate of profit would understandably fall. This falling rate of profit is an example of the average rate of profit. If a series of firms were to multiply (some chair-making firms, perhaps) and employ a large number of out-of-work laborers, we would almost certainly see a reverse on the rate of profit’s fall, and the average rate of profit would be one that is rising. As we’ve seen, this amounts to the moving around of the value in the system, locked into what Gilles Deleuze and Felix Guattari might describe as a “process of becoming”.

So what is the problem?

Within several years of the publishing of the third volume of Capital, Eugen Böhm von Bawerk, a marginalist economist who would bestow much influence on the nascent Austrian School, would attack Marx on the grounds of an inconsistency that arises from this very issue. While remarking that Marx was correct in that “it is quite true that the total price paid for the entire national produce coincides exactly with the total amount of value or labor incorporated in it”, he argued between the first and third volume of Capital two contradictory propositions arose:

  • That commodities sell at their value,
  • That commodities sell at their prices of production

This supposition, however, is not at all reflected in Marx’s own writings:

If prices actually differ from values, we must, first of all, reduce the former to the latter, in other words, treat the difference as accidental in order that the phenomena may be observed in their purity, and our observations not interfered with by disturbing circumstances that have nothing to do with the process in question. We know, moreover, that this reduction is no mere scientific process. The continual oscillations in prices, their rising and falling, compensate each other, and reduce themselves to an average price, which is their hidden regulator. It forms the guiding star of the merchant or the manufacturer in every undertaking that requires time. He knows that when a long period of time is taken, commodities are sold neither over nor under, but at their average price. If therefore he thought about the matter at all, he would formulate the problem of the formation of capital as follows: How can we account for the origin of capital on the supposition that prices are regulated by the average price, i. e., ultimately by the value of the commodities? I say “ultimately,” because average prices do not directly coincide with the values of commodities, as Adam Smith, Ricardo, and others believe. (Marx, Capital, Vol. 1, Chapter 5, note 24; emphasis mine)

In other words, we are back on the terrain of Marx’s attempts to go beyond the Ricardian LTV, which might very well have been the true target of von Bawerk’s attack (for an extensive examination – and rebuttal – on Ricardo, see Carson’s Studies in a Mutualist Political Economy). Otherwise, how could von Bawerk not have reconciled his understanding that ‘total produce’ was equal to ‘total value’ in the economy with the dynamic and evolutionary model that Marx had drawn from the popular sciences of their day? Andrew Kliman deals with von Bawerk’s flawed argument quite quickly, writing that

Although it is “quite true” that total price equals total value, it is also irrelevant, because it has nothing to do with “the exchange relations,” the rates at which goods exchange. Böhm-Bawerk’s point was that Marx tells us that goods A and B together sell for $3, while the question here is instead whether A sells for $2 and B sells for $1, or whether A sells for $1 and B for $2. (Kliman, Reclaiming Marx’s Capital: A Refutation of the Myth of Inconsistency, pg. 145)

Internal Inconsistency, Round 2: Ladislaus Bortkiewicz

The charge of internal inconsistency would be furthered in the early 1900s by the Russian economist and statistician Ladislaus Bortkiewicz, a neoclassicalist with Ricardian leanings. His treatment of the transformation problem would be largely overlooked for some forty years, finally getting recognition when it was released in 1949 in a single volume containing von Bawerk’s Karl Marx and the Close of His System (1896) and Rudolf Hilferding’s response (1904). For Paul Sweezy, a Marxist economist of the Monthly Review School (and the editor of the 1949 compilation), Bortkiewicz’s critique of Marx was not an attempt to shatter the foundations of Marxism (as was von Bawerk’s motiviation), but was actually a bid to rescue Marx by reconciling the reconcilable elements. As he wrote in his introduction to the volume, Bortkiewicz’s analytic starting point was

the flaw in Marx’s method of transforming values into prices of production… Most previous (and, for that matter, subsequent) critics consider the theory of value and surplus value to be the the Achilles’ heel of the Marxian system. Bortkiewcz almost alone regarded it as Marx’s most important contribution. By eliminating relatively superficial errors he hoped to be able to show that the core of the system was sound. (Paul Sweezy, “Editor’s Introduction” in von Bawerk Karl Marx and the Close of His System, pgs. xxix-xxx)

Bortkiewcz argued that when one applied Marx’s arguments to a standard neoclassical input-output table, the mathematical outcome was one that did not reflect the arguments made by Marx in Volume 3 of Capital. In Bortkiewicz’s model, constant and variable capital (measured in their value) flow into the input, and emerge from the output as commodities at the price of production – leading Bortkiewcz to suggest, in good Ricardian fashion, that prices for inputs are bought at the price of production. Yet when he plugged the price of production into the input side, the mathematics fell apart, and the three suppositions about the equalization of value, price, and profit falls apart.

This might strike the reader as odd, as it treats inputs and outputs as something whose prices are determined simultaneously. In other words, Bortkiewicz is suggesting that when the farmer utilizes $100 worth of corn seed, he or she is simultaneously determining $100 worth of corn. But this is not at all how it works in the real world. The farmer enacts labor on the seed corn, and must wait for it to grow; at the same time, the swirling miasmas of market forces and exogenous factors. Two hundred pounds of corn seed might be $150 at the beginning of the planting season, but be $130 or $175 the next. New prices of production are what determine input-costs, not the prices of production in the previous cycle.

This seems logical and sound, but the question remains: does it reflect Marx’s theory?

The Temporal Single System Solution

After Sweezy popularized Bortkiewicz’s essays, the critique became the dominant approach to Marxian economics. While its proponents hailed it as the solution that would save Marxism from the quagmire that marginalism, Austrian school, and neoclassicalism had relegated it to, it also critically undermined Marxism in multiple ways. On one hand, it effectively separated the question of price from the question of value; without the two being tied together, labor lost its centrality in the socialist debate. On the other hand, it also pushed back against notions such as the tendency of the rate of profit to fall: if price and value were separated, so was the binding together of value and rates of accumulation. It was for some of these reasons, perhaps, that the mainstays of Marxian thought – Sweezy’s Monthly Review School, for example – turned towards Keynesianism as a solution to the other problems Marx had identified.

In the 1980s a pushback against the Bortkiewiczian perspective arose in the form of the temporal single system solution (TSSI), led by people like Andrew Kliman and Ted McGone. The goal of the TSSI was to illustrate that there was, in fact, no internal inconsistency between Marx’s propositions, that a solution could be found that allowed the cohesiveness of the profit, value, and price equalization with the relationship between labor, vale, and price. Put most simply, the TSSI solution is precisely what I alluded to above – keeping in mind that the cost of production would play a role in the price of production, while understanding that one cannot determine the price of input and output simultaneously.

The TSSI followed in the wake of what was called the simultaneous single system solution (SSSI), which posed to solve the Bortkiewczian conundrum by treating value and price as separate things that would none-the-less be determined interdependently. Variable capital is treated as the sum value received in the form of wages; constant capital is treated, as Kliman writes, “as the sum of value needed to acquire the means of production.” He continues:

The constant-capital value therefore depends on the prices of the means of production, not their values. Thus the SSSIs do away entirely with the notion of a distinct value system in which the constant and variablecapital value depend on the values of inputs (means of production and subsistence). As in Marx’s own solution, there is only a single set of constant and variable capital figures. For this reason, all three of his value-price equalities are preserved by the SSSIs, at least in a formal sense. (Kliman, Reclaiming Marx’s Capital, pg. 163)

Kliman illustrates this with the following chart (found in Kliman, Reclaiming Marx’s Capital, pg. 163), which depicts the Marxian schema of Department I (labeled here as Branch 1), which produces the means of production, and Department II, (here Branch 2), which produces the commodity.  Note that in this chart, the value of labor is measured at $3 a unit. In regards to the symbols and formulas, PPU is price per unit of each good produced by one branch or another; C is constant capital; V is variable capital; S is surplus value; W is the value of the output, or C + V + S; π is the average rate of profit; P is the output’s price of production, or C + V + π; S/(C+V) is the value rate of profit; and π/(C+V) is the price rate of profit.



We see that all three of Marx’s aggregate equalities are preserved. Total price and total value both equal 288, total profit and total surplus-value both equal 48, and the general price and value rates of profit both equal 20%. These are extremely important results, since they disprove a longstanding claim of dual-system theorists [i.e., the Bortkiewiczians] that it is impossible to preserve all of these equalities at once. (Kliman, Reclaiming Marx’s Capital, pg. 164)

Yet at the same time, proponents of the TSSI solution like Kliman find the SSSI solution to be untenable, for it serves to solve one charge internal inconsistency while opening up another. This new inconsistency is based on the continued notion the Marx held that inputs and outputs would be priced simultaneously: by doing so, the “causal relationships” within the equalizations deviated from Marx’s theory. For Marx, the value rate of profit – S/(C+V) determines the price rate of value – π/(C+V). In the SSSI, it is determined by the “physical rate of profit”, which is “physical surplus divided by physical output” (Kliman, “Physical quantities, value and dynamics”). In doing so, the value rate of profit and the price rate of profit are locked into an eternal alignment. This undermines a different argument put forth by Marx: that capitalism exhibits a tendency of the rate of profit to fall. If the value rate of profit and the price rate of profit march in lockstep, then the disequilibrium which triggers this tendency cannot take place.

Kliman’s argument is that under the TSSI solution, the casual relationships with the aggregate equalization are retained in a way that allows both the mathematics to emerge in a way that reflects Marx’s theory and the tendency of the rate of profit to fall. The formulation of the TSSI is almost identical to the SSSI model, the only difference being the price and value are not determined simultaneously. The results, however, are quite different. Compare the following chart (drawn from Kliman, Reclaiming Marx’s Capital, pg. 166) with the previous chart:


Both branches’ constant capital investments are the same as before, because the input price of Good 1 and the amounts of means of production they use are unchanged. Owing to the 50% reduction in employment, however, the variable capital investments and the surplus-values produced are 50% smaller than before. Thus the value of each branch’s output falls. Since aggregate surplus-value declines by 50% while the aggregate capital value advanced declines by only 5%, the aggregate rate of profit falls sharply. All three aggregate equalities hold true, and in a substantive sense. Because less living labor is performed, there is a fall in the amounts of value and surplus value produced, which in turn causes a decline in total price and profit. And because less living labor is performed, the value rate of profit falls, which causes the price rate to fall as well (Kliman, Reclaiming Marx’s Capital, pg. 165)

A Brief Primer on Value Theory, Part I: From the Physiocrats to Ricardo


I would like to write a little clarification on the differences between various schools of thought where “value” is concerned, which I’ve noticed has become a major point of contention in debates between advocates of capitalism (specifically anarcho-capitalism) and socialism. One the major problems (besides theoretical differences, of course) is that we’re dealing with a semantic swamp, where the same word is being used by three or four groups in three or four different ways. Debate today tends to conflate these different meanings into two primary forms: on one hand, the subjective theory of value suggested by the marginalists, and a unified labor theory of value which is more a by-product of critics, and not really a reflection of much of anything. I want to identify (at the very least) four different forms of value in economic thought:

  • The Physiocrat approach to value
  • The Classical approach to value
  • The Marxist approach to value
  • The Marginalist approach to value

In this schema, there is more or less a direction line running from the Physiocrat to Classical schools, but the classical school itself can be (for our purposes here) divided into two sub-sections:

  • Smithian
  • Ricardian

Now, Marxian value theories, while emerging from the Classical lineage, serves as a repudiation of its predecessors, specifically the Ricardian sub-section. The marginalists constitute another break, but what is important to consider is that one of the major elements in this break is a complete and total methodology. In other words, what we are dealing with are several different “apparatuses” through which economics can be approached. Differences in apparatuses, of course, will always yield different outcomes concerning the object or system in question, but the divergence where value theory is concerned is operating at the semantic, discursive level. One can argue the merits of one school vs. the other school and seek to disprove them through various means – but using the marginalist definition of value to discredit early value theories cannot happen, for the terms are not in any alignment. Regardless of which side one is one, one is forced to shift their arguments elsewhere.

So what is value? For the marginalists, value is individualized, the worth applied by the individual to a commodity on the market. Do I want/need this commodity, and does that justify X cost? Price emerges, in their theory, as the average of these valuation. Neat, simple, straightforward, and by the time we get to Debreu’s 1959 The Theory of Value, value and price had become synonymous with one another. This very recent conflation of two terms has only served to confuse matters more, as things get a little more complicated as we go back in time.

To understand what economists before the marginalists were talking about when they say “value”, we have to understand that it is an intermingling of three things: a metaphor, a unit of measure, and a force that empowers movement. Taken broadly, value is understood as a substance that is represented, but not irreducible to, money. The Physiocrats, the classicalists, and the Marxists shared a common framework for approach economic life, which they defined as three spheres:

  • Production
  • Circulation
  • Consumption

Value as metaphor allowed a vantage point from which to observe the transformation of things between each sphere. Value as measure emerged from the need to study the laws governing the these transformations. Value as force was developed to explore the momentum and movement flowing through these spheres. It is this last one that is most important for the Physiocrats and Classicals: most of these economists were developing their theories in close relation with many of the scientific developments taking place at their time, and mutual influence radiates through both. As Philip Mirowski in More Heat Than Light illustrates, economics was conceived as following the same sets of rules as the emerging field of studies that would later be described as physics. So at this point we have the substance of value being roughly equated to energy itself, transforming from form to form.

The Physiocrats

The Physiocrats used the term ble to describe value, which roughly translates as wheat; their model, thus, is one in which all momentum and transformation in the economy emerges from agriculture. To quote Francois Quesnay, the father of the Physiocrats,

[Agriculture] gives rise to settled laws, weights, measures, and everything which is concerned with determining and guaranteeing possessions.

It’s kind of understandable why they would think this, given that at the time the society was largely organized around agriculture itself. But there is more to this picture. As any person familiar with the history or philosophy of science knows, slippages between metaphors have cascading effects that often mold or shape the apparatus being used. This is what happens in Quesnay’s work: it was common in this time to associate the functions of Nature (as a concept) with that of the human body. Quesnay, in addition to being an economist, was a court physician, and specialized specifically in the study of blood flow. As blood is in movement throughout the body, he came to draw a parallel between this and the movement of ble/wheat/value through the body of society. This was the foundation of his famous Tableau économique, which charts the movement of ble/wheat/value through society based on the flow of blood through the human body. As Mirowksi writes:

The parallels between Quesnay’s medical theories and his political economy are extensive. Quesnay’s understanding of the configuration of the cardiovascular and economic systems are identical; health in both instances means the unobstructed flow of a conserved substance through the system. More profoundly, just as the major vital processes had been supposedly reduced to the motion of a single substance, so, too, were the motley of economic activities reduced to the motion of a unique value substance across some class boundaries… Far from merely operating on the plane of broad analogy, Quesnay’s Tableau reflects his physical theories down to small details. For instance, the Tableau reproduces the tubes of tin, with all flows eventually returning to the pump/landlords. As the aim of bloodletting was to free up circulation in order to restore health, the physiocratic advocacy of freer trade was to free up the circulation of value to restore national wealth. Indeed, the physiocratic doctrine of a single tax was a projection of Quesnay’s surgical doctrine that a single incision during bloodletting was the most efficient and efficacious regimen. (Mirowski, More Heat Than Light, pgs. 157-158)

In other words, the healthy body requires blood to flow unimpeded, Quesnay reasoned that ble/wheat/value must also move unimpeded through society if the social body is to be healthy. Thus, we arrive as a laissez-faire understanding of economics.

The Classicalists

The transition from the Physiocrats to the Classicals must be contextualized in two developments:

  1. The transition form an agricultural economy to an industrial economy, with the subordination of the former by the latter.
  2. The discovery of the laws of thermodynamics

It’s worth pointing out that in many respects, the discovery of the laws of thermodynamics emerged from the Industrial Revolution itself. Many of those involved in unraveling the nuances of this new science, such as Sadie Carnot, developed their theories based on observations of steam pumps and heat engines. An obsession with machines reigned supreme in this time, with everything from the cosmos to the human body being defined in terms of the machine. This is what Amy Wendling has described as the

“energeticist model” of the interaction between humans and nature. In this model, human and natural forces are not distinct in kind. The human is not a spiritual or vital force at work in the natural, material world, transforming the latter in a form-giving way. Instead, concepts like “spiritual” and “vital” are progressively eliminated from scientific usage. Matter and form come to be seen as two expressions of a single kind of force: energy. Humans, nature, and machines all operate according to a single model—the model of energetic flow. Energy can be converted from a static material, to heat, to a mechanical activity, and back again. Such conversions subtend phenomena that were formerly portrayed as diverse and as operating according to different rules. In the energeticist model, the work of the steam engine, human labor, human intellection, natural events, animal actions, and even human political life are all portrayed in the same way, and they follow the same basic rule: the rule of energy transforming itself. (Wendling, Karl Marx on Technology and Alienation, pg. 62)

Or as Anson Rabinbach has put it: “The human body and the industrial machine were both motors that converted energy into mechanical work… The laboring body was thus interpreted as the site of conversion, or exchange, between nature and society-the medium through which the forces of nature are transformed into the forces that propel society.” (Rabinbach, The Human Motor, pg. 2) We can see from this perspective how the metaphors would begin to shift: from a constellation bringing together the transformation of ble/wheat/value through the movement from Nature to Society via agriculture with the healthy flow of blood through the body, to one on which value becomes akin to energy, transferred from Nature to Society via the labor of the human body. Interestingly, there are suggestions that Sadie Carnot’s diagram of the heat engine, which from the notion of the Carnot cycle sprung, was itself inspired by Quesnay’s Tableau économique.

Value in Smithian Classicalism

To continue with our exploration of value we’ll have to back up a little, and return to Adam Smith. Taken most broadly, Smith’s work was a transposition of Physiocratic frameworks into the newfound economic context. The Physiocratic system, he wrote “with all its imperfections is, perhaps, the nearest approximation to the truth that has yet been published upon the subject of political œconomy”. (Smith, The Wealth of Nations, Book IV, Chapter IX). By the same token, by “representing the labour which is employed upon land as the only productive labour” Quesnay and his intellectual kin had erred, as “the notions which it inculcates are perhaps too narrow and confined.”

That’s not to say that it is a perfect fit. In his transposition, Smith offers several contradictory positions on the question of value. In the first instance, he shifts the locus from agriculture to industry while retaining labor as the source of value, corresponding to a sort of measure of a given commodity’s pre-market price. “But Adam Smith,” as Benjamin Tucker would later write, “immediately abandoned all further consideration of it to devote himself to showing what actually does measure price, and how, therefore, wealth is at present distributed.” (Tucker, “State Socialism and Anarchism”) Thus later in The Wealth of Nations, a new perspective on value arises, one in which value is not based on labor, but on stocks. Yet while most approach stocks as composed the sum total of given firm’s commodities available for sale on the market,

Smith only compounds the problem by suggesting that stock is comprised of physical goods and education, talents, and abilities. Without hesitation over the enormity of the task of reduction, he then proceeded to treat this agglomeration as a coherent and homogeneous aggregate for the individual, much as an early merchant would lump together all of his assets (including even his household silverware) in a single stock book… stock will be analyzed independent of relative price changes, a formless incompressable jelly, effortlessly rendered suitable for either consumption of investment. In a manne r of speaking, Smith avoided the value conundrum that had so engrossed his predecessors by essentially bypassing it save for some early comments on labor, which are dropped in the subsequent analysis. The primary function of those comments were to keep open a few tenuous lines to the metaphor of body, which only later in classical political economy grows in significance. (Mirowksi, More Heat Than Light, pgs. 166-167)

Value in Ricardian Classicalism

It was precisely this tension running through Smith – value emerging from labor on one side, and value equating to the total stock of a nation, writ large – that gave rise to the much-maligned Ricardian perspective. In his brief adoption of labor as the source of value, Smith had inherited value-as-force from the Physiocrats, but ultimately abandoned this by making value into a synonym for aggregate wealth. Ricardo, however, sought to synthesize this perspectives (while perhaps narrowing stocks down to physical commodities), and in doing so turned to value-as-measure. Ricardo:

All measures of length are measures of absolute as well as relative length. Suppose linen and cloth to be liable to contract and expand, by measuring them at different times with a foot rule, which was itself neither liable to expand or contract, we should be able to determine what alteration had taken place in their length… There can be no unerring measure either of length, of weight, of time or of value unless there be some object in nature to which the standard itself can be referred and by which we are enabled to ascertain whether it preserves the character of invariability. (Quoted in Mirowski, More Heat Than Light, pgs. 173-174)

Ricardo had been associated with the Philosophical Radicals, a group of intellectuals who followed the utilitarianism of Jeremy Bentham and James Mill. The utilitarians had sought to measure the value of pleasure in terms of how much pain or toil had to be expended to ascertain that pleasure; this itself mirrored certain observations concerning labor to written by Smith in The Wealth of Nations: “The real price of everything, what everything really costs to the man who wants to acquire it, is the toil and trouble of acquiring it”. (Smith The Wealth of Nations Book 1, Chapter 5) Thus labor emerges through this selective line of reasoning, quite naturally, as the “object in nature” which things can be measured against. Ricardo reasons, for example, if two different commodities both took one laborer four hours of work to produce, then both commodities would have the same value.

Smith had argued that the actions of the market, be it the whip or competition and the ebbs and flow of demand, would drive the price of a given commodity down towards toward its “natural price”, that is, the costs that were incurred in the production process. As labor is a major component of these costs, and had previously played a role in the costs of the raw materials that labor works with, Ricardo assimilated this perspective with his treatment of value. His labor theory of value, then, is also a cost-of-production theory of value and a labor theory of price.

It is precisely here at this point here that I suggest we treat as the origins of the semantic confusion concerning value, price, and the ultimate difference between the Physiocrat-Classicalist and marginalist approaches to value theory and price theory. Indeed, whereas the Physiocrats and Smith (up to a point) treated value and price as separate forces, Ricardo appears to be collapsing them together through his reflections on costs. The marginalists did themselves no favors in untangling the ambiguities, as their own very different interpretation of what value was also a theory of price. When Stanley Jevons suggested “that value depends entirely upon utility”, this notion of value was detached from the preoccupations and interests that had fueled value theory (i.e., the metaphorical slippages and the borrowings from science – even though the marginalists did indeed import these elements in their own idiosyncratic way).

What Ricardo was describing as “value” was separated from market price, despite obfuscations that say otherwise. In his “Notes on Malthus”, he does argue that market prices “depend on supply and demand”, though in time they would “be finally determined by… the cost of production.” (Carson Studies in a Mutualist Political Economy, pg. 39) Furthermore, he took care to compile lists of the exception to his theory: scarce goods and luxury items and other non-reproducible goods. This caused several problems in the marginalist critique of Ricardo, such as the case of Eugen Böhm von Bawerk recounted by Kevin Carson:

Böhm-Bawerk was at his best in systematically analyzing the exceptions to the labor-theory and the cost-principle. In so doing, however, he was forced to admit a rough statistical correlation between cost and price in cases of reproducible goods; and in so admitting, he was forced to reduce his argument to quibbling over the required level of generality of a theory of value… (Carson, Studies in a Mutualist Political Economy, pg. 22)

This is not to say that there aren’t critiques to be had in the Ricardian approach to value, but to elucidate those is to jump into the next stage in the history of the labor theory of value: the Marxist stage. I’ll take this up in the next post, which it will also serve to elucidate the “energeticist model” that emerged in the wake of thermodynamics.