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)