The Genesis of the Transformation Problem
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The Genesis of the Transformation Problem
🎧 Articles

The Genesis of the Transformation Problem

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The infamous Transformation Problem has long stood as a supposed example of the failure of Marx’s economic theories. Ian Wright gives an explanation of the problem to help pave the way for a possible solution. Reading: Gabriel Palcic. 

You may have heard of Marx’s transformation problem. Critics of Marx use it to reject his economics. Partisans of Marx argue about its meaning and status.

A precise understanding of any problem is a necessary prerequisite to recognizing a solution or non-solution to it. My aim in this article is to explain the transformation problem as straightforwardly as possible without the use of any mathematics or numerical examples. I begin by framing the problem within the context of the historical emergence of market societies.

Exchange in classical antiquity

Money and markets have been with us since antiquity. Aristotle, writing in the 4th Century BC, described how citizens bartered their surplus product in markets, which introduced the need for money. We can imagine Aristotle, or one of his slaves, walking to the stalls in the Athenian agora to purchase fruit for the household using the silver coins he mentions in his text on the Athenian Constitution.

In consequence, the question of the nature of economic value was posed in ancient times. Why does one fish have the same value as two loaves of bread?

Aristotle recognized that the exchange of goods implies that there’s something equal about them and that the money value of goods measures that equality. But what is that value? And what determines its magnitude?

Aristotle proposed that the equality of wants between the buyer and seller determines economic value. And the magnitude of that value is determined by whatever happens to be agreed, face-to-face, at the market stall. Value, therefore, is essentially a subjective and parochial phenomenon.

Generalized commodity production

Much later, in the 17th and 18th Centuries, a new kind of society emerged, which re-posed the question of economic value in entirely new circumstances.

In Britain, during this period, large numbers of peasants were thrown off the land and into the workshops and factories in the cities. New kinds of institutions, capitalist firms, commanded hundreds of laborers to produce commodities explicitly intended for sale in the market. Identical commodities were produced, again and again, with scientific and mechanical precision.  Competition between firms stimulated the application of machinery, which significantly increased the productivity of labor. Profits were reinvested in more production. The population of waged laborers exploded. Production could be scaled up or down according to market demand. The working population became a fungible resource that could be deployed, and redeployed, to different economic ends. The British ruling class became rich from colonial conquest, the direct enslavement of millions in plantations abroad, and the exploitation of millions of workers at home.

In these circumstances, everything had a price, even people. Prices, as they did in ancient markets, could still vary depending on whether the buyer or seller struck a good deal and the strength of their respective wants. But the enormously increased scale and regularity of commodity production presented new, yet obvious, empirical truths: first, that prices fluctuated according to supply and demand; and second, despite these temporary and accidental fluctuations, the prices of commodities were clearly determined by the quantity of resources used-up to produce them. A shirt typically commands a higher price compared to its raw cotton because producing shirts uses-up additional resources, such as the labor time of the cutters and sewers in shirt-producing factories, and the costs of purchasing and maintaining any machinery and tools.

And so, in these new social circumstances, where market relations had become ubiquitous, the question of economic value was posed anew, but on a much grander scale. And this led to the emergence of a new, specialized field of human knowledge now referred to as classical political economy.

The birth of classical political economy

Sir William Petty, born in 1623, broke with the Aristotelian tradition that mutual wants, in the marketplace, determine the magnitude of value. He claimed, instead, that economic value is not a phenomenon of market exchange but is something produced outside the market when labor is combined with land. Petty proposed a cost-of-production theory of value, where value reduces to the money cost of that labor and that land. Petty pointed out that capital, such as machinery and raw materials, are the results of “past labor” — and so capital can be ultimately reduced to the price of labor too.

John Locke, born in 1632, sought to eradicate land from this theoretical picture. He traced back all the inputs that are directly and indirectly used up to produce a commodity, all the way back to a hypothetical raw state of nature, in the past, where humans first confronted the uncultivated land without tools or machinery. Lock argued that, from this point of view, labor accounts for 99% of the value of commodities. This was more parsimonious but something of a just-so story.

David Hume, born in 1711, and Adam Smith’s best friend, argued that nature is a free gift, that commodities are mere “storehouses” for labor, and labor is the active agent that produces all commodities. So Hume took the step towards reducing all costs of production to labor costs.

Adam Smith, born in 1723, proposed that labor is indeed the source of value, the true wealth of nations, and that the sacrifices made by labor is the measure of economic value. Smith proposed that, in a supposed early and rude state of society, before the emergence of capitalism, commodities would in fact exchange according to the labor sacrifices needed to bring them to market. One fish is worth two loaves of bread because the fisherman and the baker must sacrifice the same amount of labor to produce them.

But Smith said, now, in modern society, where production occurs in large workshops where the powers of co-operating labor are combined with tools and machinery, then workers do not get the whole fruits of their labor. Some of the sales revenue is distributed to landowners, for the maintenance of land, and capitalists, for their investment in capital. And so the market value of a commodity is determined not only by the quantity of labor and therefore the wage costs, but also the rent of the land, and the profit of the capitalists. 

Smith proposed that market prices typically fluctuate around “natural prices”, which are those prices sufficient to induce all three classes to co-operate in bringing the commodity to market. He reasoned as follows: Assume a change in the supply or demand for some commodities. Market prices will rise for commodities in undersupply (since buyers outbid each other to obtain the scarce product) and fall for those in oversupply (since firms underbid each other to sell to scarce buyers). This generates profits (in sectors producing too little) and losses (in sectors producing too much). So profit-rates differ across sectors.

Capitalists fund production by advancing money-capital to cover input costs, such as raw materials and labor, and then, once goods and services have been sold, recoup their advance plus a profit increment. And capitalists also seek to maximize their profits. In consequence, they continually reallocate their money-capital to high-profit sectors and away from low-profit sectors. Hence, relatively profitable firms receive additional money-capital, which they use to increase production to meet the higher demand, whereas relatively unprofitable or loss-making firms have money-capital withdrawn, and therefore decrease their production. The scramble for profit, therefore, has the side-effect of reducing mismatches between supply and demand. Market prices begin to gravitate back to relatively stable natural prices, which would empirically manifest when supply equals demand everywhere, and the profit-rates in every sector are the same, and therefore capitalists have no further incentive to reallocate their capital.

And so, in the space of about one hundred years, the leading thinkers of the emerging bourgeois order began to view economic value as being determined by objective and universal laws that control production, competition, and distribution both within a nation-state and between them — rather than by the subjective coincidence of wants in relatively isolated marketplaces where small-scale producers or merchants “higgle and haggle” with buyers over prices.

Ricardo

David Ricardo, born in 1772, wasn’t content with Smith’s cost-of-production theory because he observed that a rise in wages (or rent or profits) doesn’t mean that a commodity is therefore more valuable. Instead, a rise in wages typically causes general price inflation (so relative prices are unchanged) or lowers profits (i.e. workers get a bigger share of the revenue from sales while capitalists get less). So Smith provided a somewhat circular price theory of price, rather than a theory of economic value.

Ricardo, in order to get to the root of the matter, decided to focus on commodities that are reproducible in the sense that their supply is restricted only by the available labor force. He argued that reproducible commodities constitute the vast majority of commodities. He initially ignored rent and permanently scarce commodities, such as unique paintings.

Ricardo proposed that the natural prices of reproducible commodities are regulated by their “difficulty of production”, which is the true measure of economic value, and which he suggested we could measure in terms of labor time. “Difficulty of production” isn’t merely the direct labor supplied to produce a commodity but also includes the indirect labor supplied to produce the used-up capital, such as raw materials, tools, machinery, etc.

So in Ricardo’s theory market prices vary due to supply and demand. But behind these temporary and accidental fluctuations stands real, not monetary, costs of production: the real objective, material difficulty of making things, which we can measure in units of labor time.

The truth of a labor theory of value should become particularly clear and obvious when natural prices obtain because in these circumstances supply equals demand, and any temporary scarcity or over-supply of reproducible goods has been eradicated. We’d expect planes to fetch a higher price than pens because planes require more of society’s labor-time to produce. Natural prices should rise or fall with changes in the difficulty of production of commodities. In other words, if the quantity of labor-time required to make a commodity increases then we’d expect its natural price to proportionally increase, and market prices to start gravitating towards this new level.

In some special cases, natural prices do vary one-to-one with labor time. One special case is Adam Smith’s rude state of society without landlords and capitalists, where rental income and profits are absent. But in general, we don’t see a one-to-one correspondence. The natural prices of reproducible commodities differ from their difficulty of production. There’s still a mismatch, even when all the deviations due to supply and demand imbalances have melted away.

And this is the problem, which both Smith and Ricardo were fully aware of: natural prices can vary independently of changes in the labor-time needed to produce commodities. In other words, the natural price of a commodity can rise or fall even if its difficulty of production is constant. Understanding why this must be so is the most important step to understanding the genesis of the transformation problem.

Why natural prices vary independently of labor time

Consider a situation where market prices are at their natural prices. Then imagine, as Ricardo did, that capitalists, as a whole, raise the uniform profit-rate (e.g. from 2% to 3%) by paying workers, as a whole, a lower wage rate. In consequence, capitalists now grab a larger share of the surplus product whereas workers must make do with less. The difficulty of the production of commodities, measured by labor time, hasn’t changed at all. This is merely a change in the distribution of income between workers and capitalists. However, this change causes some natural prices to rise and others to fall. Why? 

Consider two firms: one that produces commodity A and another that produces commodity B. Assume that the production of commodity A is relatively capital-intensive and therefore requires more capital but less direct labor. But assume that the production of commodity B is relatively labor-intensive and therefore requires more direct labor but less capital. 

A wage reduction means that labor is cheaper to employ. In consequence, the natural price of B falls more than A because B benefits more from cheaper labor. That’s simply because the direct wage costs, in each firm, differ.

But in addition, an economy is an interconnected whole. Commodities A and B not only require other commodities as capital inputs but are themselves used-up as inputs in the production of other commodities. The change in the wage level affects the production costs of all commodities differently. And therefore the non-labor input costs of A and B also change. And changes in the natural price of A and B also affect the production costs of any firms that use them for inputs.

In summary, a change in the distribution of income between workers and capitalists alters the entire relative price structure of an economy. Some prices go up, and others go down, depending on differences in labor-intensity and capital-intensity of different production processes and the interconnectedness of the economy. And in consequence, natural prices can change even when their difficulty of production does not change. 

Natural prices depend on an economic conflict over the distribution of income (the division of the spoils of the revenue obtained when commodities are sold). But “difficulty of production” is a purely technical measure of direct and indirect labor costs incurred during production. Natural prices, as a purely logical matter, have an additional degree of freedom that is unrelated to labor time. They can vary independently of them. And therefore natural prices cannot be one-to-one proportional with labor time. Ricardo understood, very clearly, that this partial independence of natural prices from labor time, even when we exclude the effect of mismatches between supply and demand, constituted a theoretical problem.

Ricardo’s labor theory of value couldn’t fully explain the structure of natural prices. And so Ricardo searched for other measures of real cost, other measures of difficulty of production, that might not suffer from this problem. He considered quantities of gold, quantities of corn, or even quantities of a hypothetical average commodity that would minimize the mismatch between natural prices and labor time. Ricardo refused to regress to an Aristotelian subjective theory of value because it could not explain the structure of prices in modern capitalist conditions.

He thought this problem was so important he worked on it in the last weeks of his life. But try as he might, he did not find an objective measure of economic value that fully explained the structure of natural prices. Ricardo finally admitted the contradiction: his objective theory of value required an “invariable measure of value”, outside the market, which explained the structure of natural prices, but he also enumerated why such an invariable measure could not exist. He stated that although “the great cause of the variation of [the price of] commodities is the greater or less quantity of labor that may be necessary to produce them” there is another “less powerful cause of their variation”, which is the level of profit. He suggested that profit might be a monetary reward for capitalists’ patience while they waited for their return of the money-capital they advanced. Ricardo, therefore, concluded that natural prices were mainly but only approximately explained by labor time. This theoretical problem ultimately led to the abandonment of Ricardo’s theory of value.

Marx’s challenge

Marx, born in 1818, was deeply influenced by classical political economy but viewed it as a contradictory ideology that aspired to, but could not achieve, scientific objectivity, because it ultimately expressed the particular and subjective class interests of the emerging bourgeoisie.

Ricardo had merely wanted to define a standard of economic value, something objective, outside of the market, that would explain prices. Marx, in contrast, claimed that the dynamics of capitalist competition instantiate objective laws that bind the form of value — such as pounds, dollars, or euros — to a specific content, which is labor-time. Quantities of money, and therefore prices, in fact represent labor time in virtue of our own social activity, not because an economic theorist decides that labor time is a convenient measure.

Marx inherited but modified the classical concept of difficulty of production. Marx defined the objective value of a commodity as fundamentally composed of two elements: first, the value of the constant capital used up to produce it, where constant capital refers to the inputs to production, including machinery and tools, etc.; and, second, the labor directly supplied to produce the commodity, which is the work that transforms inputs into the final commodity for sale in the market. Since “value” is an overloaded term I use “labor-value” to refer to Marx’s concept of value.

Marx quickly points out, however, that a labor-value isn’t simply the sum of concrete labor-time, or simple clock-times. If workers slack off, or use out-of-date, less productive techniques compared to what’s typical, they don’t therefore add more labor-value to the output. Marx’s labor-values only count “no more time than is needed on average, no more than is socially necessary” to produce commodities, which “is that required to produce an article under the normal conditions of production and with the average degree of skill and intensity prevalent at the time”. Marx controls for the heterogeneity in the conditions of production for the same commodity by considering each individual commodity an “average sample of its class”. The labour value of an individual commodity is, at this level of abstraction, the labor-time supplied to produce all commodities of the same class divided by the quantity produced. In consequence, Marx’s labour values are a property of the totality of the social conditions of production and not a property of individual labor processes.

To simplify, and help focus on the essentials, assume that all firms producing the same class of commodity use identical techniques and that workers producing the same class of commodity take the same time. Given these assumptions then Marx’s socially necessary labor-time coincides with individual clock-times.

Market prices, of course, fluctuate with supply and demand, and therefore the value that a commodity realizes in the market (its price divided by the average wage rate) will, in general, differ from its labor-value. Quantitative mismatches between labor-values determined by the conditions of production and the feedback from realized values determined in the market are ultimately how the law of value operates to reallocate the total labor of society to effective demand.

Workers, during the production of a particular commodity, transfer the labor-value of constant capital plus their own labor to the output. In consequence, a labor-value is the total direct and indirect labor time required to produce a commodity given the current conditions of production. Labor-values, as Marx repeatedly points out, only vary with changes in the productivity of labor (i.e., the conditions of production) and not with changes in market prices. For example, if a new technique is discovered, which allows the same commodity to be produced with less labor time, then its labor-value reduces.

Although Marx’s theory of value had many profound differences to Ricardo’s theory nonetheless Ricardo’s problem reappeared in Marx’s theory, although in an altered form.

Marx, in Volume 1, explicitly assumes that prices are one-to-one proportional to labor-values. On this basis, he develops his theory of surplus-value, which explains that profit is the money representation of the unpaid or surplus labor of the working class. Briefly put, workers supply more labor to the economy than they get back in the form of the labor-value of the goods and services they purchase with their wages. This quantitative difference, or surplus-value, is the substance of capitalist profit.

But Marx needed to establish the generality of this proposition in the case of natural prices, which, as we have seen, cannot be proportional to labor-values. He tackled this challenge in his unfinished notes published by Engels as Volume III of Capital.

Both Marx and Engels understood the crucial importance of resolving Ricardo’s theoretical difficulties. If Marx resolved the contradiction between the “law of value” (the determination of the structure of natural prices by labor-values) and the formation of an “average rate of profit” (which causes natural prices to deviate from labor-values) it would demonstrate the theoretical superiority of the new science of the socialist movement compared to the befuddled attempts of the bourgeois theorists. But this contradiction also had to be resolved because the proletariat needed to be armed with a correct and true theory of the objective dynamics of capitalist society.

Engels discussed the Ricardian contradiction in his introduction to Volume II of Capital. He boasted in advance that Marx had already solved the problem. Engels challenged other economists to propose their solution before the big reveal when Volume III was published.

Marx’s theory of the transformation

Marx presented his solution to Ricardo’s problem in his theory of the “Transformation of the Values of Commodities into Prices of Production” in Volume III of Capital. Marx’s big idea was to separate the origin of value, that is the production of new economic value, from its distribution to the different classes in society. Marx maintained that human labor, and human labor alone, creates new economic value in the process of production. But this new value is distributed to the different classes of society via a market mechanism that obscures its origin. In other words, the exploitative social relations of bourgeois society systematically obscure the true nature of the forces of production, specifically the value-creating powers of human labor.

Workers spend their money wages on the real wage, which is a collection of goods and services. Assume that the real wage is fixed. According to Marx, workers produce new surplus-value in two main ways. First, workers produce absolute surplus-value by working more intensely or longer. In consequence, workers supply even more labor time than what they receive in the form of the labor-value of the real wage. Second, workers produce relative surplus-value by inventing and applying new, efficient techniques that increase the productivity of labor in industries that produce the real wage. In consequence, workers supply the same labor time but now receive even less because the labor-value of the real wage has decreased. In both cases, workers produce new surplus-value because the difference between the labor time they supply and what they receive has increased. This new surplus-value takes the monetary form of capitalist profit. Capitalists then spend their larger profits on more luxury goods or additional investment in new capital to grow the economy.

According to Marx, the origin of new surplus-value is human labor alone, because, unlike other factors of production, such as capital and land, only workers possess the ability to alter the conditions of production by working harder or smarter, and only workers can adapt to changed conditions of production by switching to new tasks in the division of labor. For Marx, labor is “the universal value-creating element, and thus possesses a property by which it differs from all other commodities”.

In consequence, the quantity of new surplus-value produced in different sectors depends on how much direct labor is employed, not how much capital is employed, because the source of surplus-value is living labor. Marx’s theory of the origin of surplus-value implies that labor-intensive industries tend to produce more surplus-value compared to capital-intensive industries.

Marx, in Volume III, therefore considers an initial situation where money profits, in all sectors, are proportional to the direct labor employed in each industry — because that’s where new surplus-value and therefore profit comes from. In consequence, profit-rates are initially different, or non-uniform, across sectors. 

In this initial situation, the profits in each sector are clearly and transparently just the surplus-value produced in that sector. And, in this situation, the prices of commodities turn out to be proportional to the respective direct and indirect wage costs (because all the different profit-rates, in all the interconnected sectors, are proportional to the direct wage costs). Commodity prices are therefore in one-to-one correspondence with labor-values. So, in this initial state, everything starts out nicely.

But why would a capitalist wish to invest one dollar of their money-capital in a capital-intensive industry when they could invest that dollar in a labor-intensive industry and receive a higher return? Marx knew that, in a situation of non-uniform profits, like we have here, capitalists reallocate their capital away from low-profit and towards high-profit sectors. 

So Marx assumes that, when the scramble for profits kicks in, the economy gravitates from this initial situation of prices proportional to labor-values to a final situation where uniform profits prevail. Marx assumes, during the transformation, that the conditions of production do not change further and therefore labor-values are constant. So the relatively high profits in industries that are labor-intensive, and the relatively low profits in industries that are capital-intensive, are evened-out and become uniform. And therefore, in this final situation, prices no longer have a one-to-one relationship with labor-values. In fact, this final situation is precisely Smith and Ricardo’s natural price equilibrium.

So Marx gives us a before and after. Before we had non-uniform profit-rates and a one-to-one relationship between prices and labor-values. After we have uniform profit-rates and the absence of a one-to-one relationship. This is what Marx means by the “Transformation of the Values of Commodities into Prices of Production”.

Profit-rates, in all the different sectors of the economy, are now uniform. The economy, therefore, keeps reproducing itself through time with constant natural prices, a constant general profit-rate, and a fixed allocation of the labor force to the different sectors of the economy.

Some people think that, because this situation is a type of equilibrium state, whereas capitalism is never in equilibrium but forever turbulent and changing, that this final state is irrelevant to reality and can be ignored. Profit-rates, either in a nation-state, or across the globe, are never uniform, prices are never stable, the conditions of production are always changing, and so on. Therefore Marx was wasting his time even thinking about a natural price equilibrium.

But Marx knew this special state was important to analyze for the simple reason that it’s real, not in the sense of empirically manifesting at any moment of time, but real in the sense that it’s an attractor for the dynamics of capitalist competition. In other words, at all times the economy is being continually pushed towards this attractor state. Marx knew that it’s not possible to explain disequilibrium trajectories without understanding what equilibrium attractors are in play.

Of course, many other mechanisms are at play in economic reality, not just the scramble for profit: human innovation alters techniques; external shocks disrupt production; speculators form expectations of future revenue; the state intervenes, and so on. In consequence, the actual trajectory of capitalist economies, although always permanently and partially controlled by the gravitation toward natural prices, never reaches the equilibrium position. But nonetheless, this equilibrium state is an attractor for the economy and continually exerts a real influence. We don’t deny the existence of a law of gravity just because birds fly or shelves stay up.

Marx’s conservation equalities

Marx’s “Transformation of the Values of Commodities into Prices of Production” is intended to reflect a real process that occurs in a capitalist economy: workers produce new surplus-value unequally in different industries but, via the dynamics of profit-rate equalization, all capitalists grab a share of the total surplus-value produced according to the distributional rule that equal amounts of money-capital invested earn an equal return, regardless of whether that investment occurs in capital or labor-intensive industries.

Marx’s transformation, however, occurs purely in the realm of exchange-value because the transformation is purely a matter of changes in the price structure of the economy due to a change in the distribution of income (from unequal profit-rates to an average or uniform profit-rate across all sectors). The change in the price structure is not due to any changes in the conditions of production. In consequence, Marx’s transformation must be conservative. No new surplus-value is created or destroyed. Labor-values don’t change. So the original surplus-value is merely redistributed.

And this is the crux of Marx’s resolution of the classical contradiction: Marx says that, although the natural price of individual commodity types don’t appear to be related one-to-one to their labor-values, in fact they still are. Marx proposes that we can recover the one-to-one relationship by considering the total price and the total labor-value of larger collections of different types of commodities.

In fact, Marx claims that three aggregate equalities must hold. First, he computes the general money profit-rate (which is a dimensionless percentage rate of return) that will hold in all sectors of the economy once the transformation has completed. This uniform profit-rate is determined by labor-values: he divides the total surplus-value by the sum of the labour value of all the constant capital and all the wage goods (equality 1). This is a key equality because Marx intends to explain the magnitude of the general rate of profit in terms of the extraction of surplus-value in the process of production. In consequence, the profit-rate is, despite appearances, ultimately determined in production and by how much workers are exploited. Second, Marx states that the total sum of profit income, received by capitalists as a whole, is proportional to the total surplus-value (equality 2). And, third, he states that the total price of all commodities sold is proportional to their total labor-value (equality 3). Together these three aggregate equalities re-establish the link between what happens in the “hidden abode of production” and the surface appearance of exchange-values in the market.

Marx explains that the transformation scrambles the one-to-one relationship between prices and labor-values at the level of individual commodity types, but it’s a conservative transformation, and therefore the one-to-one relationship reappears when we consider larger aggregates. And in Volume III Marx gives us a fully worked out numerical example that demonstrates precisely this.

Marx accepts that natural prices diverge from labor-values. But that’s because capitalists grab shares of the surplus-value created by workers proportional to their investments. But those shares, ultimately, are just redistributed surplus-value. The true underlying cause, the origin of profits in human labor, is hidden and scrambled by the economic rules of capitalism. The apparent logical contradiction in the labor theory of value that so befuddled the bourgeois theorists turns out to be generated by a real contradiction between workers and capitalists that arises from the social relations of capitalism itself.

Marx’s transformation problem

Marx’s transformation theory re-asserts the core claims of his labor theory of value, which is that human labor is the source of value, that monetary magnitudes represent labor-time and that profit is the unpaid surplus-labor of the working class. And Marx’s fully worked out numerical example seems to solve the main problem that stumped both Smith and Ricardo.

But — and here we come to a great controversy, which started as soon as Volume III was published — Marx leaves us with a small loose thread that, when pulled, seems to unravel his theory of the transformation, and by extension his entire theory of value. In fact, these issues are so controversial, even claiming there is a transformation problem has itself become controversial. 

So what’s the problem? 

The problem, quite simply, is that Marx’s transformation cannot be conservative. The one-to-one relationship between prices and labor-values is destroyed during the transformation.

And the reason why is actually very simple. 

Natural prices, as we have seen, vary with changes in the distribution of income between workers and capitalists, that is with any alterations in the level of money wages or profit-rates. As Ricardo argued, most of the variation in, and therefore the structure of, natural prices can be explained by labor-values, but not all of it. Labor-values, in contrast, are completely independent of changes in the distribution of income because they only vary with the productivity of labor, that is how much labor time is required to produce different commodities, which depends on the conditions of production. In consequence, the “Transformation of the Values of Commodities into Prices of Production”, being essentially a change in the distribution of income, alters prices due to a change in the profit-rates across the economy, but leaves labor-values unchanged.

The natural prices of individual commodity types, as Marx pointed out, must deviate from their respective labor-values because of a real process in which industrial profit-rates tend toward uniformity and away from proportionality to the surplus-value generated in each industry. The deviation of individual natural prices from their respective labor-values necessarily implies that, in general, the total price of any large collection of heterogeneous commodities also deviates from its total labor-value. The disconnect between natural prices and labor-values therefore reappears, just on a larger scale. In consequence, Marx’s three aggregate conservation equalities between prices and labor-values cannot be preserved during the transformation process. 

In some special cases Marx’s three equalities do hold: the zero profit situation of Smith’s rude state, uniform capital-intensity across all sectors of production, or when the quantity of commodities produced in different sectors of the economy happen to be in certain very special proportions. But, in general, Marx’s equalities do not hold. The profits in the final state, once the transformation process has been completed, cannot be viewed as redistributed surplus-value from the initial state. 

But what about Marx’s numerical example that seemed to satisfy his conservation claims? Marx’s example works only because it doesn’t fully take into account the interconnectedness of an economy. And Marx, who was no fool, was the first to notice this limitation.

Marx, after presenting his successful numerical example, immediately points out that he assumed that the prices of input goods are proportional to their labor-value. But when an economy is reproducing itself over time at natural prices then this assumption is false. The prices of input goods are also at their natural prices, and therefore not proportional to labour-values. Marx, in a way, mixed up his before and after situations and didn’t fully numerically explore the final situation of his transformation process. Marx warns us that “there is always the possibility of an error” if this simplifying assumption is maintained (that is, “if the cost-price of a commodity in any particular sphere is identified with the [labour-]value of the means of production consumed by it”). But Marx, in what after all are his unfinished notes, does not pursue this point further and instead remarks that “our present analysis does not necessitate a closer examination of this point”.

And that’s what Marx left us with: a brilliant theoretical solution to a longstanding problem of classical political economy, but with one small loose thread.

The unbroken thread

And, of course, all the critics pulled the thread. 

In the subsequent 150 years or so since the publication of Marx’s solution the core logical problem — that Marx’s transformation cannot be conservative — has been demonstrated, again and again, in many different ways, with different degrees of exegetical and mathematical sophistication. And, in consequence, Marx’s transformation theory has become known as Marx’s transformation problem. 

The transformation problem has always been controversial, and remains so to this day. It has generated decades of controversy and volumes of literature. Critics argue that it invalidates the entirety of Marx’s theory of value because it demonstrates that prices cannot be regulated by labor-values and that profits are not surplus-value, and therefore the economic arguments of anti-capitalists are built on sand. Defenders of Marx’s theory of value tend to either deny the transformation problem exists, typically by misinterpreting key elements of Marx’s theory to impose surface consistency at the expense of scientific substance, or argue that it’s a minor technical problem that cannot be resolved but nonetheless does not invalidate the main thrust of his theory. The transformation problem is responsible for multitudes of creative re-interpretations and misinterpretations of Marx’s text designed to deny, circumvent or dissolve the logical contradiction. The chances are that your favourite modern interpretation of Marx’s theory of value was originally motivated by a desire to avoid the transformation problem.

Marx’s theory of the transformation was the first, and largely successful, attempt to understand how capitalists appropriate profit on money-capital invested despite its origin in the activity of human labor in production. My view is that the transformation problem is indeed a genuine problem in Marx’s theory of value. And therefore we must acknowledge not deny its existence in order to further Marx’s critique of political economy. The transformation problem indicates the need to generalize Marx’s theory of value in order to fully understand the contradictory reality of capitalist production. Once we do this, we discover a more general theory that preserves all the insights and core claims of Marx’s theory yet lacks a transformation problem. From this perspective, Marx’s theory of the transformation was merely incomplete.

My aim in this article has been to explain what the transformation problem is. A precise understanding of any problem is a necessary prerequisite to recognising a solution or non-solution to it. Despite the lack of consensus on its status, even amongst followers of Marx, the transformation problem is important because it’s essentially concerned with what profit is, where it comes from, and whether capitalist social relations are fair and equitable, or inherently unfair and exploitative. The transformation problem is also intimately related to what money really is, about the meaning of this social symbol that we hold in our pockets, throw around the entire world, and which dominates our lives. Marx’s theory provides an answer to the very same, fundamental question regarding the nature of economic value first posed millenia ago when we began to exchange our surplus produce in busy marketplaces using coins made of silver and gold.

Supplementary material

  • Capital, Volume I. Karl Marx, 1867.
  • Capital, Volume III. Karl Marx, 1894.

On classical political economy and Marxism:

  • “A History of Economic Thought”, Isaac Rubin, Pluto Press, 1989.
  • “Theories of Value and Distribution since Adam Smith: Ideology and Economic Theory”, Maurice Dobb, Cambridge University Press, 1973.

On generalizing Marx’s theory of value:

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