What Transformation Problem?

Nerd alert: I know that my videos normally represent the height of fashion. I know that my massive popularity, on the account of all the violence, sex appeal, and sports references have launched me into the top ranks of viral culture, making me a real trendsetter.

But this video will not be like that. So I’m warning you now, this video gets an extremely high nerd rating. It will try to explain the details behind probably one of the nerdiest theoretical debates in marxist economics. But if you watch this video you could very well be set to join the ranks of other fashionable revolutionaries like these guys… (nerd quiz: can anyone name these guys?)….
That being said, the topic I am going to discuss is an important one, but only because the debate behind it lies at the core of claims that Marx’s labor theory of value is “discredited”, “contradictory”, etc. One does not have to look to far into Marxist economic theory before one stumbles upon the quagmire that is “the transformation problem”. And the sheer magnitude of algebra and technical gobbledy-gook involved in most of the discussion of the transformation problem scares most people away from ever really looking into the debate further.

Over the last 100 years there has been furious debating back and forth over the meaning of Marx’s theory of “the transformation of values into prices of production” and over the various criticisms of it- debates of such a stunningly polarized and mathematical nature that it is hard for us normal folks to wrap our mind around the issues at stake enough to know what to make of it all.

The goal of this video is to explain the basic nature of the problem and to defend Marx’s transformation procedure on the basis of some new scholarship on the topic. I will do all of this without any math or any algebra. On my wordpress blog ( https://kapitalism101.wordpress.com/transformation-math-supplement/ ) you will be able to find a supplement with a more detailed discussion and some math examples for all of you super-nerds who want to plow into some simple math. [If you aren’t afraid of a little division and subtraction I recommend you check out the math supplement and learn how to solve some transformation problems of your own. It’s kind of fun- like a sudoku puzzle for marxists. Then you can scribble them out on paper napkins at bars and parties to impress people. It’s always a real hit.]


So everything in Marxist economics centers around the idea of value. Without a theory of value we wouldn’t be able to make most of the arguments that are considered a crucial part of marxisim: exploitation, crisis, class, etc. Value is not some abstract, metaphysical concept. It is a real tangible thing that effects all of us everyday. It is the reason we go to work in the morning. It’s what allows us to buy groceries. It’s why countries go to war. It’s why we have banks and railroads and stockmarkets. The unfolding of the “law of value” is the unfolding of the inner mechanisms of a capitalist society. So it’s important that the concept of value is internally consistent and logical or else its status an explanatory concept is questionable.

If you’ve seen many of my videos then you probably know by now that value is created by human labor, and human labor only! Machines can’t create value. Buying and selling commodities doesn’t create value. Differences in subjective preference don’t create value. Let’s review a few different arguments as to why this is the case. The point of any economy is to coordinate human labor in such a way as to provide stuff for people. There are many different ways this labor has been coordinated throughout history, and there will likely be many more ways it will be coordinated in the future. In a capitalist economy labor is coordinated via commodities.  That is, I make a commodity and you make a different commodity. When we exchange them we are exchanging our labor. That’s how our collective labors are organized.

The only reason all of these diverse commodities can exchange with each other is because they are all products of human labor in the abstract. This is what gives them their value. But commodities don’t walk around with their value written all over them. (If they did, capitalism would be a lot easier to understand and you wouldn’t need to watch this video.) You can’t buy a toothbrush and read on the toothbrush how many hours it took to make it, how many people worked to make it, what their working conditions were, how it was shipped to the store, who put it on the shelf, etc. Value has to be expressed through money. Money prices are an expression of value.

But here is where things start to get confusing. How is value measured in money prices? Is price always equal to value? What happens when price doesn’t equal value? Since anyone can set any price they want when they sell a commodity it may at first seems hard to see how price could realistically reflect value. But we know from our own lives that there seem to be some sorts of forces at work in the universe- some hidden hand of the market that keeps prices from being totally arbitrary. A toothbrush or a new car costs more or less the same anywhere you buy it. Not only that, but the car will always cost more than the toothbrush. So what are these forces that make prices converge? And is it just a coincidence that things that take more work to make usually cost more than things that take little time to make?

The more perfect competition is in a capitalist society, the harder it is to arbitrarily set prices above values. Perfect competition makes it impossible to just conceive of prices as arbitrary or of profit as a mere “mark-up” above costs. (Of course competition is never perfect, but if we are building an abstract model of a capitalist economy we have to identify the inner logic of capitalism in the abstract before we see how outside forces distort this model.) We also can assume that supply and demand balance each other. Obviously if supply ever shrinks this will create a rise in prices above values. But this rise in prices means a rise in profits for those capitalists producing scarce goods. This rise in profits encourages more capitalists to invest in producing this good and this, in turn, increase the supply until prices are back down to an equilibrium point. The opposite happens with decreases in demand.

The argument of the labor theory of value is that, behind all of these fluctuations there lie equilibrium prices and that these equilibrium prices correspond to the value of commodities. Now, what happens when monopoly, trickery or demand allows someone to get away with arbitrarily charging more for a commodity than its value? The answer to this question is really crucial, so listen closely: The total amount of value in society corresponds to the total amount of prices. So if someone is getting away with arbitrarily high prices it means that someone else is not getting the full value of their commodity. In this way, though profit can’t be created through exchange, it can be shuffled around between people. Through monopoly, fads, whatever people can benefit from an inequality in exchange- a defect in the manifestation of capitalist competition. But such an inequality does not create more value! The real source of profit in a capitalist society is the difference between the value of commodities and the wage paid to workers. This, of course, is the theory of exploitation.

So if we abstract from disturbances in competition, or minor fluctuations in supply and demand we see that commodities, in general, have prices that are relatively proportional to their values…. or at least, they would if there wasn’t one other complicating factor…

It is this other factor that required Marx to theorize about “the transformation of values into prices of production” and which has created all the fuss for all these years. It is very similar to what I just described about the way supply and demand equalize. The same way in which supply and demand fluctuate around equilibrium price also creates an average rate of profit amongst capitalists. That is, if one capitalist is making more profit than the rest, other capitalists will start doing whatever (s)he is doing and thus eat into his/her profits. Through this sort of competition an an “average rate of profit” is established among capitalists.

But this average rate of profit seems, at first, to conflict with something else that I’ve talked about in other videos: the organic composition of capital.

Let’s illustrate this with an example. Let’s say there are two industries: one makes coffee and the other cars. Within both industries there is competition to make their workers the most productive by introducing the newest labor-saving machines. Thus within each industry there is about the same ratio of workers to machines. (This is what the “organic composition of capital” is- the ratio of machines to workers. When there are a lot more machines than workers we say the organic composition is high. When there are more workers, we say the organic composition is low.) But between industries this ratio differs.  Some industries just naturally have a higher ratio of machines to workers than others. In our example, the automobile industry uses a lot of machines! The coffee industry uses a lot more workers.

Now if value can only be created by human labor, it would seem that the coffee industry creates a lot more value than the car industry. And, actually this is the case- the more work that’s done in an industry, the more value it creates. Yet, under conditions of competition, under the law of the average rate of profit, both industries receive the same profits, even if one creates much less value.  An average rate of profit means that each capitalist receives the same rate of return on their total investments, regardless of what proportion of this investment goes to workers or machines. How is this possible? (Do the workers in the auto industry just work harder? Are they more exploited? There’s no necessary correlation between the ratio of machines to workers and their wages so lets assume that the rate of exploitation is equal in both industries.)

Here is the solution to this puzzle. The total amount of value in society is equal to the total amount of prices. The total amount profit is equal to the total amount of surplus value (Surplus value is the difference between the value of a commodity and the cost of paying workers and paying for raw materials, machines, etc.) The total rate of profit measured in value, in society as a whole, is equal to the total rate of profit measured in money.

These are the “three aggregate equalities” that form the holy trinity of the theory of the prices of production. Individual capitalists can have money prices or profits that diverge from their values, but in the aggregate these equalities prevail. But how?

All capitalists contribute to the total amount of surplus value according to how much labor they employ.  So if coffee makers have more workers, they contribute more to the aggregate surplus value than car manufacturers. But capitalists withdraw their money profits from this total surplus value according to the average rate of profit- that is, in proportion to the total cost of their production. Regardless of how many workers they actually employ, they all receive the same rate of return on their investment, even if all of their investment goes into machines!

Thus the price of a commodity is not the cost of inputs plus surplus value. It is the cost of inputs plus the average return on those investments. We call this price the “price of production”. The total prices of production equal the total amount of value. But individual commodities do not trade at their values. They trade at their prices of production. The price of production is still a function of value, but it is not necessarily directly equal to it.

This is why it is possible to have a falling rate or profit (see “Falling Rate of Profit video). Individual capitalists have no way of knowing that they are destabilizing the collective rate of profit, because they don’t receive less profit when they replace workers with machines. It is only when automation has spread throughout the economy to a substantial extent that it can drag down the profit rate.

This relationship between individual action and wider social forces is true to the spirit of much of marxist theory. Individuals are always free to act as they choose. That’s the easy part of social theory.  The hard part of a good social theory is to explain why those free actions coalesce around certain norms. For Marx, it is value which is the central mediating force between individuals and so it is the laws of motion of this value that ultimately govern the success or failure of individual actions.

A Little Bit Of History.

Marx took the ideas of classical political economy to their logical end. After Marx one couldn’t operate as a political economist without accepting the notions of exploitation and crisis that he had so thoroughly developed. And so those who were interested in doing truly bourgeois economic theory had to abandon the notion of a labor theory of value if they were to save economic theory from Marx. In so doing, thinkers like Leon Walras developed what is now called “neoclassical economics”. Neoclassical economists abandoned the notion of value altogether. They essentially took price as a given- refusing to look behind it for any deeper meaning. In doing so they also abandoned the whole notion of social class, and all of the other wider social phenomena that Marx had woven into his theory. Their restricted, narrowed perspective soon developed an obsession with number-crunching and fancy algebra.

I say all this because it was out of the neoclassical school that the critique of Marx’s transformation procedure developed. And it was this new way of thinking about economics that produced the sort of assumptions that led to this critique. In 1907, Ladislaus Bortkiewicz, a Russian economist, published a paper which claimed that Marx’s transformation procedure was internally contradictory- that when taken to it’s logical conclusion it produced mathematical results that simply didn’t add up. Ever since, people doing Marxist economics have had to contend with this accusation that their fundamental theoretical category, value, is not logically valid. Over the course of the 20th century many Marxist economists embraced the neoclassical models of Bortkiewicz and his successors in various, attempts to rescue Marx’s value theory from within the framework of bourgeois economics. It wasn’t until the 1980’s that some scholars began to challenge the assumptions behind this neoclassical critique and to construct a defense of Marx from within the logic of value theory. The most promising of these new defenses is the “Temporal Single System Interpretation” or “TSSI” for short. Let’s take a closer look at the Bortkiewicz argument and the TSSI response.

The neoclassical tradition that Bortkiewicz came out of had several major differences from the Marxist tradition. Where Marxist theory builds a model of capitalism that is dynamic, constantly evolving, prone to disproportion and crisis, the neoclassical school views capitalism in a static, unchanging equilibrium state where the hidden hand of the market naturally smoothes out imperfections. It is important to keep this difference in mind when viewing Bortkiewicz’s critique.

It was Bortkiewicz’s fascination with these static, equilibrium models that led him to question Marx’s transformation procedure. Bortkiewicz put Marx’s argument into a standard neoclassical input-output model.  On the input side went machines, raw materials and wages all measured in their values. On the output side came newly produced commodities, all now priced at their prices of production. Bortkiewicz then asked, quite logically, shouldn’t the inputs into the production process be bought at their prices of production and not their values?

Indeed Marx himself had acknowledged that it only made sense for inputs to be bought at prices of production, but this did not lead him to the same conclusions as Bortkiewicz. Bortkiewicz took those end prices of production and plugged them back into the input side of his equation. When he did this all hell broke loose with the math. Specifically it became impossible to maintain all three of Marx’s original equalities: total money profits equal total surplus value, total money price equals total value, total money rate of profit equals total value rate of profit. Only one equality could be maintained at a time but only by arbitrarily imposing that condition at the expense of the other two equalities. To Marx’s critics this was the end of the labor theory of value.
[Here I decided not to explain the way in which Bortkiewicz created a dual system of value and price.]

The TSSI critique of Bortkiewicz is simple and elegant. They argue that it is illogical to plug output prices back into the inputs of the same production period. They accuse him of two false assumptions: simultaneism and physicalism. Let’s look at each in turn.


For Bortkiewicz the prices of inputs and outputs are simultaneously determined. In other words, input and output prices have to be equal. Let’s say we have an industry that makes corn. It also needs seed corn as an input. Bortkiewicz would argue that if at the end of the production period corn sells for 10 dollars a bushel then it must also enter production as an input at 10 dollars a bushel. There can be no change in price. But he seems to be arguing for some theory of time travel, as if a farmer would go back in time and sell themselves corn at their future output price. In the real world, the opposite happens.  Values change over the course of a growing season due to the productivity of labor and soil, weather, changes in technology, etc. The price of corn at the end of the production period doesn’t have to equal its price at the beginning. The new prices of production become input prices for the NEXT production period, not the one that’s already happened.

In contrast to Bortkiewicz’s simultaneous determination of prices, the TSSI is “temporal”. It tracks changes in the prices of production through time, from one production period to the next. In each period the input prices are the output prices of production from the previous period. In this way the TSSI is much more faithful to the marxist project- to build a dynamic model of value as it moves through time, constantly expanding.


Bortkiewicz, in a way, defended his simultaneism by constructing his model within the framework of an economy with no growth. He argued that in an economy with no growth prices wouldn’t change over time and thus it would make sense to simultaneously determine input and output prices. This model of an economy with no growth actually came from Marx himself who theorized about Simple Reproduction- an economy with no growth in which the entire social product was produced and sold each production period. Simple Reproduction was an abstract model Marx used to simplify some arguments about exchange before he introduced his more complex model of expanded reproduction. Yet, still the theoretical possibility for simple reproduction to occur does exist and so we do need to consider whether the transformation of values into prices of production works under conditions of zero growth.

The problem is that Bortkiewicz assumed that no physical growth meant no growth in value. This is the essence of physicalism: that changes in value are directly tied to changes in the amount of actual physical commodities. ie. If I produce ten apples instead of five I have twice as much value. This seems to make sense. But look at the way this actually plays out in the real world. (21)When a supply expands its value falls. When a supply shrinks its value rises. In a drought the same amount of apples is worth more than in a glut. So just because there is more of something in physical terms doesn’t mean its value is more. In fact, value can change while physical output remains the same if the production process becomes more efficient or input values change.

This is precisely what happens in the TSSI version of the transformation “problem”. From one period to the next the physical outputs stay the same. The same amount of goods are produced and consumed. But the value of those goods changes overtime. Each production period, new work is done; new labor is added to the social product. And so total value rises each production period. This total value becomes the input for the next production period.

From the TSSI illustration it becomes clear that it would be ridiculous to take the prices from the end of the production period (prices representing an increase in value) and plug them back into the equation at the beginning of that same production period. The Bortkiewicz solution flies in the face of the basic logic of value theory and so it necessarily produces absurdist results.

Bourgeois economics is often thought of as an objective, rational science for number-crunching specialists, divorced from political bias. But all of these matrices and graphs exist within a very narrow range of assumptions. By leaving out questions of value, by treating capitalism as a static, universal entity without change, and by ignoring class it prevents itself from addressing the most essential elements of economic analysis. It is these assumptions which have led to the entire notion of a “transformation problem”, and to the general attack on marxian economics.

While it can be intimidating to wade through the specialist literature on a topic, we should never forget that underneath the numbers lie arguments and assumptions about the real world and that  these are, in the end, the crucial things to be concerned about. There is no reason why you and I should have to take a graduate course in economics in order to understand the debate over value and price. We should never be intimidated by “experts” into not thinking for ourselves and not challenging assumptions. Such timidness in the face of algebra has led to far too much meekness from the left. In the coming economic crisis it will be crucial to assert our ideas clearly and boldly, and without bowing to the tools of bourgeois economics. It is high time to put an end to this tiresome debate about the transformation problem.


“Reclaiming Marx’s Capital” by Andrew Kliman

“One System or Two? The transformation of values into prices of production vs. the transformation problem” a paper by Andrew Kliman and McGlone. This available on Kliman’s website: http://akliman.squarespace.com/

Marx’s Theory of Value and the ‘Transformation Problem- an essay by Anwar Shaikh from the book “The Subtle Anatomy of Capitalism” ed. Jesse Schwartz

“Limits to Capital” by David Harvey

“Das Kapital” vol. 3 Karl Marx

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12 Responses to What Transformation Problem?

  1. Db0 says:

    Thanks for this post. Heavy but still accessible to the non-economis (albeit with a bit of mind focus)

    I had similar questions in the past and now at least I have some arguments.

  2. Al says:

    Dear Sir: I find your many videos interesting and enlightening. I have watched your videos and those by David Harvey about Marx’s “Capital” in order to learn more about what people call “Marxism”. In general, when you say that word, “Marxism” or “Marxist” people conjure up an image of firing squads and gulags. They never bother to grasp the true crux of Marx’s work. This is why I find your videos so refreshing. Human society has overcome so many things: despotism, feudalism, slavery, etc. Why is it so difficult to invisage a different system? One that isn’t predicated on M-M1 or C-M-C? I know that you are a reader of Slavoj Zizek and he is fond of remarking that Marx’s call to action (..”Philosophers have merely explained the world, the point, however, is to change it”..) should not be blindly heeded. Zizek’s advice is to, in effect, step back, return to theory, think about it, and then try again. In that spirit, I hope you will distill some new ideas. Namely, how do we set prices without markets? This is one that I grapple with. It seems to me that markets prevent us from building houses out of Titanium when wood or bricks would do. I’m no economist, but I’m sure you get the gist of my sentence. Anyway, keep up the good work. And thanks. AAP

  3. David says:

    Thanks also from me for this post. The TP is quite complex, and reading about it on wikipedia or other net sources one could almost think it’s a theological debate. This lays out TSSI quite clearly. I’m curious about the two-system theorists, but not enough to go over their stuff 😉

    As to what to sbustitute for markets, there are two answers IMO. One is rational planning: would you rationally plan to build houses of titanium? I wouldn’t, not in planet Earth anyway. Another answer is planning can be given some aid from market mechanisms (though not necessarily full markets) on the output side, so for instance prices are initially set to the total amount of labour embodied in the commodity, and if supply is too low you raise the price, and otherwise you lower the price, but, more importantly, if you find yourself rising the price a lot over the labour value you know you probably are underproducing, and vice versa.

  4. Pingback: Interview with Andrew Kliman « Kapitalism101

  5. Murray says:

    Just as nobody has done your quiz yet to my knowledge, it’s Ernest Mandel, Paul Baran, Meghnad Desai, David Harvey. What do I win? 😛

  6. Dave Z says:

    Dear Brendan,

    Thanks for your efforts to popularize Marxist economics.

    Since you are serious about the topic I would suggest that you look into a more sophisticated framework than what has been presented here.

    In particular I’d highly recommend that you read the path-breaking book “Laws Of Chaos”, now available as a pdf here: http://iwright.googlepages.com/probabilisticpoliticaleconomy

    Also Anwar Shaikh has written some first-rate papers on his webpage: http://homepage.newschool.edu/~AShaikh/index.html Although it might be too heavy for beginners.

    • What do you think is not “sophisticated” enough about the TSSI framework? I have a more detailed explanation of it in my math supplement to the transformation problem, but really the best source is Kliman’s book Reclaiming Marx’s Capital. I am familiar with Shaikh’s work on the transformation problem. I found his work very convincing until I read Kliman’s book which convinced me otherwise- that Shaikh didn’t question the basic assumptions behind Bortkeiwicz’s transformation procedure. But I still think that the first half of Shaikh’s article (the one in “The Subtle Anatomy of Capitalism” ed. Shwartz) is a really good explanation of the relation of price to value. I have not read the Farjoun/Machover book. Do you think it is accessible to people without a mathematics background?

      • Dave Z says:

        The TSSI framework, while it correctly questions certain assumptions about equilibrium, it does not have the adequate mathematical (and from it conceptual) tools to deal with the chaotic nature of economies organized on the principles of market exchange. For that you need precisely the tools from probability theory.

        I don’t want to obscure things, but the conceptual difference is analogous to that between classical mechanics and the theoretical revolution of statistical mechanics. Therefore I strongly urge you to also look beyond the TSSI framework.

        Farjoun and Machover’s book requires some elementary maths but it is not overwhelming provided you skip Chapter Two on statistical mechanics in the first reading. At least read up to and including Chapter One to get a flavour of the arguments.

        There is a lot more to be said on the topic and some interesting theoretical and empirical results coming out of this “probabilistic” framework. But I could point to some of that research later on.

  7. Name says:

    The link to the math supplement portion of the transformation problem is broken. Has the page been moved elsewhere?

    Love the blog!

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