Das Kapital vol.3 Chapter 9: Formation of a General Rate of Profit (Average Rate of Profit) and Transformation of the Values of Commodities into Prices of Production

(This post is part of an ongoing project: a close reading of volume 3 of Kapital, one post per chapter. I hope that others who are tackling this book for the first time might find my summaries and thoughts useful. I also hope that others might leave their own thoughts, criticisms, help, etc. here so that this blog might become a good collective resource for those brave souls who take on Vol. 3.)

In all of the consternation, debate and quarreling over Marx’s value theory this chapter, chapter 9 of volume 3, lies in the center of much of that (though perhaps chapter 10 even more so). There are basically two lines of criticism leveled at Marx that draw heavily on this chapter: those associated with Bohm-Bawerk and those associated with Bortkiewicz. The latter criticism is known as “The Transformation Problem”.

Bohm-Bawerk’s main idea is that Marx’s theory of the prices of production and his theory of value contradicted each other. He said it was impossible for Marx to hold that both were true. In volume one Marx claimed that commodities traded at their socially necessary  labor time. In volume 3 he now tells us they trade at their cost price plus average profit. For Bohm-Bawerk this was a thinly disguised admission that the labor theory of value didn’t work. He does admit that the logical structure of Marx’s argument flows very neatly and convincingly from Marx’s premises. But Bohm-Bawerk takes issue with these basic premises. Because of the errors in his premises, says Bohm-Bawerk, Marx’s value theory runs into trouble when, in chapter 9 of Volume 3, it actually steps forward to confront the real world and bumps up against the “prices of production”. This leads Bohm-Bawerk to launch a rigorous critique of many aspects Marx’s value theory. I plan to write a more sustained summary and analysis of Bohm-Bawerk’s criticism elsewhere so for our purposes here I will constrain my references to Bohm-Bawerk’s argument that there is a contradiction between the theory of value and the theory of prices of production. It should be pointed out, however, that much of the lay criticism of Marx’s labor theory of value that one confronts on the internet does not come from this notion of a contradiction between value and prices of production. Instead it mostly comes from Bohm-Bawerk’s more general critique of Marx’s assumptions. (Even here, however, most of the lay criticism online presents Bohm-Bawerk’s critique in a bastardized, simplified manner that doesn’t really stand up.)

Bortkiewicz’s argument, known as “The Transformation Problem”, is of a different nature though people sometimes conflate them. I deal with Bortkiewicz’s criticism and the Temporal Single System Interpretation’s (TSSI) response to it in my video “What Transformation Problem?” and the accompanying Math Supplement, so I will not go into this in detail here. Bortkiewicz argued that if the creation of average profits led to prices of production which differed from their values then both outputs and inputs must trade at their prices of production. In the mathematical examples Marx gives in this chapter he only changes the output prices. Bortkiewicz found that if one plugs the output prices back into the input side of the equation all hell breaks loose with the math. This mathematical inconsistency has been held as proof that Marx’s theory of prices of production, and even the labor theory of value, is internally inconsistent. The TSSI response is to ask why output prices should become the input prices of the same production period. They should be the input prices of the next production period. The TSSI argues that Marx’s value theory is temporal- that it describes the movement of value through time. Attempts to collapse this temporal theory into neoclassical equilibrium models that simultaneously value input and output prices will necessarily arrive in contradiction.

My posting of this blog entry on this chapter has been delayed by many different circumstances one of which was my trip to the 2009 Rethinking Marxism conference in Amherset Mass where I heard Alan Freeman and Andrew Kliman give a tutorial on the TSSI. Freeman’s talk centered on his criticism of the idea of equilibrium price and equilibrium of supply and demand. While I have been aware of the TSSI’s temporal treatment of input and output prices as part of a larger critique of general equilibrium, for some reason I had never realized that this extended to a critique of the basic idea of supply and demand meeting. I’ve since been reading through a bunch of Freeman’s papers (as well as some by Kliman) trying to wrap my head around this idea. I think that this will most likely change my reading of volume 3 and perhaps cause me to edit both the already-posted and the yet-unposted drafts of my blog entries on volume 3. The TSSI’s distinction between value and exchange value, it’s claim that Marx’s value theory is a temporal, non-equilibrium theory have bearing on both the Bohm-Bawerk and Bortkiewicz criticism.

When reading this chapter with these debates in mind I am asking myself two questions. 1. What is the relationship between value, price of production and price and how does Marx justify the use of value if values don’t equal prices of production? 2. In relation to the Bortkiewicz critique I am looking for evidence that Marx conceives of his theory in a temporal manner. I will conclude with some thoughts on both of these points. Let’s actually see what Marx has to say.

Since the theoretical problem Marx is tackling involves how different organic compositions can have the same rate of profit Marx abstracts away all variations in surplus value and turnover time so that we can look specifically at the relation of organic compositions themselves to profit rates.

Marx begins with a table that presents 5 different capitalists, each with a different organic composition of capital. Each has a cost price of 100, but the different distribution of capital between constant and variable capital means that each produces different amounts of surplus value and therefore has a different rate of profit. The prices of the total product of each firm (value of product) are also different since the price of the total product is c+v+s.

Now what if we treat each of these 5 capitalists as if they were different branches of the same firm? Marx suggests we imagine it is a cotton mill with 5 different internal departments: spinning, carding, etc. With today’s multinational corporations scattering production all over the globe we could think of some modern examples of firms with such an internal-division of production between different departments. In such a firm the main concern is the total rate of profit. Totaling up the columns in his example Marx shows that the total surplus value is 110 and total cost price is 500. Dividing surplus value by cost price he finds that the average profit for the firm is 22%. The average profit for each department of the firm is 22%.

In order for the average profit to be 22% the “value of the product” for each department must change. Department 1, for instance, has a cost price of 80c+20v with a surplus value of 20s. The value of the product produced by department 1 is 120. But at this selling price it would only achieve a profit rate of 20%. In order to achieve average profits we must sell it for 122 which gives us a 22% profit rate. Marx then goes on to show (table 3) how by varying the value of the product in each sphere up or down the departments can obtain an average rate of profit. The total value of the product remains the same, the total surplus value remains the same, but the surplus is redistributed between departments via these changed prices. These new prices, which deviate from their values are c+v+p where p is the average profit redistributed to each firm. Marx calls this new price the “price of production”. Simplified we might say that prices of production equal cost-price plus average profits. Prices of production are still a function of surplus value, but the surplus is distributed differently than it would be if there was no average rate of profit.

Before showing this 3rd table Marx points out that the price of production for each of his firms doesn’t need to result in all “values of the product” being equal to 122. This is because different amounts of constant capital enter the actual value of the final product depending on how much constant capital is used up in production. Remember that we count constant capital differently when measuring profit rates than when figuring prices. The entire outlay on constant capital enters the figuring of the profit rate, even if little of it is only used up. But only this used up portion enters the prices of commodities.

All of these observations hold true when we break up our multi-department firm and view this as a matter of 5 different firms competing in the market. Each firm sells its product in the market at its price of production. This price allows it to recoup its cost-price. But each firm does not receive profits in relation to the total surplus value it has created. Instead it receives the average profit which could be higher or lower than the surplus value the firm actually creates. It is as if each capitalists is just a stockholder in a large-firm receiving interest on their investment in relation to the total size of their investment. It is the magnitude of their investment, the cost-price, that determines the magnitude of their profit, not the actual amount of surplus value they create.

This analogy which compares capitalists in competition with capitalists as different parts of the same firm points to an important aspect of Marx’s method. He even restates the analogy in different form a few pages later, asking us to image that all five capitals represents different investments of one man. The analogy is quite true to Marx’s method which was to treat the labor-capital relation before he treated the capitalist-capitalist relation. The observations we have made about price, value and profit from analyzing the labor-capital relation still hold. But they hold for the total labor to total capital relation. Individually between capitalists the correlation between value and price is less direct, mediated through this matter of  average profits. In the aggregate total value=total price, total surplus value-total profit, and total value rate of profit= total money rate of profit.

But then Marx points out what could be misinterpreted as a paradox. How can we say that total price=total value when we know that the prices of some commodities enter the cost-price of other firms? When a steel company sells $1000 of steel this $1000 becomes the input price of other firms. It seems like output prices can count as the input prices of some firms. This would mean that we count the value of some products twice. Surely this would cause total price to be higher than total value. This puzzle Marx poses is reminiscent of Bortkiewicz’s “transformation problem” in that it plugs output prices into input prices and results in a contradiction. And similar to the TSSI refutation of Bortkiewicz’s transformation problem, Marx refutes this puzzle with similar logic though he doesn’t explicitly refer to any temporality. He says that you can’t count surplus value twice in the calculation of total price. The profits of an individual firm can’t make up their own cost-price. They can enter the cost-price of another firm. (If a firm is producing directly for consumption its total price enters directly into the calculation of total price.) But if its product is to be bought by another firm for production we must subtract this value from our calculation of total prices. To find total prices we add up all the cost-prices of all the firms and then add up all the profits. But first we subtract all the profits from the cost-prices.

How is Marx’s point here similar to the TSSI? Marx’s point that surplus value can’t be counted twice, as both an input and and output, without reaching a contradiction is similar to the argument of the TSSI which says that we can’t plug output prices into the input prices of the same firm, in the same production period and expect to achieve the same price=value equality. Every production period new value is created and this must count toward the value of the next period, not the current one. In these two paragraphs Marx could be seen using a-temporal logic. After all, he is merging the output of one firm into the input of another, two production periods, into one. On the other hand he is saying that if one does this, you can’t count the surplus value twice. So there is an implicit understanding of the temporal nature of the problem.

Marx then turns to a more general question about input prices. Aren’t input prices also calculated as prices of production and not values? Isn’t constant capital bought at its price of production and not its value? Isn’t variable capital indirectly related to the prices of production of the means of subsistence? Yes it is, Marx says. As we move backwards in our equations we see that every c and v reduces itself to cost-price plus average profit. But for every instance where average profit exceeds the surplus value of a particular product there is a counter-instance of a product whose surplus value falls below average profit. These values add up in the end so that our aggregate equalities hold. “Under capitalist production, the general law acts as the prevailing tendency only in a very complicated and approximate manner, as a never ascertainable average of ceaseless fluctuations.”

From such an argument it is hard to buy the commonly repeated claim that Marx “forgot to transform input prices.” Bortkiewicz’s entire critique is based on this idea of a “transformation problem”- that Marx forgot to transform input prices into prices of production and that when we do so we get inevitable mathematical errors. It is true that Marx does not provide mathematical tables to demonstrate how such transformations would happen, but in this paragraph he most definitely shows that he is aware that input prices need to be transformed. But he doesn’t seem worried that this causes any mathematical problems, probably because, as he states above, he realizes the surplus value can’t be counted twice.

“Since the general rate of profit is formed by taking the average of the various rates of profit for each 100 of capital invested in a definite period, e.g., a year, it follows that in it the difference brought about by different periods of turnover of different capitals is also effaced. But these differences have a decisive bearing on the different rates of profit in the various spheres of production whose average forms the general rate of profit.” p.161(italics added)

This paragraph seems a confusing way of beginning the argument that Marx develops over the next page and a half. I think that the sentence on the following page gives us a better idea of what Marx is trying to say: “The formation of the average rate of profit is, therefore, not merely a matter of obtaining the simple average of the different rates of profit in the various spheres of production, but rather one of the relative weight which these different rates of profit have in forming this average.” (Italics added) I did some head scratching after reading that. Is the average rate of profit an average of the individual rates of profit or not?

First we must realize that the “individual rates” of profit refer to what the rate of profit would be if there was no average rate of profit. They are figured as s/(v+c). In Marx’s first example he wants to make it very obvious that each firm has a different organic composition so he picks his numbers so that the total capital invested (v+c) adds up to 100 for each firm. This allows us to think of the organic composition as percentages. Individual rates of profit can be thought of in this “percentage logic”. It doesn’t matter how much total capital is invested when we are looking at individual rates of profit. The proportion of total surplus value (s) to total cost-price (c+v) is what matters.

But things are different with the general rate of profit. The general rate of profit is formed by dividing total surplus by total cost price. This means that the magnitude of the capital invested is important. If my profit rate is a healthy 50% but I only invest 100 dollars a year I don’t add much to the average profit rate. If my profit rate is 13% but I invest a million dollars each year I have a much bigger influence on the general rate of profit. So we can’t just take the average of the different rates of profit to find the general average since firms effect the general profit rate differently according to how much they invest.

This argument, rather simple when you think about it, is made even more confusing by a mathematical typo Marx, or Engels, makes in one of his examples. Unlike the other error I mention earlier this one is not corrected in the Internet Archive version. In Marx’s numerical illustration of this concept he says:

“Let us take four capitals A, B, C, D. Let the rate of surplus-value for all = 100%. Let the variable capital for each 100 of the total be 25 in A, 40 in B, 15 in C, and 10 in D. Then each 100 of the total capital would yield a surplus-value, or profit, of 25 in A, 40 in B, 15 in C, and 10 in D. This would total 90, and if these four capitals are of the same magnitude, the average rate of profit would then be 90/4 or 22½%.”

The equation should actually read 90/400, not 90/4. 90/4 gives us 2250% rate of profit. Again, the equation for the rate of profit is found by adding up all surplus values (90 in this case) and dividing them by the total cost-price (400 here). Marx’s typo makes it look like he is dividing the 90s by the 4 capitalists which could lead to a misunderstanding of the equation for the rate of profit. The next example he gives (720/5500) is correct.

To conclude this whole point Marx gives us two factors that determine the general rate of profit.:
“1) The organic composition of the capitals in the different spheres of production, and thus, the different rates of profit in the individual spheres.
2) The distribution of the total social capital in these different spheres, and thus, the relative magnitude of the capital invested in each particular sphere at the specific rate of profit prevailing in it; i. e., the relative share of the total social capital absorbed by each individual sphere of production.”

This whole point may help to explain an earlier paragraph in which Marx says that though differences in turnover time effect the individual firm’s rate of profit they fail to effect the average rate of profit. If I understand Marx correctly on this point, I believe he is saying that total surplus value produced relative to total cost price within a given period is what effects the general rate of profit, regardless of whether or not these aggregate totals involve more or less turnovers. (I am not sure about this interpretation at all. Any thoughts from others would be welcome.)

In case we were too daft to realize what is going on Marx points out that we are now moving from a discussion of value to a discussion of prices of production. In volume one where we dealt with socially necessary labor time between commodity producers and with the aggregate labor-capital relation we could deal with value as a qualitative expression of capitalist social relations. When we introduce competing capitals we see a further transformation of value into prices of production. Firms producing at high value/organic compositions sell their products at prices of production above their real values. Firms producing below the average value composition sell their products at prices of production below the real value of the product. It should be pointed out that prices of production are still a step removed from market prices which fluctuate with supply and demand.

In moving from value to price of production is anything changed about the theory of exploitation? Clearly the relative degree of profit accruing to individual capitalists diverges from the amount of surplus value they produced, but it still remains a fact that workers must produce more value than they are paid if profit is to exist. The price of production is still higher than cost price. Now, cost-price is also modified by our new perspective because constant capital is bought at its price of production instead of its value. It is the money price of this constant capital, this means of production, which is important to the capitalist, not the actual value embodied in it. Profit still takes place even with these modified prices.

(The groundwork for this journey from value to production price is laid by Marx in chapter one of Volume one (Bohm-Bawerk could have benefited from reviewing this) when Marx explained that prices diverge from values all of the time. When exchange values diverge from values (which they do most of the time) this allows the sellers of commodities to get more or less value in exchange than the actual value of their product. This happens because money is the abstract form of value: when prices rise above values the seller appropriates more abstract labor than is represented by the commodity. Marx often assumes, for the sake of specific arguments, that prices equal values. But in the real world, he tells us in many times over, prices do not equal values. They don’t even equal prices of production. It is this constant movement of capital in search of these super-profits (these prices above value) that explains the dynamic motion of capital. This is why the law of value is better than just a theory of price- it describes the movement of prices in non-equilibrium over time.)

One could easily read over this paragraph and miss another, parallel, argument that is going on. This parallel argument is of special interest to us since we are reading this chapter with the TSSI-vs.-Bortkiewicz issue in mind. In Bortkiewicz’s critique of Marx’s transformation he attempts to do the math that Marx “forgot” to do. He plugs prices of production back into the inputs of Marx’s tables. Because new surplus value is being added each production period this keeps the numbers from adding up. The 3 aggregates (total value=total price, total profit=total sv, total money rate of profit=total value rate of profit) can’t all hold. In order for Bortkiewicz’s model to work at all he has to sever prices and values into two different columns. He has a column for input values and another for input prices, a column for output values and another for output prices. This “dual system” is another thing critiqued by the TSSI which argues for a “single system”. The TSSI argues that capitalists buy their means of production at their prices of production, not their values so it is ridiculous to have two different figures moving simultaneously through the tables.

Marx’s comments in this paragraph (p.164-165) seem to conform with the TSSI argument:

“But for the buyer the price of production of a specific commodity is its cost-price, and may thus pass as cost-price into the prices of other commodities.” “It is necessary to remember this modified significance of the cost-price, and to bear in mind that there is always the possibility of an error if the cost-price of a commodity in any particular sphere is identified with the value of the means of production consumed by it.”

Wow! Isn’t this the very same error Bortkiewicz makes? Then Marx says, “Our present analysis does not necessitate a closer examination of this point.” In other words, we don’t need to worry about the fact that means of production are bought at their prices of production. “The cost-price of a particular commodity is a definite condition which is given, and independent of the production of our capitalist, while the result of his production is a commodity containing surplus-value, therefore an excess of value over and above its cost-price.”

Capitalists buy commodities at their prices of production! So we must use these figures when calculating the new prices of production! We do this by dividing the new aggregate surplus value created by this aggregate cost-price.

Marx then gives us an updated formula for the price of production of a commodity. Before we had said price of production=k+p, or cost-price plus profit. But profit is really the average rate of profit multiplied by the size of the capital invested, or kp’ (p’ being the general rate of profit). So now our formula for the price of production is k+kp’.

This allows us to identify the 3 things which can change the price of a commodity. 1. If the general rate of profit changes the price of production can change without any change in the actual value of the commodity, the actual amount of living labor in the commodity. 2. If the productivity of the workers making the commodity changes. That is, if there are more or less workers relative to machines this changes the value of the commodity. Also, if the value of any of the elements of the cost-price change this will change the price. And 3, there can be a combination of 1 and 2.

Changes in the general rate of profit are long term changes, taking place over long periods of fluctuation. Therefore most short-term changes in prices are due to changes in the amount of labor time going into a commodity. Changes in the general rate of profit can happen through changes in the rate of exploitation, changes in the value of constant or variable capital, or changes in the overall organic composition of capital.

Marx’s next point, spanning 167 to 168, is about the difference between appearance and essence…. the way the formation of a general rate of profit obscures surplus value. We have already seen in part one of this book that since the individual rate of profit is effected by all sorts of things like the cost of constant capital, turnover time, etc. that this obscures the fact that surplus value comes from labor alone. But, back in part one, at least the total surplus value produced by a firm was equal to its total money profit. With prices of production this is severed as well. Surplus value, exploitation of workers, is even more obscured. Now that money profits depend on changes in a general rate of profit, and since this general rate of profit is shaped forces way beyond the amount of labor employed in a specific firm, the origins of profit are even more obscured. It’s obscured to the capitalist, the worker, and to the bourgeois economist alike.

A theory like Marx’s, which makes such a clear distinction between essence and appearance, should rouse suspicion in us. We want our theory to be able to explain reality. If the theory opposes itself to reality, if it claims that any real phenomenon that negate the theory are merely illusions of a world of appearance, delusions of bourgeoise ideology, then how do we know if it is true? How do we know if it has anything useful to tell us about the world?

What Marx is doing is to show us that this world of appearance is not an illusion. It is a necessity of the basic structure of surplus value and markets. We can only express the social relations of capital through the market. In volume 1 Marx explains this fetishism- that social relations take on the forms of relations between things, commodities. Much of Volume 3 seems like an extension of this framework. Marx is showing how surplus value must be expressed through prices of production and average profit rates, how it necessarily takes on an appearance that obfuscates the underlying logic.

“How could living labour be the sole source of profit, in view of the fact that a reduction in the quantity of labour required for production appears not to exert any influence on profit? Moreover, it even seems in certain circumstances to be the nearest source of an increase of profits, at least for the individual capitalist.”

It certainly is a shock to some people when they hear that Marx’s theory of crisis is that rising productivity causes profit rates to fall. It seems contradictory. But capitalism is a contradiction. The theory of prices of production really requires a theory of the falling rate of profit. We can’t have one without the other. If changes in the organic composition within the individual firm do not change the individual profit rate then we must seek theoretical confirmation in changes in the aggregate profit rate. These changes happen over long stretches of time as minor changes in fluctuations in either direction cancel each other out.

Closing thoughts

I am convinced by the Temporal Single System Interpretation and its refutation of Bortkiewicz’s “transformation problem.” The few passages that deal with the issue of temporality, input and output prices, etc. seem to suggest a temporal, single-system interpretation. When we look at the history of the transformation problem, its origins in marginalism and general equilibrium models, it is even more obvious that Marx was not theorizing within the context of a theory of general equilibrium in which output prices should be plugged back into the input-side of equations.

The Freeman papers I mention earlier make an even stronger point: equilibrium prices are not the norm. Most of the time supply and demand don’t meet and price doesn’t equal value. This is something Marx points out very early in Volume 1 of Capital. When there is too much supply products sell below their value and this causes labor to be withdrawn from a sphere of production. The opposite happens when supply is too low. But these alterations of

Bohm-Bawerk’s critique, though not as influential in the academy as the “transformation problem”, is more worth pondering. I feel a bit torn on how to characterize Bohm-Bawerk’s arguments. Some of them are cheap tricks derived from overly-simplistic reductions or mischaracterizations of Marx’s argument. Yet he also has some brilliantly crafted and well-articulated criticisms that anyone who holds to the validity of the labor theory of value should be able to respond to.

Bohm-Bawerk asks a good question: What relevance is the labor theory of value if commodities don’t trade at their values?

The most basic answer is to point out that Marx nowhere claims that prices have to equal values all of the time. This is what distinguishes his theory of value from the Smith and Ricardo and from the marginalist tradition. This theory is not just a theory of price. It is a theory of all that goes on in the motion of capital and labor. Prices fluctuate everyday with supply and demand.  But in the long term we can see relations between value and price. Yet, Freeman cautions, this doesn’t mean we should treat Marx as an theorist of equilibrium price. It’s not that in the long run values act as a center of gravity pulling prices into them. This is because values change over time as well. This means that though prices are constantly pulling away from and falling back towards values, values are constantly moving forward and prices are constantly diverging form value. The system never reaches equilibrium. It never rests. This is why it is perfectly reasonable for Marx to theorize about a divergence from value.

Yet what is the significance of the theory of value now? Has Marx replaced it with a theory of prices of production?Before we introduced average profits into the picture value was the mechanism by which the social labor process was apportioned. The formation of socially necessary labor time was what allowed consumer demand in the market to have an effect on the apportioning of social labor. Now competition leads to average profits what is explained? How does labor time exert a force upon the market? Are any of our conclusions about the qualitative aspects of the LTV still valid? How is labor apportioned? How are social production relations expressed? And is there any quantitative connection between socially necessary labor time and price or are the two irreparably split?

Both the qualitative and the quantitative aspects of the LTV still have a strong presence in the theory of the price of production. Even if the profits that accrue to a capitalist don’t correspond precisely with the surplus value of a firm, profit is still a function of surplus value. Profit is still made by getting more work for less wages. Thus all of Marx’s observations about the dynamics of the labor-capital relation still hold true.

Quantitatively there is still a correlation between price and value. Price equals cost of production plus average profit. All of the surplus value of the economy is pooled together and distributed equally among capitalists as average profit. Equal profit for equal investment. Marx has already said, earlier in this volume, that capitalists and workers value the labor time of the worker differently. For the worker an expenditure of labor is an expenditure of his own life. But, Marx explains over and over, while variable capital costs the capitalist a wage, surplus value costs him nothing. So how does a capitalist know how to price his surplus value? He doesn’t. He takes the average profit and doesn’t know any better.

Sometimes we see debate over the meaning of Marx’s first model for the LTV. He begins Kapital Volume 1 talking about commodity production in the abstract, as if he was discussing a society of simple commodity producers, each individual owning his own means of subsistence. Later he adds in the capital-labor relation and the model becomes more complex. One of the reasons for doing this, there are others, is that the labor-capital relation takes the form of market exchange anyway, of the buying and selling of labor power, and so this market mechanism (through which we first observe the LTV) presupposes the wage relation. But an important difference in the two levels of abstraction is this notion of the valuation of a commodity. For the capitalists the valuation of surplus labor is very different than it would be in a society of independent producers. No matter how much machinery I might buy to help me make shoes I have to charge enough money to compensate myself for my labor time or else there is no point in continuing to produce in an industry. For a capitalist there is no urgent need to have surplus value fully realized in price. Even if it was realized there would be no way of knowing it had happened because capitalists don’t keep close watch of the ratio of surplus labor time to paid labor time. (I wonder if these observations about the valuation of labor hint at more of a Smithian concept of value as “toil and trouble”- as a subjective valuation of labor time like that advocated by the Mutualist Kevin Carson. I think that my above points work quite well in explaining why average profit replaces surplus value in Volume 3, but I wonder if my arguments veer to close to a subjective take on the value of labor…)

Do prices of production still regulate labor time? Yes. After all, a part of the price of the price of production goes to wage labor. The cost of production must at least be realized in the market. If a capitalist can’t sell enough products to pay wages to the workers then he goes out of business. Beyond cost of wages, labor is apportioned in a more general way in the market. The amount of surplus labor might vary yet average profit stays the same. So the apportioning of labor time is less direct, more subtle. On the macro level, total value equals total price. On the macro level the capitalist class exploits the working class. Another quantitative regulator of the  relation between prices of production and value is the falling rate of profit. As the ratio of past to living labor increases profit rates start to fall, devaluing the capital invested in small proportions of labor.

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12 Responses to Das Kapital vol.3 Chapter 9: Formation of a General Rate of Profit (Average Rate of Profit) and Transformation of the Values of Commodities into Prices of Production

  1. Pingback: Das Kapital vol. 3 Part 2 chapter 8 Different Compositions of Capitals in Different Branches of Production and Resulting Differences in Rates of Profit « Kapitalism101

  2. Paul says:

    “In moving from value to price of production is anything changed about the theory of exploitation?”

    I think this move develops the theory from one of individual exploitation (one capitalist seizing one worker’s surplus value) to one of CLASS exploitation. As you say, the worker is still producing surplus value, but now instead of being able to point to the exact place where it all goes, some of it still go to his own boss, but some of it goes to other bosses, some of it goes to finance capitalists, and so on, and next year the distribution could be very different depending on market conditions. In that sense, the worker is now being exploited by the whole of the capitalist class, operating as a class. Similarly, individual capitalists can now receive surplus value from across the whole economy rather than only their own workers; the working class is exploited together, as a class.

  3. BarryM says:

    on the question of Marx’s method and the transformation of value into PoP, his letter to Engels of 27 June 1867 is helpful:


  4. craig Ireland says:

    “…but I wonder if my arguments veer to close to a subjective take on the value of labor…)””
    Not at all. You are right on target.
    A few years ago, a Bike – courrier (who must pedal furiously and expend more calories than, say, a cubicled paper -pusher, in order to produce the same surplus value) actually successfully sued the Canadian Govt into considering his extra calorie intake (more food) as tax deductible.
    “extra toil ” a la Smith is not so subjective after all.

  5. José Luiz says:

    First of all, thank you very much for your blog. It would be impossible to read the book otherwise.

    It seems to me that, though prices of production of one commodity (raw material) may enter in the price of other commodity and produce discrepancies between price and value, this does not happen for the global production. This is because, if some commodities pass to other commodities prices of production that are higher than their values, some other commodities pass lower prices of production than their values. So, the total error sums to zero, and total prices equals total values.

    This is what I understand for this passage:

    “However, this always resolves itself to one commodity receiving too little of the surplus-value while another receives too much, so that the deviations from the value which are embodied in the prices of production compensate one another. Under capitalist production, the general law acts as the prevailing tendency only in a very complicated and approximate manner, as a never ascertainable average of ceaseless fluctuations.”

  6. Room says:

    I’m making my way through volume 3 at the moment and I’m currently working on or studying chapter 9. Brendan’s notes are of great help. I’m also using Clarke’s study guide to volume 3 but he doesn’t go through the material at any great depth so I appreciate the amount of time and effort you put into writing a summary for all of these chapters, Hopefully there are others who are also going through this text and are visiting this blog! Perhaps a new discussion will open up.


  7. scott.f says:

    The confusions are due to bourgeois economists dealng in the exchange value of words rather than their use values.

  8. M says:

    “This whole point may help to explain an earlier paragraph in which Marx says that though differences in turnover time effect the individual firm’s rate of profit they fail to effect the average rate of profit. If I understand Marx correctly on this point, I believe he is saying that total surplus value produced relative to total cost price within a given period is what effects the general rate of profit, regardless of whether or not these aggregate totals involve more or less turnovers. (I am not sure about this interpretation at all. Any thoughts from others would be welcome.)”

    I know I am a bit late to the party, but anyway: average profit is not total surplus value / total cost price but total surplus value / total advance. Marx is explicit at the beginning of this chapter (and the book) that profit is related to advanced not consumed capital. Since the profit rate is the dominant standard of success it must relate to advance, i.e. the question is: “How much surplus does my investment make” not “How much surplus does my investment consumed in the process of production make”. This is also, incidentally, why his “development” to the formula `k + p’*k` is incorrect: `p’` – the general profit rate – is related to advance, not the cost price.

    “If the average value composition is 80c+20v and the rate of surplus-value is m′=100% then the average rate of profit is 20%. A capital of 100 then realise 20 surplus-value, regardless of what the cost price of its commodities. If the sum of cost prices is K, then a capital earns K+20. Average profit does not depend on cost price but on advance.

    In order to relate profit to a single commodity, a single commodity must be related to total advance. That is, if an advance produces w commodities per year then the price per commodity is k+p′⋅C/w where k is the cost price of one commodity.10 The fraction C/w can be read as advance per commodity or we can read p′⋅C/w as profit per commodity, such that the average rate of profit is realised for C.

    An example: Let C=1,100, of which 1,000 are fix and 100 circulation, m′=100%, average profit rate 20%, annual depreciation of fixed capital 500 and the annual product 100 commodities. Turnover is once per year. Then the cost price of each commodity is 1,000/200+100/100=4+1=6. Overall profit by the general rate of profit is 1,100/⋅20%=220 per year or 2.2 per commodity. The price of production is hence 6+2.2=8.2. Expressed differently: a capital of 1100 realises a profit of 220 per year. If 100 commodities are produced per year, each commodity must realise a profit of 2.2.

    This consideration, however, does not fit with Marx’ development from k+p to k+k⋅p′ where p′ is the general rate of profit.11 For the example above we would get 6+6⋅20%=6+1.2=7.2”

    from https://readingcapital.github.io/volume-3/chapter-09-commentary/

  9. Sava says:

    I wonder – can I insert a image in my comment? And how it maith be done? I think thath I found a good way to illustrate how the so called “law of value” does not contradict to the fact that the commodities are exchanged by theirs “production prices”.

  10. Sava says:

    I think that the following will be interesting for those who read this blog:
    I made a table in Excel for myself, for better understanding of the cohabitation of prices of production and the values of commodities. The table was made for six capitals and looks something like this:

    Capital I c v s k=c+v+s p’=s/(c+v) s’=s/v
    price 82,36 15,04 19,48 116,88 0,20 1,30
    value 80,13 36,75 36,75 153,63 0,31 1,00

    Capital II c v s k=c+v+s p’=s/(c+v) s’=s/v
    price 68,39 12,81 16,24 97,43 0,20 1,27
    value 87,93 9,50 9,50 106,93 0,10 1,00

    Capital III c v s k=c+v+s p’=s/(c+v) s’=s/v
    price 37,67 27,99 13,13 78,79 0,20 0,47
    value 73,61 5,18 5,18 83,97 0,07 1,00

    Capital IV c v s k=c+v+s p’=s/(c+v) s’=s/v
    price 27,67 12,99 8,13 48,79 0,20 0,63
    value 43,61 5,18 5,18 53,97 0,11 1,00

    Capital V c v s k=c+v+s p’=s/(c+v) s’=s/v
    price 186,31 2,58 37,78 226,67 0,20 14,65
    value 87,24 34,47 34,47 156,18 0,28 1,00

    Capital VI c v s k=c+v+s p’=s/(c+v) s’=s/v
    price 17,45 33,55 10,20 61,20 0,20 0,30
    value 47,32 13,88 13,88 75,08 0,23 1,00

    The price and the value are expressed in money.
    For example: If we take a look at c in the first table (Capital I) we can see that c is bought for 68,39 $, but the value of c is 87,93 $. If 87,93 $ is just a name of some quantity of gold, let’s say 100 g gold, than when we say “The value of c is 87,93 $” this means: “There is equal amount of labour (socially necessary) frozen in c and in 100 g of gold”. When we say “The price of c is 68,39 $”, this means that c is exchanged for 68,39 $ on the market and the difference between price and value is 68,39-87,93=-19,54 $. The owner of “Capital I” has payed 19,54 $ less for the value of c.

    The folloing conditions are met in the table:
    1. The sum of c in prices is equal to sum of c in values;
    2. The sum of v in prices is equal to sum of v in values;
    3. The sum of s in prices is equal to sum of s in values;
    4. The sum of k in prices is equal to sum of k in values;
    5. (c+v+s) in prices is more than (c+v) in values for every capital. This means that the price of
    commodity is more than the value of the capital invested for production of this commodity;
    6. The rate of profit in prices is 20% for all Capitals;
    7. The rate of surplus value is 100% for all Capitals.

    I used Solver add-in to met all these conditions. Here you can see the Excel file, where I think the picture is more clear:

  11. Sava says:

    It’s me again. Sory for the broken English but I hope the text is understandable.

    I found that l have to put some more constraints to the table which illustrates one possible cohabitation of “values” and “prices of production” if I want to render this cohabitation more truly. So I made a revision of the table.
    Now the constraints are as follows:
    1. The sum of “c” in prices is equal to sum of “c” in values;
    2. The sum of “v” in prices is equal to sum of “v” in values;
    3. The sum of “s” in prices is equal to sum of “s” in values;
    4. The sum of “k=c+v+s” in prices is equal to sum of “k=c+v+s” in values; (This is covered by first 3 points, but let it be here)
    5. (c+v+s) in prices is more than (c+v) in values for every capital. This means that the price of commodity is more than the value of the capital invested for production of this commodity;
    6. The rate of profit in prices is 20% for all Capitals;The rate of profit in values is different for every capital.
    7. The rate of surplus value is 100% for all Capitals.The rate of surplus price is different for every capital.
    8. For every capital: “c” in price > 0,5 “c” in value. This is because the rate of surplus value is 100% and if for the production of “c” is invested only variable capital (in value), this variable capital will be doubled (in value). So the price of c must cover at least the half of “c” in value. It is a noncence to invest only variable capital but that is some kind fo limit event.
    9.For every capital: “v” in price > 0,5 “v” in value. This is because the rate of surplus value is 100% and if for the production of “v” is invested only variable capital (in value), this variable capital will be doubled (in value). So the price of “v” must cover at least the half of “v” in value. (Maybe It is a noncence to invest only variable capital but that is some kind fo limit event.)

    The revised table, with the new constraints added, can be seen here:

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