The Falling Rate of Profit
Falling rate of profit
The financial world is a mysterious one. It appears that through trading stock, advancing credit, or swapping currencies profit can appear out of thin air- that is, money can be turned into more money just by clicking some buttons on a computer or placing a call to a stockbroker. Indeed much of the confusion and mystique we attach to the dizzying world of finance comes from this illusion of money growing from money.
This is inherently abstract. To most of us, money is something we earn from performing concrete labor. And we use this money to buy real commodities- actual physical objects or services that represent labor done by other people out there in the economy. For us, money (M) is an abstract step of measuring value that exists between two very real concrete things: the labor we perform (C) and the labor of the commodities we buy (C). C-M-C
But for the capitalist, this realm of the concrete is not the goal. It is the abstract power of money that is important. To turn money into more money (M-M1) is the goal of capitalist production. For productive capitalists (capitalists that generate profit by selling commodities) the concrete labor process that creates commodities is an annoyance along the way to making a profit. They thus seek to minimize the time it takes to make a commodity so that they can turn their commodities back into money as quickly as possible.
For financial capitalists there is no annoying stage of concrete labor. They move their money to one place and it magically turns into more money. So why then, aren’t all capitalists in finance? Why do they bother producing commodities anyway?
The answer to that should be obvious. Without commodities and human labor to make them we couldn’t even have an economy. All value in the economy eventually relates back to the labor process. And though financial capitalists may never see a worker or set foot on a shop-floor, the profit they make is ultimately, in one way or another, dependent on the value produced by productive capitalists, whether through interest on loans, stock value, rent, etc.
But if we let financial capital carry on in its own mad way, turning money into more money through increasingly exuberant orgies of investment it is not hard to see how this can create temporary bubbles of speculation. Symbols of value- credit, mortgages, even money itself- can be traded back and forth assuming prices way above the actual value of the asset until the financial sector finds itself awash in ‘fictitious capital’. This is a fancy word for symbols of value that are divorced from any real value- any real connection to the labor process- in the way an actual commodity is.
But if you have your thinking cap on you might already see that we can’t blame crisis solely on financial capital. The monstrous bubbles of fictitious values it creates are only a problem if there isn’t enough value in the economy to back up all those symbols of value. We must also look to the productive side of the capitalist class and ask “why isn’t there enough value in the economy to back up all that fictitious value?” How come there aren’t enough wages to pay off those mortgages? Why does the government have to go into debt in order to bailout investment firms and banks?
To answer these questions we need some theory about the rate of accumulation- the rate at which real value is produced in a capitalist society. The theory of the falling rate of profit is such a theory, and it is this theory that will be the topic of this video after many mentions and sneak-previews in other videos. The theory of the falling rate of profit argues that the basic way in which value is created in a capitalist society contains a basic contradiction which destabilizes accumulation. If not offset by some countervailing influence this will cause capitalism to go into crisis.
The basic argument is actually pretty simple. If capitalists see the concrete stage of commodity production (C) as an annoying step in between an initial investment (M) and profit (M1) it is in their interest to decrease the amount of time spent in this concrete stage while getting the most possible value out of it. This is basically what it means to increase efficiency. Workers produce more commodities per labor-hour, thus increasing the physical productivity relative to the initial investment.
The problem is that the more efficient capitalists are at producing commodities the less those commodities are worth. And this is simply because increased efficiency means less labor input per commodity and therefore less value, meanwhile more spending on labor-saving, efficient machines. So the very actions that capitalists take to generate more profit create a falling rate of profit.
This theory, that increased efficiency drives down the rate of profit has aspects that are both intuitively commonsensical and aspects that seem illogical. It makes intuitive sense that the more there is of a commodity the less it is worth. It doesn’t seem to make sense that capitalists would continue to behave in ways that drove down their own rate of profit. Let’s look more closely at this process and try to unravel the mystery.
The expansion of value is the essence of capitalism. Capitalists exist to turn raw materials, tools and labor power into commodities of greater value, to sell them for money and then to start the process all over again the next day. Competition between capitalists creates a race to lower prices relative to rival capitalists. But if price were ever lowered below the actual value of a commodity capitalists couldn’t make a profit at all. The only way to lower the price of a commodity and thus out-compete a rival is to produce something more cheaply than a rival capitalist. How is this done? -By increasing the productivity of labor.
Remember, commodities’ values are equal to their socially-neccesary labor time- the amount of time it takes, in general, for a commodity to be produced under average conditions. Let’s say you are a capitalist who makes widgets and the average firm produces 10 widgets an hour per worker. But your firm only produces 5. In order to make the same amount of profit as your competitors you would have to sell your widgets at a higher price. But you can’t get away with charging more for your widgets because people will just go buy from someone else who can make them cheaper. You will be forced to get your workforce to achieve average productivity or else go out of business. You will be forced to achieve the socially necessary labor time.
Now, if you can get your workers to produce 15 widgets an hour then you are producing at under the socially necessary labor time. This means your can sell your widgets at slightly less than the average cost, outselling your rivals and getting more profit per widget than them. Whereas other firms’ widgets are worth one tenth of an hour of labor time (a worker makes 10 widgets an hour) your widgets are worth a fifteenth of an hour. But you can charge anywhere from and eleventh to a fifteenth and still undersell your rivals.
How do you achieve more efficient production? Obviously you can make your workers work harder. But you will encounter some opposition if you try to get them to work too hard. After all, workers are people with a certain level of tolerance for their own exploitation. We can assume that all of your rivals are making their workers work equally hard. Your only other option is technical innovation. If you invest in better machines, new machines, fancy computers, new conveyor belts, etc. you can make your workers more productive. And this is exactly what capitalists do all the time. This is the motor behind the dazzling technological dynamism of a capitalist society.
Once you’ve achieved a more efficient production system other capitalists are going to want to do the same. It is hard to keep technological advances secret for long. Once all of your competitors are producing 15 widgets an hour per worker the socially necessary labor time of a widget goes down. Now all widgets are worth only 1/15th of an hour. The value of the commodity has fallen, and with it the amount of profit that can be made from it. The actions of individuals competing to make a profit by producing at less than the socially necessary labor time, eventually lowers the socially necessary labor time itself, thus undermining the aggregate profit rate. (repeat this)
The rate of profit is the total profit over the total price of inputs: profit/inputs. We call the profit s for surplus value- the amount of additional value added by labor, over and above the money paid to workers for their wages. We divide the inputs into two categories: wages paid to workers, and expenditures on pre-produced commodities like machines, raw materials, factories, etc. At the time of buying one of these pre-produced commodities the capitalist pays a price representing the value of the commodity. This value is then transfered onto the final product, but no additional value can be transferred by a machine or raw material, so we call the value of these pre-produced commodities “constant” and denote them with “c”. Since the wages paid to workers are not representative of a specific amount of value that will be produced per worker, that is, since there is no way of knowing how much value a worker will produce, we call their value “variable” and denote this with “v”.
We can then translate profit/inputs into s/c+v. This is the standard equation for the rate of profit (though you will sometimes see it written as s/v/c/v.) From this equation it is easy to see that an increase in investment in either c or v must correspond to a rise in the amount of surplus value in order for the rate of profit to rise or stay the same. If s stays the same while c or v increases then the rate of profit will fall.
In our example of capitalists reducing the socially necessary labor time of widgets we saw that although some capitalists gained a temporary advantage over others through increased efficiency, ultimately the same amount of workers produced the same amount of value each hour. The value was just spread out over more widgets. In terms of our equation s/c+v this means that surplus value does not rise just because physical output rises.
What does rise is c. In order to increase the efficiency of output capitalists had to spend more on machines and raw materials. This means that the denominator in the equation is increasing. And this means a falling rate of profit.
So when people say “it doesn’t make sense that capitalists would invest in ways that drove down their rate of profit” you can now explain to them the following 3 points:
1. We see the price of commodities fall all of the time due to increased efficiency. Notice the plummeting price of digital technologies, once adjusted for inflation. This means that increased productivity does not mean increased value. The same amount of workers are producing the same amount of value. This value is just spread out over more, cheaper commodities. But for some “mysterious” reason capitalists keep racing to pump out more and more cheaper commodities, even though it ultimately undermines the rate of profit.
2. Capitalists’ decisions are not centrally coordinated decisions made for the long-term benefit of the capitalist class. They are totally anarchic, the result of thousands of individual capitalists all competing against one another for temporary, short-term market advantage. The immediate, on-the-ground pressure on an individual capitalist is to increase output per worker to achieve maximum possible efficiency without regard to the effect on aggregate values or market saturation.
3. Capitalist do not operate from a conscious labor theory of value. To them, increased physical output means increased profits. This confusion of physical output with value is referred to as “physicalism”. It is the same theoretical error that confuses many of the critics of the falling rate of profit like Nobuo Okishio and John Roemer. Both capitalists and their bourgeois theorists are stuck in a theoretical quagmire where they think the value of commodities stays the same regardless of how efficient the production process is, while it is quite obvious to any lay observer that the value of commodities is constantly decreasing with rising productivity.
There are however some counter-vailing tendencies against a falling rate of profit and it is to these counter-vailing tendencies that we will turn next.
Again, if you have your thinking cap on you may have noticed that this entire thesis of the falling rate of profit is predicated on one assumption: that capitalists will increase their investment in constant capital (c) relative to variable capital (v). The ratio of c to v (c/v) is usually called the “organic composition of capital” though sometimes you will hear it referred to as the “value composition of capital”. It should be clear by now that if the organic composition of capital rises that the rate of profit falls. But if the organic composition of capital shrinks- if v rises relative to c- this should counteract the tendency toward a falling rate of profit.
Indeed this was a major strategy in response to the crisis of the early 70′s in which the west found itself with an overaccumulation of constant capital in the form of large factories and other industrial infrastructure. By an increased use of subcontracting in the 3rd world firms were able to move production overseas to take advantage of cheaper, easily exploited labor. In many parts of Asia and Latin America there was no need to increase efficiency via constant increases in technology because the labor force, displaced from their rural means of production through deregulation in trade, was so vulnerable and exploitable.
While such investment strategies stem the falling rate of profit, they do so by expanding capitalist social relations into new areas on the periphery of capital. In so doing they don’t resolve the contradictions implied in the falling rate of profit, they merely displace these contradictions in space by bringing more people and spaces into the system. In doing so all sorts of disequilibriums are created in the fabric of capitalist space. The eventual rise to economic power of some areas of the periphery has much to do with the current disequilibrium of international capitalist relations.
A second way of stemming the falling rate of profit has to do with decreasing the value of constant capital. If the race to improve efficiency is cheapening all commodities we can expect the costs of inputs like machines and raw materials to fall as well. This allows capitalists to increase the physical amount of technology they use without increasing the value of constant capital. Unlike the previous “fix” which displaced crisis in space, this “fix” is part of the internal logic of capital and, some argue, could very well be a permanent fix.
What should be added though is that many production technologies involve very large investments in fixed capital. Fixed capital is constant capital that is fixed in space like roads, bridges, damns, factories, skyscrapers, enormous machines, etc. An enormous investment in fixed capital commits the investor to the long term use of this fixed capital, preventing the capitalist from switching to new, cheaper constant capital. The turnover time of fixed capital investments can be several years to several decades, as the capitalist waits for the cost of a new building or road to pay itself off. Thus the “fix” provided by the falling value of constant capital is neutralized in the case of fixed capital investments. The longer an industry has been around, the more automated production tends to be, so there is a tendency toward increasing investments in fixed capital.
The problems of turnover time in fixed capital investments are often overcome through the credit system. By borrowing money for investments, or borrowing money in expectation of future revenues, capitalists can get the money they need now, instead of waiting decades for an investment to pay itself off. In this way the credit system creates a socially necessary turnover time which equalizes turnover time across industries allowing industries with massive fixed capital investments to stay competitive with more labor-intensive industries. This also means that the crisis of overproduction of constant capital and the subsequent falling rate of profit are displaced in time and transferred to the credit system.
And this takes us back to our starting point. If capital can make good on all of it’s credit- if it can turn all of its investments into real value, we are safe from crisis. But if capital can’t generate enough profit relative to its investments, if technological change destabilizes value creation in one way or another we get crisis in the form of bubbles of credit which can’t find value, massive factories which can’t make a profit, shelves of commodities that can’t be sold and masses of workers without jobs. The theory of the falling rate of profit provides a starting point for analyzing how all of these factors are inter-related. While there are countervailing tendencies away from a falling rate of profit, many of them are mere displacements of crisis which merely postpone crisis, bottling it up to breakout with increasing violence when it can no longer be contained. We must also remember that there is no centrally coordinating body in a capitalist society to manage investments in a way that stabilizes the rate of profit. We are almost ready to begin an analysis of the way these abstract forces have evolved historically to land us in our present state.
Limits to Capital, by David Harvey
Reclaiming Marx’s Capital, by Andrew Kliman
Class, Crisis and the State, by Erik Olin Wright
An Introduction the History of Crisis Theory, by Anwar Shaikh (from U.S. Capitalism in Crisis)
Thanks for the videos and commentary, am reposting the videos on my blog with a link to your blog post.
[...] Full Text can be read at: http://kapitalism101.wordpress.com/th… [...]
The video was very good, it definity explained the Falling Rate of Profit pretty clearly. Since the last video Ive basically came to your conclusion that while C and V can fall, ultimately S can be eliminated through complete automation so it holds true.
One thing Im curious about is your idea about Capitalism being decentralized. Capitalism since its conception has generally headed in a more centralized direction from the State Monopoly Capitalism prior to WWI to the Social Democratic/Liberal parties of Europe and the US. Couldnt an alternative system ran by Capital like Monopoly Capital as purposed by Sweezy or State Capitalism as purposed by Left Communists counter the devistating affects of the Falling Rate of Profit or a Credit Crisis?
[...] The Falling Rate of Profit « Kapitalism101: [...]
I just wanted to run this by you as it appears that the falling rate of profit could be countered by this as well, but in doing so create a new contradiction which could bring the class struggle to its conclusion.
If we assume an original rate of profit of 100s/(100c+100v) and a new rate of profit after innovation of say 100s/(300c+100v) then the profit rate has fallen from 50% to 25%. In both cases the amount of value created by workers is 200 units of value, but if workers are a variable input, shouldn’t they have the ability to produce more units of value? So through education and training, workers could produce say 400 units of labor and assuming a consistant rate of surplus value of 100%, the new rate of profit of 300s/(300c+300v) leds us back to 50% profit rates. Assuming that humans are as variable as Marx claims (as social creatures, excluding biological necessities), this could solve the falling rate of profit.
One counterargument might by the social division of labor, but according to David Harvey this doesnt hold. The point of capital is to destroy monoploy skills and create a work force with non-monopoly skills, this doesnt mean the destruction of all skills and even allows for the spread of non-monopoly skills. If this is the case, then a division of labor can incorporate intelligent workers.
This would go along with Marx’s prediction that capitalism tends to destroy old ways of thinking as it evolves, thus showing us its progressive nature as a historical epoch. Also it would offer new tools to the proletariat in terms of understandings its place in society, it would have a better chance of overcoming reification and seeing capitalism as it is. The destruction of reified consciousness would allow the proletariat to see not only through capitalism, but also through reactionary anti-capitalisms (Nazism, Leninism, Religious Fundamentalisms etc.). With these tools at hand, they could begin to challange capital and alienation as well as construct a socialist society.
Interesting article. Keep up the great work. Thanks again, Jase
http://www.isreview.org/issues/64/feat-moseley.shtml
prof. fred moseley on the falling rate of profit in the US and the current crisis. he also mentions the long-term rise in ‘unproductive labor’ in the US economy as another factor weighing down the rate of profit.
Slight error here: It is not “s/c+v” but “s/(c+v)”.
Good point. I’ve always been sloppy with math. If only I could figure out how to write the equation vertically on my computer….
Awesome work, thank you. I had a question. How do you reconcile the tendency for the rate of profit to fall due to increasing costs in constant capital with the historical increase of profits observable after the 1970s? I am aware that attempts to boost the rate of profit such as cutting social benefits, cutting wages, outsourcing to low-waged areas of the world, and other such reforms played a significant role, but do these things alone explain the steady growth of profit?
[...] book Reclaiming Marx’s Capital. Kliman talks about some of his work with the theory of the Falling Rate of Profit, criticizes some of the other theories of crisis floating around in the left today, and discusses [...]
was the place displacement Harvey? Or did Marx already come up with that?
By which you mean displacing crisis in space? This idea exists in embryonic form in scattered passages of Marx but it really is developed fully by Harvey.
ok, when technology develops to the degree that allows for more output per worker and less need for money into labor, this means that the rate of profit falls after competition reduces prices so that in order to compete, industries must sell commodities at the lowest possible price while making a bare profit? and despite increased output of goods, the coercive competition makes such output inefficient and forces capitalists to reinvest to make more money?
yes.
Is this ever criticized for being difficult to empirically prove? what’s the ‘vulgar economist’ explanation for that effect besides being good for consumers?
re: empirical proof. Andrew Kliman has just put out a paper which I think does a good job of making the empirical argument for the falling rate of profit. It is called “Persistent Fall in Profitability Underlying the Current Crisis” and can be found his website: http://akliman.squarespace.com/crisis-intervention/
I think he makes a good case for the empirical proof, but he does qualify this by saying that the sources for his statistics- bourgeois accounting practices of government agencies- are not Marxist enough in nature to form some sort of ultimate proof. But he makes a good case. It’s not an easy read if you don’t have some theoretical background and the patience to make your way through some tricky equations and graphs.
Kliman is also critical of some past attempts to track profit rates like those of Anwar Shaihk in Shaihk’s paper “The Falling Rate of Profit as the Cause of Long Waves: Theory and Empirical Evidence” at his website http://homepage.newschool.edu/~AShaikh/
It’s interesting to see that even Marxists who agree on the empirical strength of the FRP disagree on what constitutes valid empirical evidence. I am sympathetic to Kliman’s take.
What would be proof that is ‘Marxist enough’ ?
The problem comes in actually being able to decide which figures compiled through bourgeois accounting practices most accurately approximate Marx’s categories of value, surplus value, etc. Because price can diverge from value it makes it difficult to find some empirical measure that’s anything but an approximation. Marx himself criticized the idea of “proving” the labor theory of value. For him there was no such thing as a proof of the LTV. This doesn’t mean that we can’t consider how well, or not well, the LTV describes society. It just means that there will never be some sort of absolute empirical proof. No economic theory can have this. All we can do is show empirical correlation between difference phenomenon.
Is there an alternate explanation for the effect of the FRP in neoclassical economics, or is it completely ignored?
Prior to Marx there were classical, bourgeoise economists that had theories of crisis, probably the most notable being Malthus’s theory of population-caused crisis and Ricardo’s theory that attributed falling profits to declining returns on agriculture.
In the modern, credit age it’s harder to see the falling rate of profit as it is papered over by credit bubbles and the like. Keynes is one of the few bourgeois theories of crisis- his is based on lack of effective demand and was fashioned as a critique of the prevailing neo-classical views of his time. The Austrians also have a crisis theory based interests rates that blames bankers and goverments for everything. Neither Keynes nor the Austrian theory actually looks at a falling rate of profit. They are instead focused on other forms of appearance of crisis: lack of demand or credit and investment flows…
Besides crisis theories, they have no recognition of the theory of FRP, because they also have no belief in LTV?
And Marx’s FRP needs LTV correct?
i find it so hard to believe that as sound as LTV is, there is no way to prove it which would validate Marxist inquiry
Are there non-empirical tenants that are taken as truth in neo-classical thought that are equally difficult to prove in the sense that i am looking for, or is it just LTV?
I think neoclassical price theory is even harder to “prove” empirically as the notion of price is explained purely through psychological factors. Because there are no quanta of desire to measure they basically just take price as a given and refuse to look behind it.
I have not studied any empirical attempts at proving the LTV. It’s hard for me understand how it could be done, so I’d be curious to learn more about them. But I think that common-sense knowledge confirms the LTV: the social labor process is coordinated through commodity exchange. We wouldn’t be able to have a complex division of labor coordinated thru markets if there wasn’t a correlation between value and price. If people stop buying toothbrushes less labor would go into making toothbrushes. If humans beings stopped working tomorrow there would be no commodity exchange. This doesn’t happen if you take away machines or money. We can still have commodity exchange without those things. When efficiency rises prices fall, some times even to zero. These sort of common-place observations, I think, are why Marx said that the entire notion of proving the LTV was an unnecessary, misguided mistake.
Geoff Taylor wrote:
“i find it so hard to believe that as sound as LTV is, there is no way to prove it which would validate Marxist inquiry”
Since the early 1980s there has been quite a substantial body of empirical work on the scientific validity of the LTV.
See for instance, http://reality.gn.apc.org/econ/Zachariah_LabourValue.pdf
There is a lot to be said on these matters that is not so easy to convey over a blog comment. But here are to important points:
1. Empirical “proof”. This implies a misunderstanding or conflation with mathematical proofs. In contrast, scientific theories are not proved or disproved but empirically validated or falsified on the basis of their testable claims.
The LTV, unlike the marginal utility theory of value, makes testable claims and to most peoples’ surprise turned out to be validated in the 1980s.
2. I think the first part of “101s” recent comment is correct but then I think he goes off in a wrong direction regarding the strength of the claims that the LTV actually makes. It is that the material basis of economic value is social labour:
Consider a pizza and a laptop, and suppose for sake of argument that they require 1 hr and 10 hrs of social labour to reproduce, respectively. Then what can we say about their prices? The LTV makes a testable prediction: the laptop will cost approximately 10 times more than the pizza.
So a question that immediately arises is: how does the distribution of price-to-value ratios ($/hr) look for all goods across the US economy. Once the question is put on that terrain you have opened up the LTV for scientific inquiry.
What one finds then is that the LTV holds in a statistical sense, the distribution is quite narrow, i.e. price and value is highly correlated. Thereby validating a claim going back to Ricardo.
and that’s all in your dissertation abstract thing above?
But, in terms of empirical analysis, if profits are equalized all you could ever prove is that prices equal production cost plus average profits. How is this empirical proof of the LTV?
Forgive me/ correct me if I am missing something. I have not read the works you’ve linked above and have not studied this issue at all.
The short answer is that the idea of equalized profit rates is a myth. Moreover, by clinging on to this myth generations of Marxist economists have fallen into the depths of the transformation problem and effectively giving up efforts on a Marxist economic research program.
The idea that one can assume equal profit rates is theoretically untenable as Farjoun and Machover demonstrated. Furthermore, it is empirically false, and the conclusions one draws from such an assumption are tentative at best.
But if one abandons this myth and investigates what merits the LTV has on its own basis it turns out that many of Marx’s predictions in Volume 1 hold up quite well in a strong statistical sense.
This, by the way, is some thing you ought to popularize in the same excellent way you have done previously. Which is why I recommended Farjoun and Machover’s book “Laws of Chaos” to you some time ago.
Interesting. I’ll have to read all that at some time. Thanks for recommending the books again. So much to read! So many videos to make!
Dave Zachariah gives the impression here that the studies he talks about test whether “the laptop will cost approximately 10 times more than the pizza.” This isn’t true. They don’t and can’t test that.
Zachariah confuses and conflates correlation coefficients and measures of price-value deviations (“the distribution is quite narrow”) here. I wonder if this is intentional. In any case, they’re not the same thing. His statement that “the distribution is quite narrow, i.e. price and value is highly correlated” is false. Measures of deviation imply *nothing* about the degree of correlation.
Let me also mention that the measures of deviation data really doesn’t tell us anything because the studies in question rely on very aggregated data (i.e., lots of small industries are bundled together into fewer ones). The aggregation systematically reduces the size of the deviations. Imagine that we have 9 industries of equal size, and the percentage deviations of prices from values are
-70 60 40 80 -40 -80 10 -90 70
The average percentage deviation (if we take absolute values, i.e., turn minuses into pluses) is 540/9 = 60.
But let’s now aggregate them into 3 bigger industries, the first 3, the second three, and the third three. We get the following percentage deviations of prices from values:
30 -40 -10
The average percentage deviation (if we take absolute values) is now only 80/3 = 26.7 — which is less than half of what it was.
Elementary probability theory would immediately recognize that a degenerate distribution of Z = X/Y implies perfect correlation of X and Y.
“Probability wrote: “Elementary probability theory would immediately recognize that a degenerate distribution of Z = X/Y implies perfect correlation of X and Y.”
I presume this is meant to be response that challenges my statement that “Measures of deviation imply *nothing* about the degree of correlation.”
If all of the Z’s are exactly equal, the distribution of Z’s is degenerate, which makes the measure of deviation of the Z’s = 0. “Probability” is suggesting that this implies that the X’s and Y’s are perfectly correlated.
First of all, that’s a very special case. Second of all, it isn’t true. If all of the X’s are equal and all of the Y’s are equal, all of the Z’s will be equal, but the correlation coefficient can’t even be defined in this case.
This may seem to be a case that’s too special to consider, but it wasn’t I who started with the special cases. Also, the actual facts of the matter in the case of price-value deviations, aren’t far from this special case: per dollar of cost, prices (X) don’t differ much across industries and values (Y) don’t differ much. So the distribution of Z’s, the ratios of prices per dollar cost to values is pretty narrow, and this results in a small numerical value for the price-value deviations. But there isn’t a statistically significant correlation between the X’s and the Y’s. (See the final section of Chap. 11 of _Reclaiming Marx’s “Capital.)
Here’s a simple example that confirms the accuracy of my comment that “Measures of deviation imply *nothing* about the degree of correlation.” I was pointing out that Dave Zachariah’s was wrong to conflate the two, which he did when he wrote that “the distribution is quite narrow, i.e. price and value is highly correlated.”
Industry 1: price = 0.99, value = 0.99
Industry 2: price = 1.00, value = 1.02
Industry 3: price = 1.01, value = 0.99
The distribution of price-value ratios is quite narrow, ranging from 0.98 to 1.02 (and accordingly, the means absolute percentage deviation is just 0.01). But the correlation coefficient is 0. Zero. Efes. Nada.
Elementary probability theory would immediately recognize the direction of implication: a degenerate distribution of Z = X/Y implies a perfect correlation of random variables X and Y. The smaller coefficient of variation of Z = X/Y, the closer is the approximation Z = X/Y ~ E[Z]. From this it is trivially seen that a narrower distribution of Z = X/Y implies an increasing correlation between X and Y.
Elementary probability theory would quickly recognize that in the given three realizations of Z, what is perceived by an untrained eye as ‘quite narrow’ in absolute terms is in fact a high dispersion in statistical terms: Z’s coefficient of variation is greater than that of Y and about twice as high as X. Maintain the variances of X and Y and let the variance of Z progressively fall to see what happens to the correlation coefficient… Numerical examples cannot move the laws of algebra.
“Probability” wrote: “Elementary probability theory would immediately recognize the direction of implication: a degenerate distribution of Z = X/Y implies a perfect correlation of random variables X and Y.”
No. As I noted, there is no correlation, the coefficient can’t be defined, if all X’s are equal and all Y’s are equal. So the implication claimed here doesn’t exist. “Probability” hasn’t dealt with that point.
“Probability” also wrote: “what is perceived by an untrained eye as ‘quite narrow’ in absolute terms is in fact a high dispersion in statistical terms: Z’s coefficient of variation is greater than that of Y and about twice as high as X.”
This is a diversion. Dave Zachariah wrote, ““the distribution [of price-to-value ratios] is quite narrow, i.e. price and value is highly correlated.” His claim has to do with the distribution of the Z’s, the price-to-value ratios, not with their distribution *compared* to the distibutions of the X’s and Y’s. In other words, he was saying that you can look at *just* the distribution of the price-to-value ratios, declare them to be small, and therefore conclude on that basis alone that the X’s and Y’s are highly correlated. That is simply false. Right, “Probability”?
Elementary probability theory would recognize that correlation is a more general concept than the Pearson correlation coefficient. If X and Y are not stochastic varibles but assumed to be constants instead, the covariance — central to the definition of the correlation coefficient — is still defined and is equal to zero. Of course, any undergraduate would immediately recognize the irrelevance of this case for the implication under consideration, namely the distribution of Z = X/Y when X and Y are stochastic variables.
Elementary probability theory would also recognize that ‘narrow’ is not a probabilistic concept but a descriptive word from everyday language that only has a meaning in relative terms when comparing measures of dispersion with other random variables or as a non-stationary random process. Indeed, if one bothers to scan Mr. Zachariah’s paper for instances of ‘narrow’ Z, it is mentioned in relative terms and the estimated coefficients of variation for several stochastic variables are clearly displayed in several tables for comparison.
Mr. Zachariah’s claim still holds even if expressed simplistically in this forum. Narrower distribution of Z = X/Y implies stronger correlation between X and Y. It follows from the laws of algebra.
The assertions made by Mr. Kliman in this forum, however, puts serious doubts on his mathematical skills. For the sake of his publisher one genuinely hopes that Mr. Kliman has not reproduced arguments like these in his book. They would not pass the standards of a peer-reviewed scientific journal.
If you find the article above too technical I would suggest that you only read:
Section 1: Introduction.
Section 2.1: Value bases and the peculiarity of labour
Section 3: Conclusion
They will give some key ideas.
Keep up the good work of popularizing Marxist economics!
Typo: That should be the final Section 5: Conclusion.
I am really impressed by all the work you have done on this website. I am a graduate student in Economics and am currently writing a paper on the FRP. Your help in the matter was invaluable- I didn’t quite understand Kliman and Freeman’s critique without the help of your interpretation. You make a very coherent argument using all aspects of Marx’s foundational thoughts of LTV. It has been a long journey trying to gather all of Marc’s thoughts on the matter, which also evolved as he explored the FRP more intensely.
Anyways, I am curious what your thoughts are on the Okishio Theorem, that suggests that FRP is not possible if Marx implied real wages were constant?
Mary,
Thanks for the kind words about the site. I am curious what graduate program allows its students to engage in such dangerous and subversive theory.
I am convinced by the TSSI argument that the Okishio theorem only applies to models where Input and Output prices are forced to remain the same. Marx’s theory is not such a theory. It is a dynamic theory of change over time in which output prices reflect the value created in production. The Okishio theorem can only measure a physical rate of profit. It cannot measure a value rate of profit. Have you read Kliman’s book?
Hi Mary,
I could point to some up-to-date theoretical and empirical research on the theory of average profit rate is you wish.
I think the objection by Kliman and Freeman is misplaced. The Okishio Theorem compares two *static* cases: both with equal flow profit rates and real wages. In this scenario the average flow profit rate will *rise* due to technical change. The Okishio Theorem is mathematically correct. Its empirical validity then rests on its assumptions.
While I think the impetus of the so-called TSSI school to formulate a dynamic, rather than static, mechanism of price formation is correct, the resulting theory is very weak in my view. See my comments here:
http://ricardo.ecn.wfu.edu/~cottrell/OPE/archive/0711/0217.html
My e-mail is also shown in the link if you want me to send you some references.
Hey! Ive seen most of your videos and I am pleased to see a simple and understandable account of Marx’s theory. There is just one thing I dont seem to grasp on the whole theory.
When Marx says that the rate of profit and wages will fall, does he mean in value-terms or real-terms?Otherwise said, would the VALUE of the commodities produced in a capitalist economy fall or will the NUMBER of commodities itself fall?
The reason I am asking this is that I cannot see how increasing capital can lead to lower profits on the long-run. Would not the increase of capital make labor more productive, increasing the output the economy and reduce the prices of commodities?
If this is so, then the LABOR VALUE of the output of the economy would be reduced, but the actual output (cars, pencils, shoes…etc) would increase. So wouldn´t capitalist experience a stable, if not rising rate of profit expressed in real terms (get more yatchs, more suits and more cars?) If not, who is enjoying this increase in productivity?
Andy. This is a good question which gets at the heart of what “value” is in a capitalist is economy. Capitalism is not a system which is based on just the use-value of things. If it was, things would be fine. Capitalism is able to produce an extraordinary amount of use-values- real, physical items. Even poor people have way more cell-phones, cars and gadgets than the rich people of the middle ages. Yet we still call them poor. Why? Because in a capitalist society we measure wealth not in physical quantities of commodities but in value terms: in quantitative amounts of abstract value, abstract social power, social labor. When the products of labor come to be represented as distinct quantities of exchange value (money prices) then there is a specific qualitative change in the organization of social life.
In terms of crisis theory this all means that there is a contradiction between the need to increase efficiency and the need to exploit the working class. Capital exploits labor by getting more value out of the worker than it pays in wages. But it increases productivity by minimizing the amount of labor that goes into a commodity. Yet competition among capitalists lead capitalists to try to out exploit each other by increasing productivity. As capital expenditures on machinery and other labor-saving innovations increases, less and less capital is actually going into wages. Less value is produced relative to expenditures. This means a falling rate of profit.
Does this make sense?
Doe it mean that capital only adds to costs?
Yes and no… What I fail to see is how an economy becoming more and more productive can experience a fall in profits AND wages at the same time. Who is getting all the stuff?
If what Marx argues is that profits and wages fall in VALUE terms but not in “real” terms, then it makes sense.
But if that is not the case, the only way I can make sense of it is by assuming that capital-cost will choke any gains in productivity. Otherwise put, in the long-run all the economy will be devoted to reemplace its own capital instead of creating more consumer goods. Then both “real” wages and profits can fall together (less stuff is produced).
But if that is the case, would not a general increase in productivity also make capital cheaper and easier to reemplace?
First, don’t worry about the wages. The wages could stay the same or shrink, or even rise slightly, and not effect the Falling Rate of Profit. In his analysis of the FRP Marx assumes that wages stay the same (that the rate of exploitation stays the same.) The total amount of physical commodities is growing and the total amount of profit is growing. But the cost of producing that surplus is growing faster than the profit grows. Therefore the RATE of profit is falling. Increasingly larger and larger amounts of capital produces smaller increments of profit growth.
Your last question is a good one. The shrinking cost of inputs into the production process through increased efficiency is what Marx calls a “countervailing tendency” which checks the fall in the rate of profit. There are other ones too. Yet, over the long run he didn’t think this countervailing tendency was sufficient to halt the FRP. For one, it creates temporal imbalances between firms or countries that modernize production at different periods. In this video (or maybe it’s my “Crisis! The Overaccumulation of Capital” video) I give the example of Detroit to illustrate this point. Even more fundamentally this countervailing tendency comes from the same source as the main tendency: the movement to replace human labor with machines. As the surplus rises it is forced to invest itself in less and less percentages of labor, more and more machines. This is a result of the inevitable nature of a rising amount of total surplus value. There is only so much labor in the world, yet the rising total surplus must try to squeeze more and more value out of it.
Andy wrote: “What I fail to see is how an economy becoming more and more productive can experience a fall in profits AND wages at the same time.”
I think this is somewhat confused. Profits P can certainly be rising while the profit *rate*, P/K, where K is the capital stock, can be falling at the same time. It is precisely this *rate of return* that Marx’s theory concerns.
If productivity is raising then for a given amount of labour the net output will increase, and which is split into profits and wages. So, in general a productivity rise will increase profits, but may or may not lead to a lower profit *rate*.
Marx gives some conditions for when it will fall, although I think his theory is slightly obscure and can be cast in much more rigorous terms today.
So, for example, lets assume that a factory produces 10 “commodity X” who sells for 10$ each, assuming that wages are 10$ and Capital Costs are 10$ then profits are:
(10×10)-(10)-(10)=80$
So, what Marx is implying is that when adding more capital, the VALUE of the commodity output remains the same while costs incerease so now the price is 2$ the quantity is 50$ and Capital Costs are 30$:
(2×50)-10-(30)=60$
Im I getting this right?
What I meant by (2×50) is that there are 50 comodities produced but at a price of 2$
Yes. This is the idea.
Now from an individual point of view you might wonder why a capitalist would spend more on inputs when they are getting the same amount of output in value terms. The answer lies in distinguishing between what is true for the individual and what is true for the aggregate. Individual capitalists compete to increase their profits above the social average. They do this be increasing efficiency which means producing more output per hours worked. When they produce under the socially necessary labor time they still get to sell at the socially necessary labor time. This means they get a super-profit, a profit above what they actually contribute to society. But in the aggregate, as all capitals do this, this means that less and less value is being produced relative to capital inputs.
Ok, then I think I got it. Just one thing, when I see your calculations, I see you dividing the surplus value by wage and capital costs instead of substracting them… Why?
Sorry its me… again. I am still a bit confused so bear with me, please!
Ok, so the Rate of Profit is equal to profits divided by total investment, profits only come from workers being paid less than what they produce, capital only increases the productivity of the worker but in itself produces nothing. Ok then:
Marx expresses the rate of profit as s/(v+c)
s = profits or surplus value
v = wages
c = capital
But s can also be represented by the wage multiplied by the rate of exploitation +1 so we could rewrite the equation as:
(VxE)/(V+C)
Where E equals the rate of exploitation +1
So, lets assume that:
Wages are 50
Capital is 10
And the rate of exploitation is 100% (so E=2)
(50×2)/(50+10)= 100/60 = 1.67 or a rate of profit of a 67%
Now, Marx point is that an increase in capital, say from 10 to 20 will bring rates of profit down:
(50×2)/(50+20)= 100/70= 1.43 or a rate of profit of 43%
Ok then, but the above is expressed in VALUE, not in PRICES. I might be (probably am) mistaken about this, but should not we have to compare the two profit rates in the context of the prices each of them generates? The first rate of profit is higher, but so are the prices produced in that economy. The second is lower, but so are the prices under more capital.
I’m not following you on this last point. We aren’t talking about 2 different economies, but one economy at different periods in time. As total rate of profit in value terms declines so does total amount of profit in price terms. Price levels can be inflated above value levels, but only through expanding fictitious value, ie. credit bubbles which eventually pop.
I might be misunderstanding the FRoP theory, but what it seems to me is that its saying this:
The economy is like a pie which is divided between capitalists, workers, and machines. Capitalists get surplus value, workers wages, and machines dont produce anything but must be fixed, oiled, cleaned, repaired, reemplaced etc…
But because workers are more productive using machinery, the more mechanized an economy is, the larger the pie itself becomes.
In other words, the FRoP means that capitalists will get an increasingly smaller portion of the pie vs machinery.
My point is that yes, it is a smaller slice OF A BIGGER PIE. Should we not try to compare them both in absolute terms? Are not capitalists, in commodity terms getting richer?
That is what I meant by lower prices, a bigger pie manifests itself in lower prices
I see your point and I think it is an important one to clear up. I’m going to post a few paragraphs from my yet unposted summary of Part 3 of VOl. 3 of Kapital. I’ve been so busy that I haven’t had time to edit these blog entries and post them.
As with everything in Marx, it is the relative proportions not the absolute magnitude that matter. The absolute magnitude of surplus value is always growing. This is what M-C-M1 tells us. Money is invested in production and it creates more money. This “more money” must be reinvested in larger proportions. Thus capital accumulates. Thus the total mass of surplus value is always growing. In the course of this accumulation capital is concentrated in larger and larger fixed capital expenditures. Capital is concentrated and centralized. There is a finite amount of labor to be employed, but there is an infinite amount of constant capital that can be added to this capital expenditure over time. The only limit is the falling rate of profit. It’s not that less labor is being employed. The absolute mass of laborers employed increases as capital brings more and more of the mass of humanity under its power. But in relative terms, in relation to the total capital expended on production, the amount of labor employed decreases. Marx is so emphatic on this idea of a rising mass of surplus value and a falling rate of profit that he repeats it over and over in different versions throughout part 3.
and later:
his law of a falling rate of profit is a “double edged law” because while the rate of profit is falling the total mass of profits rises. Thus there is an incentive to raise the organic composition of capital in search of this additional surplus value even though less and less profit is squeezed out per capital. In other words the percentage of surplus gained from, say, $100 in invested capital is less and less. Viewed from the perspective of this percentage per $100 of investment it doesn’t make sense why capitalists would raise the organic composition. But if we look at the amount of profit on the total capital invested we see greater and greater masses of profit arising from greater and greater investments in capital. If the profit is falling capital requires greater and greater masses of capital investments in order to attain the same or greater mass of profit. The compulsion to accumulate inherent in M-C-M1 acquires an even greater sense of necessity and scale when we realize that investments must increase in size in order to compensate for a falling rate of profit.
and later:
A similar process can be observed in the prices of commodities. As productivity increases the individual commodity becomes cheaper and cheaper because it contains less and less labor. Yet the mass of profits increase. Why? Though each commodity contains less labor, the ratio of surplus labor to necessary labor (labor which goes into reproducing the value of the wage) rises.
and:
Thus we can see the same forces that cause the falling rate of profit in the falling prices of commodities. However we can’t calculate the falling rate of profit just by looking at the proportion of c to v to s contained in a single commodity. This is because the rate of profit is calculated on total capital expenses including fixed capital that does not enter directly into the price of a commodity. C does not equal k. Cost price is not the same as total capital invested.
And from my notes on chapter 15:
As the social productivity of capital grows the minimum amount of capital required for a producer to actually produce at the socially necessary labor time grows. Smaller capitals are crowded out of the market or confined to marginal sectors of production. Even though these larger capitals have a lower real rate of profit they amass a larger amount of surplus value. We’ve heard this all before, but Marx takes the argument in a new direction. This accumulation eventually leads to overproduction of capital. This overproduction doesn’t just mean over-production of commodities (although capital does take the form of commodities and so this can manifest itself as overproduction of commodities) but of capital in general. It is an overaccumulation of capital. Harvey uses this term “overaccumulation” to characterize capitalist crisis. (I have reasons to agree with Harvey’s preference for “overaccumulation” as well as some criticism, but again I’ll save this for later.) What does overaccumulation mean? It means the same thing Marx has been saying all along: a rising mass of surplus value with a shrinking pool of profitable alternatives to employ this capital. At some point this mass of capital grows to such a size relative to the rate of profit that the amount of surplus value produced is the same or less then that mass of capital. This is when a crisis breaks out. This is not a crisis of a particular industry, not a business cycle, but an all-out crisis of the system.
I hope this may help. I agree that it is a tricky topic to wrap one’s head around. I wish that my initial FRP vidoe had done a better job of making these things clear.
Andy, consider the following example when the annual profits P earned *rises*, from one year to another:
$100 $200 $300 $400
In other words a capitalist firm is earning greater profits in absolute terms. But suppose that the stock of capital K it has invested also rises:
$1000 $4000 $9000 $16000
Then the *rate of profit* per annum P/K falls:
10% 5% 3.3% 2.5%
In other words, the mass of profits can rise while the rate of return on capital invested is falling. It is the latter term that we take as a measure of profitability and is relevant to the investment decisions taken by firms and hence the trajectory of capitalist economies.
Dave Zachariah (Dec. 15, 2009, above) wrote:
“I think the objection by Kliman and Freeman is misplaced. The Okishio Theorem compares two *static* cases: both with equal flow profit rates and real wages. In this scenario the average flow profit rate will *rise* due to technical change.”
I responded to similar retroactive efforts to absolve Okishio and the physicalist tradition of error in _Reclaiming Marx’s “Capital”: A refutation of the myth of inconsistency_, pp. 135-36:
“I noted above that Foley has come to accept the substance of the temporalist disproofs of the Okishio theorem. Yet he refrained from drawing the conclusion that the theorem is false, because “I personally think Okishio thought he was stating and proving” that the physical rate of profit cannot fall unless real wages rise (Foley 2000b: 281). Laibman (2000: 275, emphases in original) defended the logical status of the Okishio theorem in the same way, though more forcefully: “If a viable technical change is made, and the real wage rate is constant, the new MATERIAL rate of profit must be higher than the old one. That is all that Okishio, or Roemer, or Foley, or I, or anyone else has ever claimed!” In other words, the proponents of the Okishio theorem have always been talking about the simultaneist rate of profit, and nothing else. They have simply told us how the rate of profit would behave in the imaginary special case in which input and output prices happened for some reason to be equal.
“I find all of this extremely implausible, to say the least. As Freeman and I noted in our rejoinder (Kliman and Freeman 2000: 290), these claims seem simply to be “an effort to absolve the physicalist tradition of error.” The LTFRP is clearly not based on an imaginary case in which input and output prices are equal. In his presentation of the law, Marx (1991a : 332–38) analyzes the fall in prices resulting from productivity growth at considerable length. Moreover, the law clearly assumes continuous technological progress (Marx: 1991a: 318–19), a factor that continually counteracts any tendency of input prices and output prices to equalize.
“Let us therefore ask:
• Could Okishio have intended his theorem to refer exclusively to what would happen under imaginary conditions that differ so radically from those that Marx’s law assumes?
• Could he have thought that such a theorem had any bearing upon the LTFRP, much less that it constituted a refutation?
• Have commentators throughout the last three decades really been claiming that failure to accept such an irrelevant theorem as a definitive refutation of the LTFRP “has done much damage to the intellectu-al credentials of Marxian political economy”? (Howard and King 1992: xiii).
• Have Brenner (1998: 11–12, n1) and many others really invoked the Okishio theorem as “proof[ ]” that Marx’s theory of the falling rate of profit is false, while knowing perfectly well that the theorem is irrelevant?
• Have the commentators really been claiming that the LTFRP deserves to be “relegated to the dust bin of history” (Hahnel 2005:58) by a theorem that pertains only to a different rate of profit from Marx’s?
“Here is a far more plausible explanation. Okishio and others set out to prove a theorem on Marx’s actual LTFRP. They noted that he had assumed the re-establishment of an equilibrium rate of profit after a technological innovation occurs. They recognized that the tendency of prices to adjust to their equilibrium levels is what gives rise to the tendency of rates of profit to equilibrate as well. They then concluded, reasonably but wrongly, that if an equilibrium rate of profit is to be re-established after a technological change, an “equilibrium” price level (the equality of input and output prices) must also be achieved. This error then went mostly undetected and uncorrected––and later, the corrections were ignored––probably because of factors such as ignorance, physicalist intuitions, political opposition to the LTFRP, the quest for academic respectability, etc. And all along, everyone has understood that “the equilibrium rate of profit cannot fall” refers to Marx’s equilibrium rate of profit.
“Yet even if we suppose, for the sake of argument, that the Okishio theorem was not originally meant to be a theorem on Marx’s rate of profit, that is certainly what it is now, for that is how it is now understood. And as a theorem on Marx’s rate of profit, the Okishio theorem is simply false; the recent debates have made this clear. The record should be set straight, and Marx’s critics should do their part to help set it straight.”
One more comment. In _Through the Looking Glass_, Humpty Dumpty says, “in rather a scornful tone”:
“When I use a word, it means just what I choose it to mean––neither more nor less.”
When he had a great fall, and broke, and all of the king’s horses and all of the king’s men couldn’t put him back together again, he got what he deserved.
Hi Andrew,
The mathematical proof for the Okishio Theorem, with all of its assumptions, is valid. But we should rightly question the empirical validity of the assumptions and hence the relevance of the result.
I think there is a central problem with your project, which becomes clear in the second part of this sentence:
“The record should be set straight, and Marx’s critics should do their part to help set it straight.”
I think this is an illusion and what leads the project to be ultimately a waste of effort. Suppose for a moment that we one day found a text by Karl Marx in which he clarified all ambiguities in a straight-forward way.
Who would seriously expect that bourgeois economists or Marxist critics would suddenly praise Marxist political economy and “help set the record straight”? It is an illusion to think that the economics discipline operates like a normal science.
Dave, I am fairly content to sit back and enjoy just watching the dialogue between you and Andrew unfold. However on this most recent point about disproving Marx’s critics on logical grounds as a waste of time I have to add my two cents. For me, the value of the TSSI work is in allowing Marx to be approachable by myself and other newcomers to the theory without having to worry all the time about which parts of it are no longer “acceptable” economic theory. When I first began the personal study that later became this blog I didn’t start with Marx. I began with 20th century Marxists. I did this specifically because I knew that there was this thing called the transformation problem that had supposedly rendered parts of Marx’s work untenable. I felt that to start off reading Marx would be a waste. I wanted to situate Marx in modern terms, to understand modern interpretation of value theory, before I plunged into reading a ton of Marx.
After reading Andrew’s book I changed my mind. In fact I felt like an asshole for spending all this time reading about Marx w/o really reading that much Marx. I think the idea of letting Marx “speak for himself” is really crucial right now in the context of an economic and ideological crisis of capitalism. In such times we need a social theory that is capable of interpreting and critiquing the dominant order. I’m flattered to have academics even look at this blog let alone post here, but really I am not making these videos to change the minds of academics. I think a popular revival of Marx’s value theory is crucial if we are to reconstitute a left in any form and I hope that this blogging project can contribute to that. This popular audience is very interested in whether or not Marx’s theory of value is logically coherent. The #1 response I get from viewers is that Marx’s theory has been “discredited”. Yet, 90% of them don’t even know what argument they are referring to by this. This idea that Marx’s value theory is logically invalid is deeply entrenched in our culture.
You wrote:
“This popular audience is very interested in whether or not Marx’s theory of value is logically coherent. The #1 response I get from viewers is that Marx’s theory has been “discredited”. Yet, 90% of them don’t even know what argument they are referring to by this. This idea that Marx’s value theory is logically invalid is deeply entrenched in our culture.”
I agree with you here. We need to show how Marxist political economy is relevant today, and this includes showing how a labour theory of value is *empirically* relevant. But my problem is with Andrew’s method.
Instead of a positive research program, rooted in Marx’s questions, that analyzes the established economic order (like many Marxists have done) and proposes concrete policies (sadly too few), the emphasis is shifted to textual interpretation of sacred scripts. Ultimately unproductive with the risk of being counter-productive.
I seriously doubt whether any of the debates surrounding the TSSI-problematic have advanced a scientific research program (as opposed to a series of numerical examples). Instead they have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity. It was never the Okishio theorem that blocked the revival of Marxist political economy there.
I wish to emphasize that I am *not* an economist in the academia. I studied Marxist political economy more or less like you have done.
Hi Dave,
You wrote (February 15, 2010, above),
“I think there is a central problem with your project, which becomes clear in the second part of this sentence:
‘The record should be set straight, and Marx’s critics should do their part to help set it straight.’
“I think this is an illusion and what leads the project to be ultimately a waste of effort. Suppose for a moment that we one day found a text by Karl Marx in which he clarified all ambiguities in a straight-forward way.
“Who would seriously expect that bourgeois economists or Marxist critics would suddenly praise Marxist political economy and “help set the record straight”? It is an illusion to think that the economics discipline operates like a normal science.”
Huh? What I wrote–”The record should be set straight, and Marx’s critics should do their part to help set it straight”– says nothing about what I *expect*. It says what they *should* do. Do you agree or disagree?
There’s a very serious *ethical* issue here. Intellectuals should tell the truth. They have a responsibility to the public.
You also seem to misinterpret my phrase “Marx’s critics,” rendering it as “Marxist critics,” by which you evidently mean “critics of Marxism.” But a great many of Marx’s critics who have had a role in perpetuating the myth of his inconsistency are *themselves* Marxists, or quasi-Marxists. In the short passage from which you quote, for instance, I mention Okishio, Roemer, Foley, Laibman, and Brenner. Hanhel is a radical who was once a Marxist, and Howard and King were very sympathetic to Marxism when they wrote their book.
Of course I do not *expect* Marx’s critics to set the record straight voluntarily. They are not that ethical. But their refusal to set the record straight can then be brought to public attention — see, I’ve just done so! — and shown to be the reason why people keep encountering the charge that Marx’s value theory and law of the tendential rate of profit are inconsistent.
And as I argue in the new issue of _Capital & Class_ (the piece is called “The Disintegration of the Marxian School”),
“people outside the field need to appreciate how profoundly the myth of Marx’s internal inconsistencies has damaged it. If Marxist economists will not do their part to set the record straight, people outside the field should take charge—-and take them to task. And since a false charge of inconsistency issued knowingly is the moral equivalent of defamation, it would not be unreasonable for the public to ask those who have perpetuated the myth of inconsistency to make restitution. The funds obtained could be used to help re-establish Marxian intellectual work outside of academia.”
The Okishio theorem is logically invalid. The problem is not the math symbols or the Perron-Frobenius theorem. The problem is a logical problem known as _equivocation_. It means that a term is used in two different sense at different stages in an argument, and so the conclusion doesn’t follow:
Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal.
It is indeed a consequence of the Perron-Frobenius theorem that r’ > r. Would I then be entitled to “define” r’ as Karl Marx and r as Paul Samuelson, and announce that I’ve proved that Karl Marx was greater than Paul Samuelson.
Of course not.
By the same token, the Okishios and Roemers are not entitled to “define” r’ and r as “the rate of profit” before and after a technical change. Again there’s an equivocation, because r’ and r are simply NOT RATES OF PROFIT IN THE NORMAL SENSE OF THE WORD.
So we’re back to the Humpty Dumpty problem that I noted above.
Humpty Dumpty said, “in rather a scornful tone”:
“When I use a word, it means just what I choose it to mean––neither more nor less.”
No it doesn’t.
When he had a great fall, and broke, and all of the king’s horses and all of the king’s men couldn’t put him back together again, he got what he deserved.
Dave Zachariah (February 17, 2010 @ 5:47 am, above) quoted Brendan (kapitalism101:
“This popular audience is very interested in whether or not Marx’s theory of value is logically coherent. The #1 response I get from viewers is that Marx’s theory has been “discredited”. Yet, 90% of them don’t even know what argument they are referring to by this. This idea that Marx’s value theory is logically invalid is deeply entrenched in our culture.”
And then Dave commented:
“I agree with you here. We need to show how Marxist political economy is relevant today, and this includes showing how a labour theory of value is *empirically* relevant.”
This is NOT agreement with what Brendan wrote.
Brendan was discussing “Marx’s value theory.” Dave changes the subject to “Marxist political economy.”
Brendan was discussing logical coherence and the popular audience’s keen interest in whether Marx’s theory is logically coherent. Dave changes the subject to “relevance,” empirical and otherwise.
Everything else Dave goes on to say is consequently a non sequitur.
I wouldn’t say that Brendan’s comment or mine are “sacred scripts,” but they do deserve textual interpretation that’s much more adequate than that which Dave is giving them. If you can’t even get right what we say, Dave, I hardly think you’re in a position to criticize it.
The same thing holds true for those who charge that Marx’s value theory is logically inconsistent.
On the ethical issue: You write the “debates surrounding the TSSI-problematic … have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity.” Are you suggesting that the view that Marx’s value theory is not logically coherent should have been suppressed and kept from the Swedish public?
Andrew, I distinguish between political economy and the history of economic thought. My interest is in the first domain, and find the second one of secondary importance both from a scientific and political point of view.
While your ethical task may be in principle right, I prefer showing how Marx’s questions and insights are relevant rather than the numerical examples and counter-examples thrown around to prove or disprove “consistency”. Especially since I remain unconvinced by the arguments and the entire framework surrounding the transformation problem and later TSSI debates.
Btw, your argument about logic above is misleading. The Okishio theorem is mathematically proven and hence, by definition, logically valid. But we are certainly entitled to question the relevance of the assumptions or definitions and hence the results. For instance, you question the meaning of ‘rate of profit’ in the theorem, while I would question the assumption of equal rates of profits in real capitalist economies.
Your own deduction
“Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal.”
is in fact an example of this. It is a logically valid and correct deduction. But clearly we may question relevance of the assumptions of rational animals and the concept of “man” used. But these are scientific and empirical questions. They don’t alter the *logical* (as opposed to scientific) validity by a jot.
Same goes for all proven mathematical theorems, irrespective of what names they happen to carry.
The last sentence of my last comment should read “is logically coherent.”
I don’t think a single philosopher, from Aristotle (who first singled out equivocation as a logical fallacy) to the present, would agree that an argument which equivocates can be logically valid. Just google “equivocation,” and you’ll find scads of sites that refer to it as a logical fallacy, which it is.
It’s not an empirical or “scientific” (whatever that means here) issue.
The Okishio theorem contains an equivocation, and is therefore logically invalid.
[Sorry if I re-post this since the first post did not appear to get through.]
Andrew, I think you are simply wrong here. This is not how logic proper operates, and this is not what a ‘logical fallacy’ means.
Consider
1. If P then Q
2. P
3. Therefore Q
The above argument contains no logical fallacies, it is a logically valid deduction irrespective of the validity of statements 1 or 2.
Similarly, if a mathematical theorem is proven it is logically valid by definition but may be informally invalid if the premises are invalid on other grounds.
Your statement thus obscures the meaning of mathematical proofs and fails to distinguish the crucial difference between formal and informal fallacy (anyone interested could consult Wikipedia).
Deductive informal fallacies are actually logically valid, with the hidden co-premise false, making the argument unsound. That is the case for the Okishio theorem.
Andrew, I think you are simply wrong here. You are not making the crucial distinction between a logical fallacy and an informal fallacy, arguably known to most philosophers since antiquity.
The following argument
1. If P then Q
2. P
3. Therefore Q
contains no logical fallacies. It is a logically valid deduction, irrespective of the content and regardless of what statement 3 entails.
If the assumptions embodied in statements 1 or 2 are invalid for other reasons, it does not alter the logical validity of the statement by a jot. However, statement 3 would then be invalid or irrelevant on other grounds. That is the meaning of an ‘informal fallacy’ as opposed to a ‘logical fallacy’. Hence your assertion is at best a misleading account of logic. It obscures the meaning of mathematical proofs.
Similar to the deduction above, the Okishio theorem is proven and hence by definition logically valid, but its result is arguably questionable due to irrelevant assumptions.
Give me a break. You suggest consulting Wikipedia on formal and informal fallacies. Why not also consult the Wikipedia entry on “Equivocation”?
The 1st sentence reads:
“Equivocation is classified as BOTH A FORMAL and informal fallacy” (my caps)!!!!!
The error of form is this or something like it:
1. If P then Q
2. P*
3. Therefore Q
The error (that P* is not immediately implied by P) is merely disguised by using the same term for P* and P.
Let me give an example.
1. If R [the rate of profit to which Marx referred] cannot fall because of labor-saving technical change (given that the rate of profit is uniform, etc.), then his law of the tendential fall in the rate of profit is false.
2. R* [the simultaneist-physicalist monstrosity that is not a rate of profit in any normal sense of the term] cannot fall because of labor-saving technical change (given that the rate of profit is uniform, etc.).
3. Therefore Marx’s law of the tendential fall in the rate of profit is false.
This is an unsound argument because the *form* is bad. The conclusion doesn’t follow from the prior steps. Therefore the theorem is false.
The (formal) fallacy is disguised by using the same term for R and R*.
But actually, this doesn’t matter. You imagine that there’s an implicit premise to the effect that “The mathematical object R* is identical to object R of Marx’s text.” (Can you please tell me where it is? Aren’t they modeling, and don’t the objects in models differ by definition from the objects they model?)
If that were so, then, as you say, the Okishio theorem would be false because the “implict premise” is false.
So it doesn’t matter, because THE OKISHIO THEOREM IS FALSE IN EITHER CASE.
Right?
Andrew, I’m afraid writing in capitals doesn’t improve the argument. Yes, an equivocation is *both* a formal and informal fallacy. But as was clear above, I was saying that the theorem in question is not a formal or logical fallacy as you portray it.
In fact your rendering of the form of the Okishio theorem is symptomatic. At best it is misleading, at worst it is frankly dishonest.
If one has read the Okishio theorem and its proof it is hard to take your last comment seriously. It is not at all what the theorem is about. It uses a model of an economy in which all profit rates (as it defines it) are equal and compares two static cases, which differ only in technology as formalized in an extended input matrix. *These* are the assumptions of the theorem.
It can and has been proved mathematically that in this model, and under the given assumptions, the equalized profit rate is higher in the technically more advanced economy.
Whether or not the assumptions are relevant to you, me, Marx or anyone else makes no difference to the mathematical proof and the form of the argument. That is how logic operates, and I’m afraid no amount of capital letters can change that.
Excuse me, Dave,
YOUR TENDENCY TO DIVERT AND NOT TO CONCEDE WHEN YOU ARE WRONG IS SHOWING. I AM NOT PUTTING THINGS IN CAPS TO IMPROVE ANY ARGUMENT. I AM PUTTING THEM IN CAPS BECAUSE I AM SHOUTING AT YOU. I AM SHOUTING AT YOU BECAUSE YOU BEHAVE IN AN UNETHICAL MANNER. YOU YOURSELF HAVE ADMITTED THAT YOU CARE MORE ABOUT YOUR “SCIENCE” THAN YOU DO ABOUT ETHICS.
The facts are these. You wrote that
“Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal”
“is a LOGICALLY VALID and CORRECT deduction” (my caps).
I said it contains an equivocation (just as Okishio’s theorem does), and therefore it IS NOT logically valid.
You then proceeded to lecture me on the difference between informal and formal fallacies.
But your lecture was irrelevant, if not an intentional diversion, because equivocation is a formal fallacy as well as an informal one. You have now admitted this: “Yes, an equivocation is *both* a formal and informal fallacy.”
There are now ONLY THREE possibilities:
(1) You do not think the above “syllogism” equivocates by using “man” in more than one sense.
(2) You think the “syllogism” is “a LOGICALLY VALID and CORRECT deduction” (my caps) even though it equivocates and therefore commits a formal fallacy.
(3) You are contradicting yourself and not making sense.
Which is it? Door number (1), door number (2), or door number (3)?
Please cite the page number of Okishio’s 1961 paper in which he states as an assumption that he is only considering a static case, or the page number in the paper in which he states that his conclusion has been deduced only for a static case. I can’t seem to find either statement. I do see a statement that his “conclusions are negative to [the] Marxian Gesetz des tendeziellen Falls der Profitrate.”
So it would seem that Okishio’s theorem is about the Marxian Gesetz des tendeziellen Falls der Profitrate, as I said. Somehow, that is missing from Zachariah’s rendition of what the theorem is about. And this is crucial, because the equivocation takes place in the move from Marx to math. If the fact that the theorem is a theorem on Marx’s law of the tendential fall in the rate of profit can be suppressed, then the equivocation can be covered up.
Speaking of suppression, Dave, I have not forgotten your failure to respond on the following ethical matter:
You write that the “debates surrounding the TSSI-problematic … have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity.”
ARE YOU SUGGESTING THAT THE VIEW THAT MARX’S VALUE THEORY IS LOGICALLY COHERENT SHOULD HAVE BEEN SUPPRESSED AND KEPT FROM THE SWEDISH PUBLIC?
Please don’t divert from this again. It’s your statement. You’re responsible for its implications.
Andrew, your last replies in this and other thread suggests to me that scholarly and civilized discussions with you is ruled out by your writing. The fact that you say that you are shouting speaks volumes in itself.
Anyone who is interested in the model and proof of the theorem could for instance look up Fujimori’s concise paper “Innovation in the Leontief economy”, which is where I learned it first. They can also compare the rigour of the arguments with the ones you put forward here as well as the meaning of comparative statics.
I’m afraid I can’t go on discussing in the style you have just displayed. In this light your concern for ethics do not appear very genuine. Best of luck with your project Andrew.
Readers can find Yoriaki Fujimori’s paper “Innovation in the Leontief economy” here:
http://dspace.wul.waseda.ac.jp/dspace/handle/2065/6146
The model and theorem is given on the third page, and the interpretation is given on the final page in “Concluding remarks”. One is struck by how different the theorem is from how Andrew is portraying it above.
As I note in a comment I just posted, it doesn’t matter what some *secondary* source says Okishio’s theorem says. What matters is what the *primary* source says.
Where is the empirical evidence, from Okishio’s paper, that Fujimori’s account of the theorem matches the actual theorem itself?
Okishio (1961) wrote that his “conclusions are negative to [the] Marxian Gesetz des tendeziellen Falls der Profitrate.” The theorem is a theorem on Marx’s law (Gesetz).
Fujimori’s paper fails to mention this. The name Marx does not appear in his paper, nor does “law of the tendential fall in the rate of profit” or synonyms.
As an account of what Okishio himself attempted to deduce, Fujimori’s paper is extremely inaccurate.
Of course, anyone who is familiar with mathematical theorems knows that there is no need to go to the original papers and articles of Gödel, Fermat, Cauchy or Okishio to deal with the theorems that carry their names; more elegant proofs and generalizations of them are given long after the originators are dead.
There *is* indeed a need to consult the primary source. How does our “empiricist” know that the “elegant proofs and generalizations” match the original theorem? He doesn’t. He just TAKES IT ON *FAITH*!!! Might as well take on faith what the priests tell us that the gods have communicated to them.
There is especially a need to consult the primary source when the validity of the theorem has been challenged, as is the case with Okishio’s theorem. (Note that it’s called “Okishio’s theorem,” not “Fujimori’s theorem.”)
And there is especially a need to consult the primary source when the issue is whether the original theorem has been represented accurately. In the present case, both sides claim that the other side misrepresents Okishio’s theorem.
Or is Zachariah only claiming that I misrepresent what Fujimori *calls* Okishio’s theorem, instead of Okishio’s theorem? But I haven’t represented what Fujimori *calls* Okishio’s theorem, much less misrepresented it.
Please clarify this, Dave.
Please also say which of the following is the case:
(1) You do not think that
Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal
equivocates by using “man” in more than one sense.
(2) You think that this “syllogism” is “a logically valid and correct deduction” even though it equivocates and therefore commits a formal fallacy.
(3) You are contradicting yourself and not making sense.
Please also answer the following. When you write:
“debates surrounding the TSSI-problematic … have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity”
are you suggesting that the view that Marx’s value theory is logically coherent should have been *suppressed* and kept from the Swedish public?
This is the THIRD time you’ve been asked this question
Again, this betrays an unfamiliarity with how mathematical theorems are disseminated and treated in scholarly literature. I don’t have the original papers of Turing, Gödel or Okishio, yet oddly enough I have the theorems that carry their names and proofs in books and papers written by later scholars.
The objection raised has no bearing on the mathematics community; unless of course one is suggesting that generations of work in mathematics is not reviewed by peers to check the original citations.
(You could always link the original paper if you wish to demonstrate how Bowles, Foley, Fujimori and a generation of economists have proved some other theorem than Nobuo Okishio had set up. It would be interesting.)
Zachariah’s latest nasty comment
“Again, this betrays an unfamiliarity with how mathematical theorems are disseminated and treated in scholarly literature. I don’t have the original papers of Turing, Gödel or Okishio, yet oddly enough I have the theorems that carry their names and proofs in books and papers written by later scholars.”
is completely ridiculous. Okishio’s theorem is not a mathematical theorem. The math it employs is a Perron-Frobenius theorem that was proved long before Okishio.
Okishio’s result is what economists call a theorem, an *economic* theorem if you will. There is often extensive debate about what’s called “X’s theorem” correctly represents the original theorem. That’s the case, for instance, with Coase’s theorem.
It’s very clear that Zachariah’s disdain for poring over “sacred texts” is actually disdain for accuracy and truth. I wouldn’t by any means suggest that Okishio’s paper is a sacred text, but I am nonetheless concerned to represent it accurately. Zachariah is not.
If Zachariah is not discussing Okishio’s own, original theorem — and it seems pretty clear at this point that he hasn’t even read Okishio’s paper, and thus that he is not competent to discuss it — then he has no business trying to challenge what I say about it, because I am discussing Okishio’s OWN, ORIGINAL theorem.
Indeed, since I have been talking about Okishio’s own, original theorem all along, while Zachariah has continually been talking about something else, none of his criticisms of what I say are valid.
And I mean not valid in the strict logical sense. He is equivocating:
1. Kliman says that OKISHIO’s theorem is false.
2. “Okishio’s” theorem is not false.
——–
Therefore, Kliman is wrong.
This is logically invalid because the same term is being used to mean two different things.
Is Zachariah only claiming that I misrepresent what Fujimori *calls* Okishio’s theorem, instead of Okishio’s theorem? (I haven’t represented what Fujimori *calls* Okishio’s theorem, much less misrepresented it.)
Please clarify this, Dave.
Please also say which of the following is the case:
(1) You do not think that
Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal
equivocates by using “man” in more than one sense.
(2) You think that this “syllogism” is “a logically valid and correct deduction” even though it equivocates and therefore commits a formal fallacy.
(3) You are contradicting yourself and not making sense.
Please also answer the following. When you write:
“debates surrounding the TSSI-problematic … have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity”
are you suggesting that the view that Marx’s value theory is logically coherent should have been *suppressed* and kept from the Swedish public?
This is the FOURTH time you’ve been asked this question.
Let the record show that:
A. Dave Zachariah has diverted once again. Instead of apologizing for his unethical, diversionary behavior–or even simply answering the questions I posed–he feigns anger at my “style” and flees the scene.
B. Before he fled the scene, Dave Zachariah claimed that
Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal
“is a logically valid and correct deduction.”
With “logic” like this, is it any wonder that he maintains that Okishio’s theorem is also logically valid?!
C. Dave Zachariah fled the scene without answering which of the following is the case:
(1) He does not think the above “syllogism” equivocates by using “man” in more than one sense.
(2) He thinks the “syllogism” is “a logically valid and correct deduction” even though it equivocates and therefore commits a formal fallacy.
(3) He was contradicting himself and not making sense.
I’m pretty sure that the correct answer is (2).
D. Dave Zachariah made statements concerning what Okishio’s theorem is about. Instead of producing empirical evidence, from Okishio’s paper, that supports these statements, or instead conceding that the statements are false, he has chosen to flee the scene.
E. Dave Zachariah has diverted from the issue of what Okishio’s own theorem is actually about, by citing a *secondary source* (“Fujimori’s concise paper ‘Innovation in the Leontief economy’”) in a case in which the primary source–Okishio’s own paper–is very widely available, so that Zachariah could easily have produced the evidence I asked for if in fact it existed. (Given his citation of a secondary source, I strongly doubt that Zachariah has read what Okishio himself wrote. Yet he acts as if he’s some authority on the theorem.)
F. Dave Zachariah wrote that the “debates surrounding the TSSI-problematic … have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity.” He was asked TWICE whether he is suggesting that the view that Marx’s value theory is logically coherent should have been *suppressed* and kept from the Swedish public. Rather than admit that this is so, he has chosen to flee the scene.
Andrew, I will be happy to answer any questions that Brendan may have. But in your case, I’m afraid pursuing any lengthy replies is a wasted effort given your mode of communication.
The reason it is a wasted effort is that I am not letting you get away with your diversions, but showing that you are not making sense, etc. Your effort to emerge victorious is being thwarted, so it is wasted effort.
Let me note for the record that you like to go on and on and one about what *you* want to talk about, things that help you achieve your aims. But you don’t want to answer my questions–questions about what *you’ve* written–because doing so would not help you achieve your aims. You want to control the dialogue, and you throw a hissy fit when I don’t let you get away with that.
As I said, I will be more than happy to answer the same questions if they are raised and replied by Brendan or anyone capable of civilized discussion.
I’ve been on internet forums long enough to detect trolling.
Zachariah complains about the way I discuss things. These complaints come from someone who accuses me of trolling and of being incapable of civilized discussion.
Instead of these ad hominem attacks, I suggest that Zachariah stick to the issues:
A. Is he only claiming that I misrepresent what Fujimori *calls* Okishio’s theorem, instead of Okishio’s theorem? (I haven’t represented what Fujimori *calls* Okishio’s theorem, much less misrepresented it.)
B. Which of the following is the case:
(1) He does not think that
Man is the only rational animal.
No woman is a man.
——————–
Therefore, no woman is a rational animal
equivocates by using “man” in more than one sense.
(2) He thinks that this “syllogism” is “a logically valid and correct deduction” even though it equivocates and therefore commits a formal fallacy.
(3) He is contradicting himself and not making sense.
C. When he write:
“debates surrounding the TSSI-problematic … have taken valuable effort and printed pages in Marxist journals. Their publication in Sweden, for instance, has deepened the belief that Marxist economics is just a sterile academic obscurity”
is he suggesting that the view that Marx’s value theory is logically coherent should have been *suppressed* and kept from the Swedish public?
This is the FIFTH time he’s been asked this question.
I suspect that if Marx was alive today he too could not resist the gravitational pull of online comment-wars. Had it been in style in his day, perhaps much of the Critique of the Gotha Program would have been written in all-CAPS. That being said, I sometimes wish the Left was as good at diplomacy as it is at critiquing.
Dave, taking your cue, I’d like to pose a few questions that might help focus the discussion. I’m much more familiar with Andrew’s work on this topic than I am with your angle, yet the Okishio Theorem has not been a major interest of mine in reading up on the TSSI. I guess the reason that I haven’t been motivated to read further on it is that it seems rather obvious that for Marx an increase in physical productivity can manifest itself as a decrease in value productivity. The distinction between value relations and physical quantities that the TSSI school makes in their critique of “physicalism” seems like a pretty reasonable interpretation of Marx as far as I can see. When thinking back on discussions/debates I’ve had online with viewers, the need to make this distinction between an increase in physical productivity and value productivity seems one of the most relevant and important points to make. People are constantly saying to me things like “capital creates profits, not workers, thus exploitation doesn’t exist,” and “an increase in productivity is good for workers and society”. It seems that demolishing ideas like this was a crucial goal of Marx’s.
So, I guess I am confused by what your position is. It seems like you, Dave, are saying that Okishio’s math is logically valid. It seems like Andrew is saying that Okishio’s interpretation of Marx is invalid. But in the heat of the argument the discussion has narrowed down to what constitutes a logical proof, something I’m less interested in. Dave, I only cracked Laws of Chaos once and haven’t had time to return to it (swamped with work on my new video series) so I don’t really have background on your theoretical position. But what I think I am hearing is that either 1. you don’t think it is important to establish the logical rigor of Marx’s value theory but rather to prove it empirically; or 2. you think logical consistency is important but you disagree with the TSSI take on Marx; or 3. you disagree with Marx on what value is, or 4. you think statistical correlation replaces logical theoretical constructions- that correlation trumps causality.
Are any of these accurate understandings of your position? If not, please explain.
Andrew, I guess my question for you would be what parts of Marx’s value theory, in an ideal research situation, would be viable for empirical research? I know that you have already worked on profit rates. What about price-value? I remember your critiques of other empirical attempts in your book, but I can’t remember if you proposed alternative approaches. I can’t really understand what relevance any empirical research on values and prices can have in the context of prices of production. I know that Dave Z argues that prices of production are not obtained. Yet even if they are tendential, or totally un-obtained it doesn’t seem to me that the actual realized rate of profit in an industry can be inversely proportional to its organic composition. If this were the case industries wouldn’t increase their organic composition. (Here I would even agree with Bohm-Bawerk’s critique of the historical interpretation of prices of production: that one can’t argue that prior to the “historic” equalization of profit rates individual money profit rates resembled individual value profit rates.) I can’t see how any empirical studies can get around this fact. I’m also not sure what the point would be if they could.
Hi Brendan,
You ask, “what parts of Marx’s value theory, in an ideal research situation, would be viable for empirical research?”
That’s too big a question for me to answer, especially on the internet, but the short answer is: potentially everything.
It’s now pretty well understood that individual propositions aren’t generally testable one by one, owing to the internal relations among the concepts of a theory. The theory as a whole, or some cluster of it, is testable.
With regard to the relationship between individual commodities’ prices and values, Marx predicts, so to speak, only one thing: all else being equal, a rise or fall in a commodity’s value will lead to a rise or fall in its price. This is in fact the case. But it’s not controversial; neo-classical economics, for instance, predicts the same thing.
My view of the theoretical significance of the “empirical” stuff that shows that the total price and total value of output are high in large industries and low in small industries seems to be consonant with what you’re saying. My view is that the theory of the proponents of this stuff and Marx’s theory are *opposites* with respect to the issue of whether profits per dollar of advanced capital are higher in industries whose variable capital is a larger share of total capital.
Marx’s really important empirical proposition concerning price and value, IMO, is that the total price of commodities is equal to and determined by the total value of commodities. Thus, technical progress tends to lower the total price of output. This turns out to be the case, and it’s key to the tendential fall in the rate of profit.
Specifically, in Part VIII of my recent study of the profitability of U.S. corporations, “The Persistent Fall in Profitability Underlying the Current Crisis: New temporalist evidence” (akliman.squarespace.com/persistent-fall), I show that the rate of growth of a proxy for the monetary expression of labor-time(MELT) has been trendless and fairly constant throughout the whole period since WWII. If the rate of growth were exactly constant, then any rise or fall in the growth rate of total value would lead to an equal rise or fall in the rate of growth of total price. So that is close to being the actual case.
Now, what this implies is that the fluctuations in the labor-time (or constant-MELT) rate of profit have been the *dominant* cause of fluctuations in the money rate of profit. So, since the labor-time rate of profit has more or less consistently fallen for over a half-century, so has the money rate of profit (except temporarily–during the period of accelerating inflation in the 1970s and during the bubble-induced, unsustainable boom preceding the latest crisis).
This is a remarkable fit between theory and empirical evidence. It is so remarkable that it shocked me when I first plotted the graph, and I’m still amazed by it.
On another matter: I am saying Okishio’s interpretation of Marx (or modeling of Marx’s theory) is incorrect, but not only that. More importantly, I’m saying that because it is incorrect, his theorem is false. In other words, he did not prove that profit-maximizing capitalists will never introduce technical changes that cause Marx’s *equilibrium* rate of profit to fall. But that’s what he claimed. Therefore his alleged disproof of the law of the tendential fall in the rate of profit fails.
“But in the heat of the argument the discussion has narrowed down to what constitutes a logical proof, something I’m less interested in.”
This really doesn’t have anything to do with the “heat of the argument.” The cover-up of the fact that Okishio’s theorem is false has been going on for a VERY long time. So the logical status of the theorem has been an issue for a VERY long time. Please see the last section of Chap. 7 of _Reclaiming Marx’s “Capital”: A refutation of the myth of inconsistency_ (part of which I quoted here a few days ago).
In other words, Zachariah did not invent the strategem of retroactively claiming that the theorem has nothnig to do with Marx–Foley and Laibman tried it a decade ago in print, and the strategem goes back probably 5 years earlier than that. But of course it is preposterous.
They are all trying to absolve the physicalist tradition of error (in many case, this means trying to avoid admitting that they themselves were wrong–don’t concede anything to those terrible dogmatic unscientific TSSI Antichrists!) and to avoid anything that would enhance the reputation and visibility of Marx’s *own* theory (especially his law of the tendential fall in the rate of profit, since it has revolutionary implications and is, as you say, antithetical to physicalism).
But there’s also something else, something very deep, going on. A tremendous amount of economics is logically invalid for the same reason that Okishio’s theorem is: it is guilty of equivocation. They take some real-world relationship or theory, distort it (they call this “modeling” and/or “abstraction”), and prove something deductively about the distorted version (that they can’t prove without distorting the real-world relationship or theory). Then comes the logically invalid part: they claim that they’ve proved something about the real-world relationship or theory.
Mathematical economics would collapse like a house of cards if this weren’t accepted. (By them–mathematicians on the other hand continually point out that it is simply impossible to mathematically prove anything about the real world.) So, when Okishio’s theorem is challenged, the economics profession’s practice of illogic is being challenged. The Marxist economists are part of the profession, and I think that at some level their resistance to the idea that the theorem is false is, consciously or not, a way of protecting and defending the profession’s practice of illogic.
Zachariah’s attempt to defend the theorem has everything to do with this issue. It’s why he blundered so badly, writing that
Man is the only rational animal.
No woman is a man.
————–
Therefore, no woman is a rational animal
“is a LOGICALLY VALID and CORRECT deduction” (my caps).
This is actually the way they *all* think. It’s how they do economics:
[Real-world relationship or theory] is X.
No Y is [a distorted version of the real-world relationship or theory].
——–
Therefore, no Y is X.
But until the other day, I’d never encountered anyone who claimed that an argument that a deduction based on equivocation “is a LOGICALLY VALID and CORRECT deduction.”
It was a very serious blunder, partly because it (and Zachariah’s accompanying explanation of why it is “logically valid and correct”) exposes the whole mind-set for what it is: an ultra-sophisticated way of “proving” things by means of equivocation.
There are other examples of equivocation in _Reclaiming Marx’s “Capital”: the discussion of Screpanti near the start of Chap. 4, and the section entitled “The Most Effective Whiggish Strategy” in Chap. 1.
I have a serious reservation to commit myself to the following passage:
“The rate of profit is the total profit over the total price of inputs: profit/inputs. We call the profit s for surplus value- the amount of additional value added by labor, over and above the money paid to workers for their wages. We divide the inputs into two categories: wages paid to workers, and expenditures on pre-produced commodities like machines, raw materials, factories, etc. At the time of buying one of these pre-produced commodities the capitalist pays a price representing the value of the commodity. This value is then transfered onto the final product, but no additional value can be transferred by a machine or raw material, so we call the value of these pre-produced commodities “constant” and denote them with “c”. Since the wages paid to workers are not representative of a specific amount of value that will be produced per worker, that is, since there is no way of knowing how much value a worker will produce, we call their value “variable” and denote this with “v”.”
I don’t see any reason that a machine should not generate Surplus value. A machine or tool is nothing less than an embodiment of ‘past labor’ and it can produce more value than it has consumed for its production. In that case every means of production can be seen as producing surplus value and thus can not be termed as ‘Constant Capital’. And in that case it’s impossible to argue that the profit rate will fall just because constant capital shoot up – owing heavy CAPEX (Capital Expenditure) by Capitalist for there is no such thing as Constant Capital !! Everything capital is of variable in nature and capable of producing surplus value. I got the following idea from the following blog:
http://www.massline.org/PolitEcon/ScottH/Keen_LTV.htm.
I would like to hear from you and be convinced that why a machine can not generate Surplus value and if it can how it’s possible to explain the falling rate of profit aspect of Marx’ Crisis theory from the perspective of LTV? Can you please explain. I searched a lot in the Internet but could not find any plausible answer.
Best Regards Sabya
I find Keen’s take on this topic to be extremely misleading. He does not accurately represent Marx’s argument but instead mixes up categories and mixes up the sequence of Marx’s idea. Keen wants Marx to prove that labor is the source of value in the middle of his argument on exploitation. But Marx deals with the issue of the substance of value chapters before this.
The answer to your question is quite simple: machines can’t create value because they are not people. Value is a social relation between people. Keen’s view makes it seem like the production of physical quantities of objects is the same as the production of value. Value becomes a redundant category. When Keen says he is trying to improve Marx’s value theory this is pure sleight-of-hand. He is trying to destroy it. He wants us to believe that anything that can produce an object can create value. But this takes the social relations out of economics.
Dear Brendan,
I’ve been visiting your blog for some time now, and well, I just wanted to post a long overdue thank you. You have created an intelligent platform for discussing some of the most fascinating and controversial topics within Marxism ! Keep up the good work. I found your notes on Capital to be extremely helpful. Andrew makes a really damn good argument as well.
Cheers,
Dear Sabya
First, Marx examines the value embedded in the means of production broadly defined to include both instruments of production and raw material (vol.I 293-5).
The value of the raw material is determined by the SNLT required for its production, and this value reappears in the final commodity.
Similarly, the value of the instruments of production reappears in the commodity but only in the proportion of the wear and tear that went into the production of that commodity.
Therefore: 10s worth of cotton reappears in the yarn made out of it and the 2s worth of wear and tear on the machinery reappears in the same yarn.
Second, he analyzes what ‘kind’ of labor produces value (295-299).
1) concrete labor transfers the value of the means of production to the commodity and makes for the specific qualities found in the commodity;
2) abstract labor creates value, i.e. new value, found in the commodity.
Marx defines constant capital as ‘That part of capital…which [comprises the] means of production [and] does not undergo any quantitative alternation of value in the process of production.’ (307)
He also defines variable capital as ‘That part of capital which is turned into labor power [and therefore] does undergo an alteration of value in the process of production. It both reproduces the equivalent of its own value and produces an excess, a surplus-value,m which may itself vary..’ (Ibid.)
This two fold nature of the production is to be explained by the two fold nature of the labor that produces commodities (308) i.e. concrete, specific labor of the worker that the value of the means of production is transferred and preserved in the product and abstract social labor which is part of the nature of labor in the production of commodities. And the *amount of new value* is determined by the *amount of SNLT* embedded in the commodity.
Marx shows how this ‘two fold effect’ results from the two fold character of labor’ by giving two examples: one of which there is a rise in productivity due to technological progress and the other in which there is *change in the exchange value* of the commodity (309)
In the first example, new value absorbed by each unit of production declines with the rise of productivity, while the value transferred from the means of production increases — both the increase and decrease take place as a result of the same process.
In the second, even though the exchange value may vary, ‘as long as the conditions of production remain the same, the more value the worker adds by fresh labor, the more value he transfers and preserves’ (310)
I still feel there is still much more to be said about your question so I will have to leave this comment unfinished for the time being. I apologize if it didn’t really help clarify how Marx’s LTV really works.
Dear Room,
It’s so kind of you to answer this question. And I also thanks to the excellent site for nurturing Marxist school of thought.
I’m not really satisfied with my previous answer because it doesn’t help explain, how or why for example, newly automated machines, such as those producing automobiles, are able to produce value without the aid of workers. Of course, the obvious answer would be that those automated machines, like you said, embody ‘past labor’ (SNLT required to produce them) and so they pass on that value onto the product. But this value contained in the ‘past labor’ or in the SNLT that went into producing these machines and the raw materials that they use, do not produce any new value, correct? I mean the value embedded in the means of production (instruments of production and raw material in the factory) reappears in the commodity or automobile but then where does the new value come from?
I believe, if not seriously mistaken, that you’re actually implying that automated machine can produce surplus value unaided by labor. But that is not true. Only labor – abstract labor and not concrete labor – can produce surplus value. True, a machine , when produced, accumulate surplus value, but the moment it’s exchanged it’s surplus value gets realized and that’s end of its surplus value. In the next production process all it transfers to the product made it is concrete labor and not abstract labor. A machine machine can produce no more value than a Missile can be ‘persuaded’ to kill more people than it’s originally designed to kill !! If that’s the case then we can fairly conclude, as Marx held, that labor-saving technology increase the OCC and thus reduce the value in the commodity. The only way Capitalists can sustain its profit rate is to reduce labor’s wage , given that he is obsessed with advancing means of production in pursuit of producing more and cheap and thus depressing the price further down. That perhaps explain the success of Japanese Car industry in 80s and 90s. It can be attributed to low labor cost rather than advanced technology.
I don’t know what I said is completely correct or can be taken seriously. I am a novice in Marxist economics and still trying to get my foot.
Sabya