For Marx, Prices Coordinate Distributed Labor Activities Under Capitalism

Marx provides a supposed proof of the labor theory of value (LTV) in the first section of the first chapter of the first volume of Capital. The worth of his analysis depends on neither the soundness nor the validity of this argument about the third thing. If you are interested in Marx, you should be willing to see where he goes after chapter 1. I find most insightful the last section in chapter 1, the bit on commodity fetishism.

Manufacturing goods in an ongoing society depend on many activities happening in parallel. For example, somebody must be mining iron for the blacksmith to be manufacturing horse shoes out of steel. Under capitalism, nobody is coordinating these activities. For Marx, this coordination results from prices under the anarchy of production characterizing capitalism. Capitalists see whether they are making lots of profits or not in marketing the commodities produced under their direction. Each capitalist adjusts their establishments accordingly.

Marx explains his overall approach to the theory of value in a much-quoted 11 July 1868 letter to Ludwig Kugelmann:

Dear Friend,

The children are getting on well, though still weak.

Thank you very much for the things you sent. Definitely do not write to Faucher, otherwise this mannequin pisse will feel too important. All he has achieved is that, if a second edition appears, I shall aim a few necessary blows at Bastiat where I speak about the magnitude of value. This wasn't done before, since the 3rd volume will contain a separate an extensive chapter about the 'vulgar economy' gentry. Incidentally, you will find it quite natural that Faucher and consorts derive the 'exchange value' of their own scribblings not from the amount of labour power expended, but from the absence of such expenditure, that is from 'saved labour'. Moreover, the worthy Bastiat did not even himself make this 'discovery', so welcome to these gentry, but just 'cribbed' it, in his usual manner, from much earlier authors. His sources are of course unknown to Faucher and consorts.

As for the Centralblatt, the man is making the greatest concession possible by admitting that, if value means anything at all, then my conclusions must be conceded. The unfortunate fellow does not see that, even if there were no chapter on 'value' at all in my book, the analysis I give of the real relations would contain the proof and demonstration of the real value relation. The chatter about the need to prove the concept of value arises only from complete ignorance both of the subject under discussion and of the method of science. Every child knows that any nation that stopped working, not for a year, but let us say, just for a few weeks, would perish. And every child knows, too, that the amounts of products corresponding to the differing amounts of needs demand differing and quantitatively determined amounts of society's aggregate labour. It is SELF-EVIDENT that this necessity of the distribution of social labour in specific proportions is certainly not abolished by the specific form of social production; it can only change its form of manifestation. Natural laws cannot be abolished at all. The only thing that can change, under historically differing conditions, is the form in which those laws assert themselves. And the form in which this proportional distribution of labour asserts itself in a state of society in which the interconnection of social labour expresses itself as the private exchange of the individual products of labour, is precisely the exchange value of these products.

Where science comes in is to show how the law of value asserts itself. So, if one wanted to 'explain' from the outset all phenomena that apparently contradict the law, one would have to provide the science before the science. It is precisely Ricardo's mistake that in his first chapter, on value, all sorts of categories that still have to be arrived at are assumed as given, in order to prove their harmony with the law of value.

On the other hand, as you correctly believe, the history of the theory of course demonstrates that the understanding of the value relation has always been the same, clearer or less clear, hedged with illusions or scientifically more precise. Since the reasoning process itself arises from the existing conditions and is itself a natural process, really comprehending thinking can always only be the same, and can vary only gradually, in accordance with the maturity of development, hence also the maturity of the organ that does the thinking. Anything else is drivel.

The vulgar economist has not the slightest idea that the actual, everyday exchange relations and the value magnitudes cannot be directly identical. The point of bourgeois society is precisely that, a priori, no conscious social regulation of production takes place. What is reasonable and necessary by nature asserts itself only as a blindly operating average. The vulgar economist thinks he has made a great discovery when, faced with the disclosure of the intrinsic interconnection, he insists that things look different in appearance. In fact, he prides himself in his clinging to appearances and believing them to be the ultimate. Why then have science at all?

But there is also something else behind it. Once interconnection has been revealed, all theoretical belief in the perpetual necessity of the existing conditions collapses, even before the collapse takes place in practice. Here, therefore, it is completely in the interests of the ruling classes to perpetuate the unthinking confusion. And for what other reason are the sycophantic babblers paid who have no other scientific trump to play except that, in political economy, one may not think at all!

But satis superque [Enough and more than enough]. In any case, it shows the depth of degradation reached by these priests of the bourgeoisie: while workers and even manufacturers and merchants have understood my book and made sense of it, these 'learned scribes' (!) complain that I make excessive demands on their comprehension.

I would not advise reprinting Schweitzer's articles, though Schweitzer has made a good job of them for his paper.

You would oblige me if you sent me a few issues of the Staats-Anzeiger.

You should be able to get Schnacke's address by enquiring at the Elberfelder.

Best greetings to your wife and Fränzchen.

Yours,

K. M.

Apropos. I have received an article by Dietzgen about my book; I am sending it to Liebknecht.

I fault Marx for spending so much time in rewriting volume 1 of Capital after its publication. He should have put more time in preparing the later volumes for publication. Some have recommended that on a first reading, you skip the first chapter. I could see an argument that Marx should have worked on rewriting chapter 1 a few more times.

Marxist Mathematicians

I have been looking at Marx's notes to himself, late in life, on the calculus. Marx relied on an out-of-date textbook, J. L. Boucherlat's 1828 Elementary Treatise on the Differential and Integral Calculus, as well as other out-of-date primary texts.

The foundations of calculus were a mess at that time. Marx was totally correct about that. Echoing Bishop Berkeley, Marx finds that the mathematicians were operating with fractions of the form 0/0. He tried to make sense out of this.

Unbeknownst to Marx, the foundations were being relaid in his day. I will mention the epsilon-delta definition of a limit, the construction of the real numbers as Dedekind cuts, and Cantor's set theory. I suppose Fourier series goes into this story. Marx never knew about any of this.

Some, sympathetic to Marx, argue that he treated the derivative as an operator.

Some mathematicians have been Marxist and socialists. These views have influenced their activities in developing mathematics, at least to the extent of the settings in which they did their mathematics. For this post, I am not going to sort through mathematicians in the Soviet Union or in China. I limit myself to a few in the United States.

• I know little of Chandler Davis' mathematical work. He lived from 1926 to 2022. The University of Michigan fired him in 1954 for refusing to cooperate with the oppression being practiced by the House UnAmerican Committee (HUAC). He went to jail for six months and then into exile into Canada.
• F. William Lawver was an expert in category theory, including its use to describe Hegelian dialectics. He was dismissed in 1971 partly for his political activities.
• David Schweickart has written a number of books outlining how socialism might be implemented. He is both a philosopher and a mathematician. I am not sure that he is a Marxist.
• I know of Stephen Smale principally through his horseshoe map, which is a canonical model for dynamical systems. He won the Fields Medal and denounced the United States for invading Vietnam.
• Dirk Jan Struik (1894-2000) could not get a job in Holland, partly due to his political commitments. He ended up at MIT. Struik co-founded and taught at the Samuels Adams School, one of several institutions set up to teach workers. These, of course, were illegally shut down by the government. HUAC went after Struik himself, and MIT chose the route of cowardice. He applied Marxist ideas to the sociology of mathematics, a field he helped create. He co-founded Science and Society. He also praised Marx's work on the foundations of calculus.

I will not be surprised if others know of more examples.

To Read Adorno's Minima Moralia Requires Understanding Of Marx

Well-known contributions to philosophy in Europe and America in the twentieth century are often divided into analytical and continental philosophy. Analytical philosophers often state their arguments with formal reasoning and notation, while concentrating on narrow points. How do you know that you have not always used 'green' to mean grue? Continental philosophers provide a more intuitive reasoning and focus on larger issues such as culture. Gender is performative. I take no issue to those who argue that the division is not well-defined. I lean more towards the analytical side, albeit I try to reject logical positivism.

Sometimes, when I read postmodernists - another ill-defined term - I can follow, but I do not retain much. I find intriguing Lukacs' essay on reification, in which he builds on Karl Marx's work on commodity fetishism and vulgar political economy. I have more use for Foucault's post structuralism than Derrida's deconstruction. I find Antonio Gramsci insightful, which is no surprise for somebody building on Piero Sraffa. Herbert Marcuse has a point about instrumental reason in the service of a system that is irrational as a whole. I am never sure when Slavoj Zizek is joking.

But here I want to focus on Theodor Adorno and his 1951 book Minima Moralia: Reflections from Damaged Life. I could not make much out of his book, Negative Dialetics. I have yet to read The Dialetic of Enlightenment.

As I poorly recall, Minima Moralia has a narrative arc, although it takes some work to perceive it. I was surprised at passages that presume an understanding of technical terms in Marx's political economy. I note a few here.

Here Adorno rejects some concepts of a post-capitalist society because they continue commodity fetishism:

"Sur l'Eau. He who asks what is the goal of an emancipated society is given answers such as the fulfillment of human possibilities or the richness of life. Just as the inevitable question is illegitimate, so the repellent assurance of the answer is inevitable, calling to mind the social-democratic ideal of the personality expounded by heavily-bearded Naturalists of the 'nineties, who were out to have a good time. There is tenderness only in the coarsest demand: that no-one shall go hungry any more. Every other seeks to apply to a condition that ought to be determined by human needs, a mode of human conduct adapted to production as an end in itself. Into the wishful image of an uninhibited, vital, creative man has seeped the very fetishism of commodities which in bourgeois society brings with it inhibition, impotence, the sterility of the never-changing. The concept of dynamism, which is the necessary complement of bourgeois 'a-historicity', is raised to an absolute, whereas it ought, as an anthropological reflex of the laws of production, to be itself critically confronted, in an emancipated society, with need..." -- Adorno: 155-156.

Adorno draws on the concept of fetishism in other places. I do not know that the above passage is consistent with Marx and Engels in The German Ideology.

In this next passage he uses the concept of the organic composition of capital to write about how working class consciousness is dimmed:

"Puzzle-picture. Why, despite a historical development that has reached the point of oligarchy, the workers are less and less aware that they are such, can be surmised from a number of observations. While objectively the relation of owners and producers to the productive apparatus grows ever more rigid, subjective class membership becomes all the more fluctuating. This tendency is fostered by economic development itself. The organic composition of capital demands, as has often been noted, control through technical experts rather than through factory owners. The latter were the counterpart, as it were, of living labour, the former correspond to the share of machinery in capital. The quantification of technical processes, however, their dissection into minute operations largely independent of education and experience, makes the expertise of these new-style managers to a large degree illusory, a pretence concealing the privilege of being appointed. That technical development has reached a state which makes every function really open to all - this immanently socialist element in progress has been travestied under late industrialism. Membership of the elite seems attainable to everyone. One only waits to be co-opted... ...Preference goes to those who fit in most exactly...That technical forces might permit a condition free of privileges is accredited by all, even those in the shadow, to the social relations which prevent it. In general, subjective class-membership today shows a mobility that allows the rigidity of the economic order itself to be forgotten..." -- Adorno: 193-194.

And, for the last passage I select, Adorno writes about the law of value and, again, the organic composition of capital:

"Novissimum organum. It has long been demonstrated that wage-labour formed the masses of the modern epoch, indeed created the worker himself. As a general principle the individual is not merely the biological basis, but the reflection of the social process; his conciousness of himself as something in-itself is the iI1usion needed to raise his level of performance, whereas in fact the individuated function in the modern economy as mere agents of the law of value. The inner constitution of the individual, not merely his social role, could be deduced from this. Decisive here, in the present phase, is the category of the organic composition of capital. By this the theory of accumulation meant the 'growth in the mass of the means of production, as compared with the mass of the labour-power that vivifies them'. If the integration of society, particularly in totalitarian states, designates subjects more and more exclusively as partial moments in the network of material production, then the 'alteration of the technical composition of capital' is prolonged within those encompassed, and indeed constituted, by the technological demands of the production process. The organic composition of man is growing. That which determines subjects as means of production and not as living purposes, increases with the proportion of machines to variable capital... Only when the process that begins with the metamorphosis of labour-power into a commodity has permeated men through and through and objectified each of their Impulses as formally commensurable variations of the exchange relationship, is it possible for life to reproduce itself under the prevailing relations of production..." -- Adorno: 228-229.

My understanding of the organic composition of capital is straightforward. I take it to be the ratio of constant capital to variable capital, evaluated either with labor values or with prices of production. I do think about the physical composition of capital goods and of issues associated with depreciation. But I certainly do not go into the cultural effects that Adorno writes about.

John Stuart Mill Explains Profits As The Result Of The Exploitation Of Labor

I find this passage based on guidance from Samuel Hollander:

"The cause of profit is, that labour produces more than is required for its support. The reason why agricultural capital yields a profit, is because human beings can grow more food, than is necessary to feed them while it is being grown, including the time occupied in constructing the tools, and making all other needful preparations: from which it is a consequence, that ff a capitalist undertakes to feed the labourers on condition of receiving the produce, he has some of it remaining for himself after replacing his advances. To vary the form of the theorem: the reason why capital yields a profit, is because food, clothing, materials, and tools, last longer than the time which was required to produce them; so that if a capitalist supplies a party of labourers with these things, on condition of receiving all they produce, they will, in addition to reproducing their own necessaries and instruments, have a portion of their time remaining, to work for the capitalist. We thus see that profit arises, not from the incident of exchange, but from the productive power of labour; and the general profit of the country is always what the productive power of labour makes it, whether any exchange takes place or not. If there were no division of employments, there would be no buying or selling, but there would still be profit. If the labourers of the country collectively produce twenty per cent more than their wages, profits will be twenty per cent, whatever prices may or may not be. The accidents of price may for a time make one set of producers get more than the twenty per cent, and another less, the one commodity being rated above its natural value in relation to other commodities, and the other below, until prices have again adjusted themselves; but there will always be just twenty per cent divided among them all." -- John Stuart Mill, Principles of Political Economy, Book II, Chapter XV, Of Profits, Section 5.

I find the above close to Marx. At the start of the chapter, Mill says that profits are the sum of interest as a payment for abstinence, "indemnity for risk", and "remuneration for the labour and skill required for superintendence". Apparently, Mill regarded this disaggregation as consistent with describring profit as the result of laborers working for more time than needed to reproduce their own necessaries and instruments. For purposes of this post, I do not go into what is wrong with the account of interest as the sum of these components.

I do not draw a connection to Mill's avowal of socialism. But then, I do not read Marx's account of exploitation as an ethical argument for socialism either.

The above quotation is evidence for those who want to argue that Marx has a certain continuity with Ricardo's theory. I do not mean to assert that differences do not exist, as well.

Ben Shapiro Being Stupid About Marx

Shapiro Explaining Critical Race Theory Correctly Before Criticizing It

I have not actually read Shapiro's Lions and Scavengers" The True Story of America (and Her Critics). I rely on a screenshot in a tweet from Matt McManus.

The above video shows that Shapiro recognizes that you should accurately set out a position before criticizing it. He also gets to boast about his law degree. (Those wanting to laugh at Shapiro probably prefer this interview with Andrew Neil on the BBC.) Anyways, here is a Shapiro take on Karl Marx:

"Marx heavily relied on the labor theory of value. He posited that if you could calculate the value of anything objectively, then anything beyond that value had to be a surplus - an unnecessary bit of profiteering added by the person selling a good, product, or service. So, if the labor value of a potato was, say, $2 - the labor put into growing the potato, harvesting it, and selling it to the grocer - and the grocer sold it for $3 to an end customer, the grocer was adding on an unfair surcharge of $1, thus increasing the price falsely so as to extract profit. Marx said the world could be made fairer and better by preventing the grocer from extracting profit, thus lowering prices and making potatoes more affordable. The grocer was actually exploiting his customers when he 'earned' a profit.

The answer, said Marx, was to set prices from the top down. Simply set the price of potatoes at $2, remove the grocer’s evil profit, and make everything more plentiful and cheaper." – Ben Shapiro. Lions & Scavengers: The Tue Story of America.

The above is so far from anything Marx wrote that I do not think any comment is needed. Nevertheless, I will go on.

Marx does not explain profits as the result of a seller tacking a surcharge on the price of a commodity, where that price is the labor value of the commodity. In fact, he specifically rejects that idea.

For purposes of exposition, Marx assumes, in volume 1 of Cqpital, that prices tend towards labor values, under the capitalist mode of production. He wants to explain the origin of profit under the assumption that prices are 'fair' that many pro-capitalists and his predecessors put forth shortly before.

Surplus value, the source of profits, are obtained by capitalists not paying out the full value added by labor as wages to workers. The distinction between labor-power and labor is central to Marx's explanation. Labor-power is the ability to work under the direction of the agents of capital.

The suggestion that Marx thinks profit is only obtained by the merchant selling a commodity to the consumer is another absurdity. For Marx, surplus value is obtained at every step of production. The farmers hiring workers to plant, grow, and harvest potatoes exploits their workers. Shapiro can only be joking when he suggests that Marx thinks merchants exploit customers.

The final bit of silliness I want to highlight is that Marx argues a post-capitalist economy should set prices top-down to labor values. Marx is descriptive in Capital. He does not provide a blueprint for post-capitalist societies. He mocks the idea in the afterword to the second German edition of volume 1. In The Poverty of Philosophy, he specifically attacks Prodhon's idea of setting prices to labor values. Anarchists might argue that Marx is inconsistent and draws on Proudhon's ideas in his letter, Critique of the Gotha Programme. But any use of labor values in socialism differs from Marx's theory in Capital. Furthermore, many would argue that Marx's concept of value does not apply to communism, for example.

Apparently, Shapiro has been spouting nonsense about Karl Marx for years. Ben Burgis once noticed.

Update: Ben Burgis has a substack article about the above. And a YouTube video discussion with Stefan Bertram Lee.

Matt McManus and Nathan J. Robinson give the book a negative review.

Shapiro's book has a lot more wrong with it.

Sraffa On The Use Of The Notion Of Surplus Value

Sraffa, in his archives in the 1940s and 1950s, is quite appreciative of Karl Marx's analysis of capitalism. This appreciation contrasts with the opinion embodied in the label 'neo-Ricardian', which Bob Rowthorn invented.

I know about the passages below in the Sraffa archives from Riccardo Bellofiore. The archivist, Jonathan Smith, has dated this entry from 1955-1959, late in the writing of Production of Commodities.

I do not want to focus on whether Marx or Sraffa are correct or not. I would want to work out a simple example. Besides, Sraffa seems not convinced of how to analyze the reduction in the working day, when starting at prices.

But I want to note that Sraffa is very much using Marxist concepts: vulgar economics, labor values, prices of production, surplus value, exploitation, and rates of exploitation. And the analysis is based on Marx. Surplus value comes from extending the working day past the point at which workers reproduce their labor power.

"Use of the Notion of Surplus Value

"The prolongation of the working day beyond the point at which the labourer would have produced just an equivalent for the value of his labour-power ..." (Cap., Engels transl. p. 518) cp p. 539 [Chapter Sixteen: Absolute and Relative Surplus-Value]

Put it the other way round. If starting from capitalist society the working day is shortened till there is no surplus value left, this shortening must be equal for all: if it is, the prices of the commodities will change [owing to change in the rate of profits, which vanishes], but the wages will remain unchanged : if it is not, and the working day is reduced to the extent of the profits made in each industry, then prices would remain unchanged* after the shortening [for the number of (shorter) labor days, in industries having a high organic composition of capital, would increase in the same proportion as the fall of profits] but wages would be different.

[Footnote:] *(28.12.41) But profits would be different (after the reduction) in different industries!

[Marginal note:] c/p Letters of M and E 129-32 (letter of M. 2.8.62)

In other words, if we start from profits (as vulgar economy does) we reach the conclusion that the rate of exploitation is different in different industries, being higher in the more highly capitalised ones – which is not [and indeed contrary to] the fact. If we start from surplus value, which is equal in all industries, we get the correct measure of exploitation. The former conclusion is patent nonsense, and no view of exploitation could be based on it.

Note that the former (profits) goes with a theory of prices, the latter, of value (as defined below).

12.11.40 [Price is an exchange ratio which equalises rates of profit on capitals. Value is an exchange ratio which equalises rates of surplus-value on labour. If commodities exchanged at their values, profits would be different for different capitals, and capitals would move: therefore, this competition of capitals causes them to exchange at their prices.

The question is: are the rates of exploitation different? and if so why doesn’t labor move, and restore values and equality of rates of surplus value?]

The starting point is "the prolongation of the working day beyond the point at which the labourer would have produced just an equivalent for the value of his labour power" (Cap., Engels Tr. 518)

This point cannot be determined without reference to the value of the product (unless the labourer produces himself all the commodities he consumes).

But the point varies if we take value and if we take price.

Now, we are comparing the actual state with a hypothetical one in which only the necessary labour is performed.

In the actual state commodities are exchanged at their prices, whilst in the hypothetical state (where there would be nothing to be paid out in profits) at their values.

Which scale should we adopt for both states, in comparing them? It may be said: neither – each state has its own scale and that only is appropriate to it. No comparison can be made directly between the two extreme states. [marginal note says, "wrong, see p. 56.] We cannot imagine to move gradually from the actual state, shortening the working day; as we start from the actual state, we use its own scale, i.e. prices, in determining the ultimate goal towards which we move [and that will give different reductions for different branches of industry; but as we pass to successive other states, with shorter and shorter working days, the scale to be used changes, and prices move nearer (as the rate of profits is reduced) to values – so does the "point" aimed at change; until, on the threshold of the state in which only the necessary labour is performed, the prices will practically coincide with values, and the point aimed at with that determined by the scale of values, i.e. all labourers will have had their hours reduced in the same proportion. [The converse is true: if starting from the hypothetical state we prolong the working day by this method, we reach the actual state, having prolonged it for all labourers proportionally/equally, but through the change in prices having raise the profits in each branch proportionally with its capital]

Note that if we had adopted straightway values, and made the comparison between the two extreme cases, we should have obtained the same, correct, result. But if we had adopted prices, and made that comparison, it would have led us astray: the 'point' indicated by prices [i.e. different reductions in different industries] would have been false when the hyp. state was reached – for on the basis of values some labourers would be working more, and some less, than the necessary hours.

The imaginary process (described above, p. 3 bottom) of gradually shortening the working day, on the basis of the prices appropriate to each intermediate point, and therefore in different proportions for different industries, requires further consideration. As it stands, it is only correct at the wo extreme points [or rather only at the final point], but false at all intermediate ones: for, e.g., on the first step, when the rate of profit is reduced from 6 to 5%, the day of every worker must be reduced in one and the same proportion, and not in different proportions: it is clear that the latter method would give immediately absurd results.

In fact, this shows that the way in which I have argued the point on p. 1 is wrong (too weak). The objection of the vulgar economist is that the surplus produced in each industry (or firm) is measured by its profits. If he agreed to call it exploitation he would say that this is higher (absorbs a larger proportion of the working day) in the industries having more capital per worker. Therefore, he would have to conclude that, if exploitation has to be reduced in the different industries in such proportions as would maintain the rate of profit equal between them, at the lower level, this would require a larger reduction of the working day in the more capitalised industries. It can be shown, by a numerical example, that this is not the case. That on the contrary if the was reduced equally in all industries, the rate of profits would also be reduced equally. This result is made possible by a simultaneous change in prices – those of highly capitalised industries falling (when the rate of profits falls) relatively to the other prices. So that the larger fall in the surplus of such industries has two sources: a) the reduction in working way (common to other industries), (b) the fall in the relative price of their product (peculiar to the highly cap. industries)

29.12.41 [A third source, working in the same direction, would at first sight appear to be the increased depreciation allowances for capital, as the rate of interest falls. However this is a delusion: the 10 loom case shows that it is constant. That is to say, it is constant if real capital has to be maintained intact, though allowing value of semi-used capital to fall as rate of interest falls - and this is the relevant case. Its rise only if money value has to maintained as originally, in case

29.12.41 The previous paragraph is misleading. There is a third source, even if depreciation allowances are regarded as constant. For the value (or rather, in M's sense, the "price") of capital goods falls with the fall in the rate of interest. Therefore, when the rate of s.v. falls, the profits of industries with a large amount of capital per man fall still more owing to this third source - even if the capitals are no more (but no less!) "durable" than in other industries (if they are more durable in the highly capitalised industries than in others, this is a fourth source - for with fall in interest the more durable capitals falls more than that of the less durable ones).

[The whole subject of the "measure of capital" requires investigation in this connection. It has a striking similarity to the contradiction of "prices" and "value" of commodities, and it also depends on the equalisation of the rate of profits. One should start from the "value" of capitals (i.e. quantity of labour necessary to construct them) and see how the requirement of equal rates of profits leads to "prices" of capitals different from their "values".]

30.12.41 This business of 3 or 4 sources is wrong. There are only two sources: a) the reduction of working time in the industry, which reduces the quantity of goods produced; b) The reduction in the price at which the product is sold. The fall in the value of capital of certain industries along with the fall in the general rate of profits and other possible causes, contribute to source b, but don't add anything besides b.

[N.B. The fact that the value of capital (and therefore its "quantity" or magnitude) varies with the rate of profits (and generally cannot be known without knowing prices and rate of profits) makes nonsense of many cornerstones: 1) "Sacrifice of waiting", but how if they don’t know what they are abstaining from? 2) rate of interest, or marg. prod. of cap., as criterion for distribution of resources; but how, if the same resource (in "value") becomes larger or smaller (in "price") according as it used in one way or another?

5.1.42 Those who regard Marx's transition from values to prices, by the necessity of equalising the rate of profit, as a trick, should say the same of Ricardo's (and the whole marginal school) method of determining cost of production by considering only that on the marginal land, by the necessity of equalising the price of all bushels of corn, on whichever land they may be procured. Cannan does so (Rev. of Ec. Theory, p. 178): Ricardo 'did the trick by little more than an arbitrary exercise of the right to define terms ..." -- Piero Sraffa D3.12.46/57r – 63r

Nothing like the above is in Sraffa's book. Connections to Marx are less apparent, although some reviewers perceived them. Counterfactual reasoning is mostly eschewed. The length of the working day is not discussed, but taken as given.

Sraffa does not seem very confident about whether he should start with value or prices and how he should proceed if he adopts the latter. He does see the importance of what was later called price Wicksell effects. I want to note that the next pages in the archive are a draft of the chapter on land in Sraffa's book.

By the way, Ian Steedman has a chapter towards the end of Marx after Sraffa illustrating the analysis of the length of the working day. Consistent with his general approach, he uses data on physical quantity flows and does not take the point at which prices are values and labor is not exploited as a reference point.

Extensive Rent And Labor Values

1.0 Introduction

Do scarce natural resources provide additional difficultes for modern reconstructions of classical and Marxian theories of value? After all land can be sold or rented, and labor cannot produce more land. (I put aside Holland.)

This post presents an exposition of the theory of extensive rent, a start on examining possible difficulties. This type of rent provides the least dificulties, as I understand it, for such modern reconstructions. As usual, I present an example, close to the minimal complexity, needed to make my points. The model can obviously be generalized to include many more produced industrial commodities; many more types of agricultural commodities; and many more types of land, each specialized to support the production of one kind of agricultural commodity.

2.0 Technology

Table 1 specifies the technology for this example. Each column defines the coefficients of production for a process. For example, the only iron-producing process requires a_0,1 person-years of labor, a_1,1 tons of iron, and a_2,1 bushels of corn as inputs for every ton iron produced. I assume that each process requires a year to complete and exhibits constant returns to scale. The corn-producing processes each have an upper limit on how much corn they can produce.

Table 1: A Technology

	Iron Industry	Corn Industry
	Process a	Process b	Process c
Labor	a0,1	a0,2	a0,3
Land, Type 1	c1,1 = 0	c1,2 > 0	c1,3 = 0
Land, Type 2	c2,1 = 0	c2,2 = 0	c2,3 > 0
Iron	a1,1	a1,2	a1,3
Corn	a2,1	a2,2	a2,3
OUTPUTS	1 ton iron	1 bushel corn	1 bushel corn

I assume two types of land exist, distinguished by the processes that can be operated on them. A single corn-producing process can be operated on each type of land. Only a certain number of acres of each type of land exists. Each corn-producing process leaves the land unchanged at the end of operating the process. The given quantities of land limit how much corn can be produced. This model cannot accomodate a positive steady-state rate of growth without technical progress.

A full specification for this model should include requirements for use. I assume that the net output must be such that both types of land are farmed, but only one type is fully farmed. Two techniques for production exist, as shown in Table 2. All three processes are operated in each technique, but only one type of land is fully used.

Table 2: Specification of Techniques

Technique	Type 1 Land	Type 2 Land
Alpha	Partially farmed	Fully farmed
Beta	Fully farmed	Partially farmed

3.0 Parameters and Variables

I have already implicitly defined certain parameters above. Table 3 lists certain parameters I use in this model. Table 4 lists variables that I need. Some assumptions are imposed on the matrices A_α and A_β:

• All produced commodities are basic. Iron and corn enter directly or indirectly into the production of both commodities.
• The technology expressed by these matrices is productive. Each matrix satisfies the Hawkins-Simon condition.

Table 3: Selected Parameters

Symbol	Definition
a0, α	Two-element row vector consisting of first two labor coefficients.
a0, β	Two-element row vector consisting of first and third labor coefficients.
Aα	2x2 matrix, with columns consisting of iron and corn coefficients of production for first and second processes.
Aβ	2x2 matrix, with columns consisting of iron and corn coefficients of production for first and third processes.
d	Two-element column vector consisting of iron and corn quantities in the numeraire.

Table 4: Variables

Symbol	Definition
vα	2-element row vector of labor values when type 1 land is free.
vβ	2-element row vector of labor values when type 2 land is free.
p	2-element row vector of prices of unit quantities of iron and corn.
p1	The price of iron, in numeraire units per ton. The first element of p.
p2	The price of corn, in numeraire units per bushel. The second element of p.
rho1	The rent of type 1 land, in numeraire units per acre.
rho2	The rent of type 2 land, in numeraire units per acre.
w	The wage, in numeraire units per person-year.
r	The rate of profits.

4.0 Labor Values

Given the technique in use, how much additional labor would be employed throughout the economy if the net output was such that one additional unit of iron were produced? This is the labor value of iron, and it easily calculated in the theory. The answer to the same question for corn is its labor value.

Suppose type 1 land is free. Then labor values are:

v_α = a_{0, α} (I - A_α)^-1

Labor values, when type 2 land is free, are the corresponding Leontief employment multipliers for the Beta technique. Variations in net output require varying the amount of the land farmed on the type of land that is not fully farmed.

5.0 Prices of Production

With market prices, some operated processes will be obtaining a higher rate of profits than average, and some will be obtaining a lower rate. These variations in the profit rates are perhaps a signal to capitalists that they should disinvest in some industries or processes and increase investment in others. Models of cross-dual dynamics and other models explore these disequilibria.

Prices of production are such that these signals are absent. All operated processes obtain the same rate of profits. I assume profits, rents, and wages are paid out of the surplus product at the end of the year. The following three equations express the condition that all processes obtain the same rate of profits:

(p₁ a_1,1 + p₂ a_2,1)(1 + r) + w a_0,1 = p₁

(p₁ a_1,2 + p₂ a_2,2)(1 + r) + rho₁ c_1,2 + w a_0,2 = p₂

(p₁ a_1,3 + p₂ a_2,3)(1 + r) + rho₂ c_2,3 + w a_0,3 = p₂

The next equation expresses the condition that the price of the numeraire is unity:

p d = 1

Finally, one of the rents must be zero:

rho₁ rho₂ = 0

The last equation is a defining feature of the theory of extensive rent.

Suppose one of the types of land is rent-free. For deiniteness, let type 1 land be only partially farmed. Then the first four equations are in terms of five variables (p₁, p₂, rho₂, w, r). Just as in the case with only circulating capital, prices of production are specified up to one degree of freedom. In classical political economy, the wage is take as given.

6.0 Choice of Technique

Suppose the wage is non-negative and does not exceed a maximum defined by the technology. The system of equations for prices of production has two solutions. Each solution has the rent on one type of land set to zero. The cost-minimizing technique is the one in which the rent on the other land is positive. If, for a technique, the rent on a type of land is negative, that technique will not be adopted by capitalists. At a switch point, the rents on both types of land are zero.

But the analysis of the choice of technique can be expressed in terms of wage curves. Suppose rents were zero. Consider the first two equations in the system of equations for the prices of production and the equation setting the price of the numeraire to unity. These equations yield a function in which the wage decreases with an increase in the rate of profits. Similarly, the first and third equations yield another decreasing wage curve.

In the case of circulating capital alone, the cost-minimizing technique is found by the wage frontier formed out of the outer envelope of these wage curves. At a given wage, the cost-minimizing technique maximizes the wage.

In this example of extensive rent, the cost-minimizing technique is found by the wage frontier formed out of the inner envelope of the wage curves.

In either case, the appropriate wage frontier shows that a lower rate of profits is associated with a higher wage and vice versa. The maximum wage occurs when the rate of profits is zero. The maximum rate of profits arises when the wage is zero.

7.0 Special Cases

Which land is free and which land pays a rent depends on either the wage or the rate of profits, whichever is taken as exogenous in the system of prices of production. At any rate, a wage frontier exists in which the wage is higher the smaller the rate of profits. This frontier is not the outer frontier of the wage curves for the technique.

Without loss of generality, suppose the Alpha technique is cost-minimizing. Type 1 land is not fully farmed and pays no rent. Then labor values are defined, based on the iron-producing process and the process on type 1 land.

Consider the special case in which a_{0, α} is an eigenvector corresponding to the maximum eigenvector for A_α. Then relative prices of production are equal to relative labor values.

On the other hand, suppose that the numeraire is the standard commodity, as found from a_{0, α} and A_α. Suppose only the standard commodity is produced. In this case, only the process on the rent-free land would be used, in contradiction to the analysis of the choice of technique. And suppose the wage is paid out in the form of the standard commodity. Then the following hold:

• The labor value of gross output is equal to total gross output, evaluated at prices of production.
• The labor value of net output is equal to net output, evaluated at prices of production.
• The labor value of the proportion of the standard commodity paid out in wages is equal to wage goods, evaluated at prices of production.

This special case seems especially forced in the case of extensive rent. Is some reformulation available in which surplus value can be treated as the sum of profits and rent?

I do not address the use of labor values in Marx's account of exploitation, Marx-biased technical change, and so on. The special cases in which the labor theory of value hold make obvious that, for a given technology, a higher rate of profits require a lower wage. And this wage frontier continues to hold in models of extensive rent.

8.0 Conclusion

The inclusion of natural resources, insofar as they can be modeled by extensive rent, does not seem to pose any additional issues for modern formulations of classical and Marxian political economy. It does highlight some issues that arise in models with circulating capital.

Labor values can be calculated for all produced commodities, given the technique in use. They are calculated from the marginal land that receives no rent. But suppose that a choice of technique exists. Then, an analysis at the level of prices of production must be prior to the calculation of labor values. The theory of extensive rent highlights this issue.

As Ricardo and Marx noted, prices of production are generally not proportional to labor values. They are equal in the special case, in which all industries have equal organic compositions of capital, in both models of circulating capital and of extensive rent. In the latter case, the organic composition of capital is found for agriculture from no-rent lands partially farmed.

A commodity of average organic composition is picked out in both models. Total labor values and the labor value of wages are equal to the corresponding aggregates in the system of prices of production when this average commodity is used as numeraire and is produced. These invariants, though, have to restricted to the production of the numeraire with the iron-producing process and the process on no-rent land. It is not clear to me that Marx thought his invariants held in his chapters on rent, given their location towards the end of volume 3 of Capital.

Obviously, these observations on natural resources and rent are just a start. They do seem to match what Ricardo was about in the second chapter of his Principles. The analysis of the choice of technique can be thought of, somewhat, as a critique of Ricardo.

At any rate, prices of production are well-defined in models of extensive rent. And they can be used in an analysis of the choice of technique. As usual, I present the analysis with no mention of utility maximization, preferences, or tastes.

The History Of No-Longer-Existing Socialism Validates Marx

Marx, like Adam Smith and Walt Rostow, had a stages theory of history. Feudalism was succeeded by capitalism, and capitalism is to be succeeded by socialism. Socialism is to arise first in the most advanced capitalist countries. (The theory of history is not my favorite part of Marxist theory.)

Russia, in 1917, was a semi-feudal country with peasants as the largest class. I guess China was the same, before Mao. A Marxist would not expect socialism to be successful in either country.

I think Lenin and the Bolsheviks agreed with this thesis when they first came to power. They expected their revolution to kick off revolutions elsewhere in Europe. And their expectations seemed to be initially met, what with the Spartacist uprising in Germany, Hungary, and so on.

Lenin, knowing that Russia was not ripe for socialism, talked about state capitalism even before the October revolution. Stalin invented the doctrine of socialism in one country. Economic development in the USSR and, I guess, in China, was amazing, albeit with much brutality. But eventually, further development required some semblance of capitalism

Is this not just what a Marxist would expect?

References

• Steve Paxton. 2021. Unlearning Marx [I have barely started this].
• Terry Eagleton. 2011. Why Marx was Right.

William Baumol On Marx

This is more for my commonplace book. The first two quotations are part of a symposium with Morishima and Samuelson:

"This paper will suggest that the meaning of the relationship between values and prices described in Capital has been widely misunderstood. Commentators as eminent as Mrs. Robinson and Professor Samuelson have sought in the transformation discussion issues which Karl Marx never meant it to contain. Writers on 'the transformation problem' since L. Bortkiewicz have focussed on an issue that is largely peripheral; and others like E. B6hm-Bawerk have asserted that there is a contradiction between the analyses of Volumes I and III which is certainly not to be found there unless lne reads into them an interpretation different from that which Marx repeatedly emphasized.

Interpretation of the intentions of the writings of the dead is always a questionable undertaking, particularly since defunct authors cannot defend themselves. Yet there are some cases in which a careful rereading of the pertinent writings indicates that the author did speak for himself and spoke very clearly-the trouble in such cases seems to be that somethinv aboit the onriinal nresentation prevents most readers, even some very careful ones, from seeing what the writer intended.

A notable case in point is D. Ricardo's discussion of the labor theory of value. It is hard to understand how a careful reader of any edition of the Principles can overlook Ricardo's recognition of the role of the quantity and the durability of capital in the determination of price. The labor theory is explicitly proposed as a remarkably good approximation to the determination of competitive price. But, ultimately, Ricardo holds to a cost of production theory of pricing, not to a pure labor theory. Yet until Stigler's fine article on the subject (1958), in which this is documented beyond any shadow of a doubt, virtually any text was prepared to ascribe to Ricardo the purest of labor theories, and even J. H. Hollander and E. Cannan (see G. J. Stigler for references) suggested that Ricardo retreated grudgingly under fire to the cost of production model of the third edition. Only a few commentators, notably A. Marshall, J. Viner, and P. Sraffa, saw Ricardo's analysis for what it so plainly was from the first edition on.

I emphasize this case for two reasons; first, because I will try to show that the correct interpretation of Marx' intentions is equally evident, and second, because I will suggest that the false analogy between Ricardo's and Marx' value theories may help to explain our misunderstanding of the latter...

...In Ricardo, the labor theory of value was meant as a good approximation to a full explanation of the determination of prices. However Marx probably never intended to produce such an approximation and it certainly was not his intention when he wrote about the transformation problem; yet that objective, or something close to it, is often attributed to Marx.

I will provide evidence that Marx did not intend his transformation analysis to show how prices can be deduced from values. Marx was well aware that market prices do not have to be deduced from values (nor, for that matter, values from prices). Rather, the two sets of magnitudes which are derived more or less independently were recognized by Marx to differ in a substantial and a systematic manner. A subsidiary purpose of the transformation calculation was to determine the nature of these deviations. But this objective and, indeed, any explanation of pricing as an end in itself, was of very little consequence to Marx, for the primary transformation was not from values into prices but, as Marx and Engels repeatedly emphasize, from surplus values into the non-labor income categories that are recognized by 'vulgar economists,' i.e., profits, interest, and rent." -- William J. Baumol. 1974. The transformation of values: What Marx 'really' meant (an interpretation). Journal of Economic Literature 12(1): 51-62.

"2. I am surprised that 'On the question of whether [Marx's] purpose was successful in some sense or another [Samuelson] can find only a few relevant paragraphs in Baumol's text.' I am surprised because, so far as I know, there is no such paragraph. The only objective of my paper was to determine what Marx had set out to accomplish and how Marx believed he had accomplished his objectives, because I don't think it is appropriate to criticize anyone until we are sure we are criticizing what he actually said, not what we suspect he might have said, or should have said, or someone else says he might have said...

...4. Professor Samuelson proposes his peace terms, which require me to admit that for an explanation of 'actual wage-profits distribution,' presumably as for an explanation of actual pricing of commodities, 'the Volume I analysis is indeed a detour.' So much I admit readily and without reservations, and I contend Marx would readily have admitted it too, for in fact he did so repeatedly. Actual prices and actual wages, profits, rents and interest payments clearly were to him explainable by the classical mechanism, which is what he admittedly took over in Volume III. Marx never claimed, in fact he specifically denied, that one gets better numbers for any of these magnitudes from a Volume I than from a Volume III analysis.

Thus, for his part, all that Professor Samuelson has to do to end the disagreement between us is to admit that Marx himself was not particularly interested in the determination of these magnitudes, which he considered a surface manifestation and were important to him only because he believed them to conceal the underlying social production relationships...

...One final comment. Obviously, Ricardo is not easy reading, and our predecessors did often hold a multiplicity of views among which they themselves were not always able to distinguish, and such problems are brushed aside far too often in writings But there are some cases, albeit rare, where an author has said clearly and repeatedly, 'I do mean A, I do not mean B,' yet many people have refused to listen. Ricardo did repeatedly say that his was a cost of production model. He did say, at length, in every edition of the Principles that quantity and durability of capital make a difference to value. I suggest to any interested reader that he treat himself to a reexamination of pages 3043 (from the third edition) and 52-66 (from the first edition) of Volume I of Piero Sraffa [5, 1951] to see whether he can come away disagreeing with Jacob Viner's (humorous?) conclusion that 'Ricardo's actual words show that from the first he held that the relative values of commodities are always partly dependent on the relative amounts of fixed capital employed in their production' (Viner's italics) [6, 1930]." -- William J. Baumol. 1974. The fundamental Marxian theorem: A reply to Samuelson: Comment. Journal of Economic Literature 12(1): 74-75.

Baumol returned to Marx in 1983:

"I find few things as discouraging as the persistent attribution of positions to a writer whose works contain repeated, categorical, indeed emotional, denuciations of those views. Marx's views on wages are a prime example. Both vulgar Marxists and vulgar opponents of Marx have propounded two associated myths: that he believed wages under capitalism are inevitably driven near some physical subsistence level, and that he considered this to constitute of robbery of the workers and a major evil of capitalism. Yet Marx and Engels tell us aggain and again, sometimes in the most intemperate language, that these views are the very opposite of theirs. These observations, incidentally, are hardly new discoveries..." -- William J. Baumol. (1983). Marx and the iron law of wages. American Economic Review 73(2): 303-308

Francis Spufford On Commodity Fetishism As A Dance

I have expressed an appreciation before of the section in Capital on commodity fetishism. Perhaps this section stands up to a critique of Marx's theory of value.

"But Marx had drawn a nightmare picture of what happened to human life under capitalism, when everything was produced only in order to be exchanged; when true qualities and uses dropped away, and the human power of making and doing itself became only an object to be traded. Then the makers and the things made turned alike into commodities, and the motion of society turned into a kind of zombie dance, a grim cavorting whirl in which objects and people blurred together till the objects were half-alive and the people were half-dead. Stock-market prices acted back upon the world as if they were independent powers, requiring factories to be opened or closed, real human beings to work or rest, hurry or dawdle; and they, having given the transfusion that made the stock prices come alive, felt their flesh go cold and impersonal on them, mere mechanisms for chunking out the man-hours. Living money and dying humans, metal as tender as skin and skin as hard a metal, taking hands, and dancing round, and round, and round, with no way ever of stopping: the quickened and the deadened, whirling on. That was Marx's description, anyway. And what would be the alternative? A dance of another nature, Emil presumed. A dance to the music of use, where every step fulfilled some real need, did some tangible good, and no matter how fast the dancers spun, they moved easily, because they moved to a human measure, intelligible to all, chosen by all. Emil gave a hop and shuffle in the dust." -- Francis Spufford, Red Plenty, Graywolf Press, 2010: 66-67.

I may write a short review of this novel. If I do, I think I will not first review the seminar at Crooked Timber on it.

A Derivation Of Prices Of Production With Linear Programming

1.0 Introduction

This post illustrates a derivation of prices of production, based on certain properties of duality theory as applied to linear programming. I strive to be more concise and elementary than previous expositions. This exposition is based on John Roemer's Reproducible Solution (Analytical Foundations of Marxian Economic Theory, Cambridge University Press, 1981).

You will find no utility maximization or supply and demand functions below. I have no need for such hypotheses. Nevertheless, one can read this derivation as consistent with marginalism.

2.0 Technology and Endowments

Two commodities, iron and corn, are produced in this example. Managers of firms know a technology consisting of the processes defined in Table 1. Each column shows the inputs and outputs for a process operated at a unit level. All processes take a year to complete and provide their output at the end of the year. Each process exhibits constant returns to scale (CRS). For convenience, assume all coefficients of production defined in the table are positive. The inputs to production are totally used up by operating these processes.

Table 1: The Technology

INPUTS	Processes
	Iron Industry		Corn Industry
	a	b	c	d
Labor	a0,1(a)	a0,1(b)	a0,2(c)	a0,2(d)
Iron	a1,1(a)	a1,1(b)	a1,2(c)	a1,2(d)
Corn	a2,1(a)	a2,1(b)	a2,2(c)	a2,2(d)
OUTPUT	1 ton iron	1 ton iron	1 bushel corn	1 bushel corn

The endowments of iron and corn in the firm's inventory at the start of the year are also given parameters. Table 2 lists the remaining variables in this post. Presumably, the endowments are from production during the previous year. They are unlikely to be in the proportions needed to continue production. For example, if the managers of a firm decide to specialize in producing corn, they will have no endowments of iron.

Table 2: Parameters and Variables

Additional Parameters
ω1	Endowment of iron (in tons) for the firm.
ω2	Endowment of corn (in bushels) for the firm.
Parameters taken as given by managers of the firm
p	Price of iron (in bushels per ton).
w	The wage (in bushels per person-year).
Decision Variables
q1(a)	Quantity of iron (in tons) produced by the first process.
q1(b)	Quantity of iron (in tons) produced by the second process.
q2(c)	Quantity of corn (in bushels) produced by the third process.
q2(d)	Quantity of corn (in bushels) produced by the fourth process.
r	The rate of profits.

3.0 The Primal Linear Program

Managers of firms choose the quantities to produce with each process to maximize the increment z in value, subject to the constraint that they can buy the needed inputs at the start of the year out of the revenue obtained by selling their endowment. The objective function for the primal linear program is:

z = {p - [p a_1,1(a) + a_2,1(a) + w a_0,1(a)]} q₁(a)

+ {p - [p a_1,1(b) + a_2,1(b) + w a_0,1(b)]} q₁(b)

+ {1 - [p a_1,2(c) + a_2,2(c) + w a_0,2(c)]} q₂(c)

+ {1 - [p a_1,2(d) + a_2,2(d) + w a_0,2(d)]} q₂(d)

The quantities in the square brackets above are the costs of operating each process at a unit level. A bushel corn is taken as numeraire. The quantities in the squiggly brackets are the net revenues (also known as accounting profits) of operating each process at a unit level. Scaling these net revenues by the level of operation for each process results in the total accounting profit for the firm.

The constraints are:

[p a_1,1(a) + a_2,1(a)] q₁(a)

+ [p a_1,1(b) + a_2,1(b)] q₁(b)

+ [p a_1,2(c) + a_2,2(c)] q₂(c)

+ [p a_1,2(d) + a_2,2(d)] q₂(d) ≤ p ω₁ + ω₂

q₁(a) ≥ 0, q₁(b) ≥ 0, q₂(c) ≥ 0, q₂(d) ≥ 0

The statement of the constraints is based on the assumption that wages are paid at the end of the year, not advanced at the start.

4.0 The Dual Linear Program

The above linear program has a dual. In the dual, the rate of profits r is chosen to minimize the charge y on endowments:

y = (p ω₁ + ω₂) r

Such that:

[p a_1,1(a) + a_2,1(a)](1 + r) + w a_0,1(a) ≥ p

[p a_1,1(b) + a_2,1(b)](1 + r) + w a_0,1(b) ≥ p

[p a_1,2(c) + a_2,2(c)](1 + r) + w a_0,2(c) ≥ 1

[p a_1,2(d) + a_2,2(d)](1 + r) + w a_0,2(d) ≥ 1

r ≥ 0

Each constraint in the dual specifies that the revenues obtained from operating a process at the unit level do not exceed the costs, where costs include a charge for the going rate of profits. In other words, no super-normal profits can be obtained.

5.0 Some Observations About Duality

The value of the objective functions are equal in the solutions to the primal and dual LPs. In other words, the increment in value obtained by the decisions of the manager of a firm is charged to the value of the endowment.

Suppose the solution of the primal LP results in some process being operated at a positive level. Then the corresponding constraint in the dual LP is met with equality in its solution. Likewise, if a constraint in the dual is met with inequality, then that process will not be operated in the dual.

If the rate of profits in the solution to the dual is positive, then the constraint in the primal LP will be met with equality. That is, the whole value of the endowment will be used for further production.

6.0 Prices of Production

I introduce a final assumption. The solution to these LPs must be such that the economy can continue. In the context of this exposition, some firms must produce iron, and some must produce corn. Thus, one of the first two constraints in the dual LP must be met with equality. One of next two constraints must also be met with equality.

Consider the case when only one of the processes for producing iron is operated, and the same is true of the processes for producing corn. The dual LP yields a system of two equations in three variables: the price of iron, the wage, and the rate of profits. This system specifies prices of production.

This formulation solves for the choice of the technique, as well as prices of production. It can be generalized to allow for the production of many more commodities and many more processes for producing each commodity. A generalization can allow for heterogeneous labor. Another generalization allows for the production and use of fixed capital, that is, machines that last for many years. For a given wage, prices and the rate of profits drop out of the equations for prices of production for the chosen technique. These prices do not support the parables often told in introductory economics classes with supply and demand. For example, unemployment cannot necessarily be eliminated by lowering the wage and encouraging firms to thereby hire more labor.

7.0 Conclusion

The above illustrates some elements of a theory of value. This is neither a labor theory of value, nor Marx's theory of value. The theory is focused on production and has implications about how labor is allocated among industries, a central concern of Karl Marx.

How Ownership Obtains A Return According To Marx

1. Introduction

Elsewhere on the internet, I have been explaining my understanding of some rudiments of the political economy of Karl Marx.

Marx's concept of surplus value is a generalization of the concept of profit, in some sense. Surplus value takes in all returns to ownership, whether they be profits, interest, rent, and so on. Surplus value arises from the distinction between the use value and the exchange value of labor power, a peculiar commodity. Because capitalists own the means of production, they can ensure through their domination of the workers, that laborers work longer than the time needed to reproduce their means of subsistence.

2. A Simple LTV as the Setting of Marx's Theory

Marx explains the generation of surplus value in volume 1 of Capital. For the sake of argument, he assumes a special case in which a simple labor theory of value holds. Market prices tend towards prices of production. When the organic composition of commodities does not vary among industries, prices of production are proportional to labor values. Marx knows this is a special case.

Why assume the labor theory of value? It was a dominant theory at the time. Marx can take it over from Ricardo, albeit he modifies it and critiques it. It also accords with what some socialists think is fair. Marx wants to explain surplus value when nobody is cheating anybody:

"This sphere [of simple circulation or of exchange of commodities] that we are deserting, within whose boundaries the sale and purchase of labour-power goes on, is in fact a very Eden of the innate rights of man. There alone rule Freedom, Equality, Property and Bentham. Freedom, because both buyer and seller of a commodity, say of labour-power, are constrained only by their own free will. They contract as free agents, and the agreement they come to, is but the form in which they give legal expression to their common will. Equality, because each enters into relation with the other, as with a simple owner of commodities, and they exchange equivalent for equivalent. Property, because each disposes only of what is his own. And Bentham, because each looks only to himself. The only force that brings them together and puts them in relation with each other, is the selfishness, the gain and the private interests of each. Each looks to himself only, and no one troubles himself about the rest, and just because they do so, do they all, in accordance with the pre-established harmony of things, or under the auspices of an all-shrewd providence, work together to their mutual advantage, for the common weal and in the interest of all." -- Karl Marx, Capital, volume 1, chapter 6.

This emphasis on fairness in exchange also justifies a lack of focus on market prices. Marx does not want to explain surplus value as 'profits on alienation', on cleverness in buying low and selling high. He is looking for a system-wide explanation, not an explanation arising from lucky transactions.

3. Labor-Power as a Commodity

According to Marx, what workers sell is the capacity to labor under the direction of the capitalist and with materials and equipment provided by the capitalist. Like all commodities, labor-power has an exchange-value and a use-value. The exchange value is its labor value, that is, the amount of labor-time needed to produce the commodities needed to sustain the worker.

The value of labor-power depends on social conventions about what is needed for consumption. Marx, unlike Ferdinand Lassalle, does not hold an 'iron law' of wages. In chapter 25 of volume 1 of Capital, Marx describes how the wage varies with the increase and decrease of the 'industrial reserve army'. Richard Goodwin has a formal model of this aspect of Marx's theory.

The use-value of the commodity of labor power is the expenditure of labor in production. It is the realm of production that we are arriving at after leaving the realm of exchange above. But, before discussing this commodity and its use-value further, I want to note one more statement of Marx's problem domain:

"In order to be able to extract value from the consumption of a commodity, our friend, Moneybags, must be so lucky as to find, within the sphere of circulation, in the market, a commodity, whose use-value possesses the peculiar property of being a source of value, whose actual consumption, therefore, is itself an embodiment of labour, and, consequently, a creation of value." -- Karl Marx, Capital, volume 1, chapter 6.

4. On The Existence of Labor-Power

Marx is searching for the preconditions of capitalism and of political economy. He wants his reader to realize that some properties of a commodity-producing economy are not eternal natural-laws, but have a history and a start. They thus might also have an end.

The availability of labor-power for purchase on the market is one aspect of capitalism that has a history. For labor-power to be a commodity, workers must have a double freedom:

"In themselves money and commodities are no more capital than are the means of production and of subsistence. They want transforming into capital. But this transformation itself can only take place under certain circumstances that centre in this, viz., that two very different kinds of commodity-possessors must come face to face and into contact; on the one hand, the owners of money, means of production, means of subsistence, who are eager to increase the sum of values they possess, by buying other people's labour power; on the other hand, free labourers, the sellers of their own labour power, and therefore the sellers of labour. Free labourers, in the double sense that neither they themselves form part and parcel of the means of production, as in the case of slaves, bondsmen, &c., nor do the means of production belong to them, as in the case of peasant-proprietors; they are, therefore, free from, unencumbered by, any means of production of their own. With this polarization of the market for commodities, the fundamental conditions of capitalist production are given. The capitalist system presupposes the complete separation of the labourers from all property in the means by which they can realize their labour. As soon as capitalist production is once on its own legs, it not only maintains this separation, but reproduces it on a continually extending scale. The process, therefore, that clears the way for the capitalist system, can be none other than the process which takes away from the labourer the possession of his means of production; a process that transforms, on the one hand, the social means of subsistence and of production into capital, on the other, the immediate producers into wage labourers. The so-called primitive accumulation, therefore, is nothing else than the historical process of divorcing the producer from the means of production. It appears as primitive, because it forms the prehistoric stage of capital and of the mode of production corresponding with it." -- Karl Marx, Capital, Volume 1, Chapter 26 (my emphasis)

For surplus value to exist, workers must be constrained to work longer than needed to reproduce their wage. The division of the working day into the time to replace wage goods and the time that produces surplus value is not obvious in looking at a single industry. Many workers are producing capital goods, not goods that they consume. Here too one must look at the economy as a whole.

Capitalists can constrain workers to work long enough to produce surplus value because they own the means of production. Production requires labor to work with produced capital goods. These were previously produced by other workers. Because of the products of labor are alienated from the workers, capitalists are able to use their domination of the production process to acquire surplus value. Under this domination, productivity increases and it becomes even more difficult for a group of workers to go into business for themselves.

5. An Exception

In his first draft for Capital, Marx explicitly recognizes that some workers can escape having to sell their labor power. But this cannot be true for workers in general:

"When we look at social relations which create an undeveloped system of exchange, of exchange values and of money, or which correspond to an undeveloped degree of these, then it is clear from the outset that the individuals in such a society, although their relations appear to be more personal, enter into connection with one another only as individuals imprisoned within a certain definition, as feudal lord and vassal, landlord and serf, etc., or as members of a caste etc. or as members of an estate etc. In the money relation, in the developed system of exchange (and this semblance seduces the democrats), the ties of personal dependence, of distinctions of blood, education, etc, are in fact exploded, ripped up (at least, personal ties all appear as personal relations); and individuals seem independent (this is an independence which is at bottom merely an illusion and it is more correctly called indifference), free to collide with one another and to engage in exchange within this freedom; but they appear thus only for someone who abstracts from the conditions, the conditions of existence within which these individuals enter into contact (and these conditions, in turn, are independent of the individuals and, although created by society, appear as if they were natural conditions, not controllable by individuals). The definedness of individuals, which in the former case appears as a personal restriction of the individual by another, appears in the latter case as developed into an objective restriction of the individual by relations independent of him and sufficient unto themselves. (Since the single individual cannot strip away his personal definition, but may very well overcome and master external relations, his freedom seems to be greater in case 2. A closer examination of these external relations, these conditions, shows, however, that it is impossible for the individuals of a class etc. to overcome them en masse without destroying them. A particular individual may by chance get on top of these relations, but the mass of those under their rule cannot, since their mere existence expresses subordination, the necessary subordination of the mass of individuals.) These external relations are very far from being an abolition of 'relations of dependence'; they are rather the dissolution of these relations into a general form; they are merely the elaboration and emergence of the general foundation of the relations of personal dependence. Here also individuals come into connection with one another only in determined ways. These objective dependency relations also appear, in antithesis to those of personal dependence (the objective dependency relation is nothing more than social relations which have become independent and now enter into opposition to the seemingly independent individuals; i.e. the reciprocal relations of production separated from and autonomous of individuals) in such a way that individuals are now ruled by abstractions, whereas earlier they depended on one another. The abstraction, or idea, however, is nothing more than the theoretical expression of those material relations which are their lord and master. Relations can be expressed, of course, only in ideas, and thus philosophers have determined the reign of ideas to be the peculiarity of the new age, and have identified the creation of free individuality with the overthrow of this reign. This error was all the more easily committed, from the ideological stand-point, as this reign exercised by the relations (this objective dependency, which, incidentally, turns into certain definite relations of personal dependency, but stripped of all illusions) appears within the consciousness of individuals as the reign of ideas, and because the belief in the permanence of these ideas, i.e. of these objective relations of dependency, is of course consolidated, nourished and inculcated by the ruling classes by all means available." -- Karl Marx. Grundrisse (my emphasis)

I am not sure where I should have cut the above quotation. I need some reference for "case 2" in the highlighted part. As far as I can see, the Grundrisse reads mostly like the above. By contrast, Capital mostly reads as if it is positivist social science.

Back in the 1960s, one might have thought that the exception would become the rule over a worker's lifetime. If retirement were universal, a group of elderly people would be living off surplus value, so to speak, generated by working-age population. But that is only true for those in the 'formal' part of the economy, and maybe not even always then.

6. Conclusion

Surplus value, according to Marx, is generated by the use value of labor power being potentially a longer time to work than the time needed to reproduce the labor value of labor power. Because of the separation of the means of production from the workers, the capitalists can constrain the workers to generate surplus value. This explanation relies on institutions needed to sustain capitalism.

Is The Labor Theory Of Value Compatible With Automation?

Automation Of Chinese Ports

With automation, many processes for production and distribution now execute with minimal human oversight. How can the labor theory of value, as in volume 1 of Capital, be compatible with this?

Marx has some comments on this subject in the Grundrisse:

The exchange of living labour for objectified labour – i.e. the positing of social labour in the form of the contradiction of capital and wage labour – is the ultimate development of the value-relation and of production resting on value. Its presupposition is – and remains – the mass of direct labour time, the quantity of labour employed, as the determinant factor in the production of wealth. But to the degree that large industry develops, the creation of real wealth comes to depend less on labour time and on the amount of labour employed than on the power of the agencies set in motion during labour time, whose 'powerful effectiveness' is itself in turn out of all proportion to the direct labour time spent on their production, but depends rather on the general state of science and on the progress of technology, or the application of this science to production. (The development of this science, especially natural science, and all others with the latter, is itself in turn related to the development of material production.) Agriculture, e.g., becomes merely the application of the science of material metabolism, its regulation for the greatest advantage of the entire body of society.

Real wealth manifests itself, rather – and large industry reveals this – in the monstrous disproportion between the labour time applied, and its product, as well as in the qualitative imbalance between labour, reduced to a pure abstraction, and the power of the production process it superintends. Labour no longer appears so much to be included within the production process; rather, the human being comes to relate more as watchman and regulator to the production process itself. (What holds for machinery holds likewise for the combination of human activities and the development of human intercourse.)

No longer does the worker insert a modified natural thing as middle link between the object and himself; rather, he inserts the process of nature, transformed into an industrial process, as a means between himself and inorganic nature, mastering it. He steps to the side of the production process instead of being its chief actor. In this transformation, it is neither the direct human labour he himself performs, nor the time during which he works, but rather the appropriation of his own general productive power, his understanding of nature and his mastery over it by virtue of his presence as a social body – it is, in a word, the development of the social individual which appears as the great foundation-stone of production and of wealth. The theft of alien labour time, on which the present wealth is based, appears a miserable foundation in face of this new one, created by large-scale industry itself. As soon as labour in the direct form has ceased to be the great well-spring of wealth, labour time ceases and must cease to be its measure, and hence exchange value [must cease to be the measure] of use value. The surplus labour of the mass has ceased to be the condition for the development of general wealth, just as the non-labour of the few, for the development of the general powers of the human head. With that, production based on exchange value breaks down, and the direct, material production process is stripped of the form of penury and antithesis. The free development of individualities, and hence not the reduction of necessary labour time so as to posit surplus labour, but rather the general reduction of the necessary labour of society to a minimum, which then corresponds to the artistic, scientific etc. development of the individuals in the time set free, and with the means created, for all of them.

Capital itself is the moving contradiction, [in] that it presses to reduce labour time to a minimum, while it posits labour time, on the other side, as sole measure and source of wealth. Hence it diminishes labour time in the necessary form so as to increase it in the superfluous form; hence posits the superfluous in growing measure as a condition – question of life or death – for the necessary. On the one side, then, it calls to life all the powers of science and of nature, as of social combination and of social intercourse, in order to make the creation of wealth independent (relatively) of the labour time employed on it. On the other side, it wants to use labour time as the measuring rod for the giant social forces thereby created, and to confine them within the limits required to maintain the already created value as value. Forces of production and social relations – two different sides of the development of the social individual – appear to capital as mere means, and are merely means for it to produce on its limited foundation. In fact, however, they are the material conditions to blow this foundation sky-high. 'Truly wealthy a nation, when the working day is 6 rather than 12 hours. Wealth is not command over surplus labour time' (real wealth), 'but rather, disposable time outside that needed in direct production, for every individual and the whole society.' (The Source and Remedy etc. 1821, p. 6.)

Nature builds no machines, no locomotives, railways, electric telegraphs, self-acting mules etc. These are products of human industry; natural material transformed into organs of the human will over nature, or of human participation in nature. They are organs of the human brain, created by the human hand; the power of knowledge, objectified.

The development of fixed capital indicates to what degree general social knowledge has become a direct force of production, and to what degree, hence, the conditions of the process of social life itself have come under the control of the general intellect and been transformed in accordance with it. To what degree the powers of social production have been produced, not only in the form of knowledge, but also as immediate organs of social practice, of the real life process. -- Karl Marx, Grundrisse, Contradiction between the foundation of bourgeois production (value as measure) and its development. Machines etc.

I take the paragraphing above from David McLellan's severely abridged version. I think I need a hard-copy version if I am ever going to fully read the Grundrisse. For what it is worth, John Von Neumann has a theory of value for a fully automated economy.

Marx above seems to offer one story of how capitalism will end. An issue exists with finding supposed anti-Marxist arguments echoed in writings unpublished in Marx's lifetime. It is not clear how to working class has a role in the above story. Is this story consistent with what Marx says in Capital, as quoted in Section 4 here? Sundry observations do not neccessarily add up to a consistent theory.