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.

Adam Smith's 'Effectual Demand'

"There is in every society or neighbourhood an ordinary or average rate, both of wages and profit, in every different employment of labour and stock...

There is likewise in every society or neighbourhood an ordinary or average rate of rent...

These ordinary or average rates may be called the natural rates of wages, profit and rent, at the time and place in which they commonly prevail.

When the price of any commodity is neither more nor less than what is sufficient to pay the rent of the land, the wages of the labour, and the profits of the stock employed in raising, preparing, and bringing it to market, according to their natural rates, the commodity is then sold for what may be called its natural price...

The actual price at which any commodity is commonly sold, is called its market price. It may either be above, or below, or exactly the same with its natural price.

The market price of every particular commodity is regulated by the proportion between the quantity which is actually brought to market, and the demand of those who are willing to pay the natural price of the commodity, or the whole value of the rent, labour, and profit, which must be paid in order to bring it thither. Such people may be called the effectual demanders, and their demand the effectual demand; since it maybe sufficient to effectuate the bringing of the commodity to market. It is different from the absolute demand. A very poor man may be said, in some sense, to have a demand for a coach and six; he might like to have it; but his demand is not an effectual demand, as the commodity can never be brought to market in order to satisfy it...

When the quantity brought to market is just sufficient to supply the effectual demand, and no more, the market price naturally comes to be either exactly, or as nearly as can be judged of, the same with the natural price. The whole quantity upon hand can be disposed of for this price, and can not be disposed of for more. The competition of the different dealers obliges them all to accept of this price, but does not oblige them to accept of less...

The natural price, therefore, is, as it were, the central price, to which the prices of all commodities are continually gravitating. Different accidents may sometimes keep them suspended a good deal above it, and sometimes force them down even somewhat below it. But whatever may be the obstacles which hinder them from settling in this centre of repose and continuance, they are constantly tending towards it.

The whole quantity of industry annually employed in order to bring any commodity to market, naturally suits itself in this manner to the effectual demand. It naturally aims at bringing always that precise quantity thither which may be sufficient to supply, and no more than supply, that demand." -- Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, Book I, Chapter VII.

I prefer the term 'prices of production' to Smith's 'natural price'. Smith calling something 'natural' does not mean he approves of it, but I prefer to avoid the argument.

I wish I had access to Alex M. Thomas' 2021 article in The European Journal of the History of Economic Thought.

Adam Smith speaks of supply and demand in the above quotation. These are levels of quantities. Neither is a schedule showing how the quantity quantity supplied and demand varies with prices. These supplies and demands are thus not the curves graphed in introductory courses in contemporary mainstream economics.

I think of 'effectual demand' as being dependent on income distribution. It depends on how landlords, for example, divide up their income among savings, consumption on luxury commodities, and consumption of staples.

Some literature builds on and critiques Smith's metaphor of market prices gravitating towards or around prices of production.

Anyways, suppose all industries are producing at the level of effectual demand. Market prices match prices of production. In this situation, the total labor force of the country is distributed among industries in definition proportions. "The masses of products corresponding to the different needs require[s] different and quantitatively determined masses of the total labor of society."

Karl Marx described these quantities of labor being expended in each industry as "socially necessary".

A Personal Note: My Mind Is Going. I Can Feel It.

So my computer crashed. I hadn't backed it up in a while. But, even so, my backup failed, too. I am currently paying for some specialist organization to restore the data, and they are on their third attempt. The cost seems a lot for an individual, but I feel like I need a lot that is on it.

I am going to buy a new computer, and I have been slow about this. Until I do this, I will not be able to post any mathematical examples. I think that I have posted enough that I can recreate these examples. But I have lost draft introductions and conclusions not in posts. This is always my difficulty, and what I had should probably have rewritten those parts anyways.

I have also lost code, some for applications I do not recall. I have lots of PDFs, some for works I have also in books. I had downloaded PDFs for collected works of Ricardo, Marx & Engels, and Lenin. I am not sure whether these are still freely available.

Anyways, maybe I will post less frequently for quite a while.

Selected Difficulties In Reading Marx's Capital

Infinite are the arguments of Marxists. This very selective survey needs references.

A first difficult is that everybody knows Marx has something to do with the Soviet Union. Many come to reading Capital with certain preconceptions. A couple comments in the book, for analytical reasons, contrast capitalism and feudalism and a post-capitalist economy with common ownership. But the book is about capitalism. The book contains expressions of outrage, often ironical. But is capitalism criticized for being unjust? And the labor theory of value, for Marx, is not about what workers should be paid.

I tend to read Marx as developing a theory for political economy, a theory about how capitalism works. But should such a thing as Marxian political economy even exist? "A critique of political economy" is the subtitle of of Capital. Maybe Marx is not offering a different theory to put in place of the existing theory. A similar argument arises over Sraffa. The subtitle of his 1960 masterpiece is, "A prelude to a critique of economic theory". Perhaps the formalism should lead to more concrete, institutial, and empirical studies. On the other hand, Marx says he is investigating the "laws of motion" of a commodity-producing society.

I take my next difficulty from some comments in David Harvey's Companion What arguments are logical, in some sense? What are describing history? It is obviously not all history, since otherwise the section on primitive accumulation would be towards the start. But the sequence of chapters on co-operation, manufacture, and modern industry are set in history. I do not mean formal logic or syllogisms by 'logic', but rather something like the unfolding of concepts.

Marx often postulates an ideal system, so as to address bourgeois political economists and Ricardian socialists. On the other hand, he often describes practices that deviate from such ideals. Which is which at any point in the text?

Does Marx ever present a complete description of his method? In the introduction to the Grundrisse, Marx distinguishes between the order of presentation and the order of discovery. In some of his correspondence, he outlines his book.

I tend to present (some variant of or critique of) Marx's political economy with mathematics. How much are those who have done such true to this approach? Some of the mathematics, such as Perron-Frobenius theorems, did not exist in Marx's day. Some find analytical marxists too willing to accept methodological individualism.

Then some background is very useful to understand what Marx is writing about. I might mention British political economy, Hegel's philosophy, and previous socialists.

There are some difficulties in the presentation. I have mentioned the last footnote in chapter 5. One then needs to read thousands of pages until Marx explains the transformation problem in volume 3. One might find it difficult to accept that Marx intends volume 1 to be something like a is first approximation.

This post echoes some themes in a recent working paper by Fabio Petri. Some confusions are probably my own.

Paul Davidson (23 October 1930 - 20 June 2024)

Overview

Paul Davidson took Keynes' General Theory of Employment Interest and Money seriously. The interpretation in mainstream textboooks misses important points. Keynes' book was about theory, not primarily about (short-run?) fiscal or monetary policy. Keynes does not explain persistent unemployment from imperfections or sticky or rigid money wages or prices. A general theory is one that has less axioms than the special case treated by, say, Marshall. Davidson identified, specifically, three axioms relaxed or rejected by Keynes:

• Neutrality of money. For Keynes, money is non-neutral in all runs.
• Gross substitution. Money has no substitutes; it cannot be produced from labor.
• Ergodicity. Important time series in economics can be non-ergodic. Numerical probabilities cannot necessarily be assigned to all possible outcomes. Some might not even be known.

Davidson, following Weintraub, took overall economic activity from a Keynes-like model of aggregate supply and demand. This is neither a 45 degree diagram found in, say, Samuelson's textbook, nor what is in current mainstream textbooks. Aggregate supply and demand are curves in the space of monetary proceeds and employment. Their intersection is the point of effective demand. In Davidson's development, investment is autonomous and not a function of current income.

Davidson's perspective led to conflict with other Post Keynesians. Labor markets do not clear, given either competitive or non-competitive markets. One does not need Kalecki's degree of monopoly. At times, he appreciated the internal critique of marginalism offered by Sraffa those developing his ideas. But he thought that they did not appreciate Keynes' emphasis on uncertainty. On the other hand, some, such as Eatwell, might argue that Davidson's emphasis on money was an imperfection. I think both perspectives assert that Keynes' rejection of Say's law is not confined to the short run.

Maybe developments in the theory of endogenous money are also in tension with some of Davidson's work. Keynes assumed in the General Theory, but not in the Treatise on Money, that the monetary authority could vary the supply of money.

Davidson also wrote about various policy suggestions and international financial institutions. For example, he did not think the Tobin tax would achieve its goals.

Davidson insisted that the Post in "Post Keynesianism" should be capitalized and that no hypen should seperate the words.

Some Aspects of Professional Life

Davidson received an undergraduate degree from Brooklyn College. He performed research in biochemstry at the University of Pennsylvania during 1950-1952. He performed military service during the Korean War.

He switched to economics. Sidney Weintraub supervised his doctorate dissertation at the University of Pennsylvania. He moved to Rutgers in 1958. I think his stint as an executive at an oil company in the early 1960s influenced his views on Keynes' user cost.

He helped found the Journal of Post Keynesian Economics in 1978 and co-edited it with Sidney Weintraub.

After a purge of heterodox economics at Rutgers, Davidson moved, in 1986, to the University of Tennesee at Knoxville. I know of a number of heterodox economists who came out of Rutgers when Davidson was there. The career of Anne Mayhew, an institutionalist, overlapped with Davidson at the University of Tennesee.

In more recent years, Davidson was a visiting scholar at the New School for Social Research, Bernard Schwartz Center for Economic Policy Analysis.

Obituaries elsewhere: Chicago Tribune, Greg Davidson on his father at Daily Kos.

Very Selective Bibliography

• Paul Davison. 1968. Money, portfolio balance, capital accumulation, and economic growth. Econometrica 36(2): 291-321.
• Paul Davison. 1972. Money and the Real world. Macmillan
• Paul Davison. 1989. The economics of ignorance or the ignorance of economics? Critical Review 3(3-4): 467-487.
• Paul Davison. 1991. Is probability theory relevant for uncertainty? A Post Keynesian perspective. Perspectives on Economics 5: 29-43.
• Paul Davison. 1994. Post Keynesian Macroeconomic Theory: A Foundation for Successful Economic Policy for the Twenty-First Century. Edward Elgar
• Paul Davison. 2007. John Maynard Keynes. Palgrave Macmillan
• J. E. King. 2002. A History of Post Keynesian Economics since 1936. Edward Elgar.

Alexander Harrington Corrects Professor On Hegel's Dialectic

Michael Harrington was a great socialist in the United States. This is not to say that he did not make some political missteps, at least at Port Huron. Isserman's biography seems to have Michael making political missteps throughout the 1950s and 1960s. His son Alexander had exposure to some hard-to-understand ideas before he got to college:

My older son, Alexander, began to read Dostoevsky on his own when he was about fifteen and once told a college professor who was explaining Hegel's dialectic in terms of thesis, antithesis, and synthesis that Hegel didn't use those terms and that he should read the section on Master and Servant in the Phenomenology of Spirit for the real theory. -- Michael Harrington. 1988. The Long-Distance Runner: An Autobiography. New York: Henry Holt and Company: p. 125.

The part on the master and bondsman is the same part of Hegel that Richard Wolff recommends to 'Destiny'. I do not like Hegel. The Phenomenology seems to be about the evolution of consciousness from a purely sensuous beginning. That bit about the master and slave is about how the self-consciousness of the master is reflected within the consciousness of the servant. The master wants his consciousness recognized by the servant, but also wants to dominate the servant. (I go by the Baillie translation.) I was surprised that it ends with something like the alienation of the worker.

References

• Robert A. Gorman. 1995. Michael Harrington: Speaking American. New York: Routledge.
• Michael Harrington. 1988. The Long-Distance Runner: An Autobiography. New York: Henry Holt and Company: p. 125.
• Maurice Isserman. 2000. The Other American: The Life of Michael Harrinton. New York: Public Affairs.

A Robinson Crusoe Story

1.0 Introduction

I wrote this decades ago.

Here is a simple parable. Consider an island with a particularly simple society with two people, Robinson and Friday. Robinson and Friday live on one good, call it corn. At the start of our story, Robinson and Friday have just finished a feast. Both Robinson and Friday have each eaten food baked out of 50 bushels of corn. Also, Robinson has 50 bushels corn remaining. Friday, perhaps because he's newly arrived, has none.

2.0 The Initial Deal

Both Robinson and Friday can see that they must continue to eat in the future. They understand that their continual survival could be achieved by planting the remaining corn, saving 50 bushels corn in next year's harvest, and living off of the remainder. (In this story, Robinson and Friday are each able to go a year between meals.)

So Friday says to Robinson, "Why don't you share your seed corn with me. We'll each plant 25 bushels, and tend it half our time throughout the year. If your island is like my tribe's, that will allow us to harvest three bushels of corn for every bushel we plant. So at the end of the year, each of us will have 75 bushels. We can each eat 50 bushels and use the remaining 25 bushels for seed in the next year."

Robinson says, "Why should I give you anything? I happen to believe in property rights."

Friday says, "You don't want to see me starve, do you? What do you propose I do?"

Robinson says, "I'll tell you what. Why don't we come to the following voluntary agreement. You take the 50 bushels of corn, plant it, and tend it throughout the year. After harvesting, I'll take the 150 bushels we'll get and pay you 50 bushels for your helpful work."

Friday says, "Why should I agree to that? I do all the work, and you loaf around all year in a tropical paradise."

Robinson says, "Well, it's my seed corn."

Friday says, "Oh, all right. It's a deal."

3.0 The Story Continues

At the end of the year, Friday consumes his wages of 50 bushels. Robinson consumes his profits of 50 bushels. They are in the same situation as they were originally. They strike the same deal again and continue year after year.

4.0 Friday Reads A Book

It seems Robinson has brought the captain's library off the shipwreck with him. One day Friday happens to notice this library. He says to Robinson, "What are all these books?"

Robinson says, "I don't know. Being a practical person of the middle order of society, I never bothered to read them."

Friday says, "Well, can I have that big tome by that fellow Marx."

Robinson says, "Unlike the corn, it's of no use to me. You can have it."

Friday takes away the book and tries to read Marx. He finds it quite head-scratching in places, particularly the Hegel. That part seems so deep as to be incomprehensible. But he does get some glimmers from it.

5.0 A Debate

One day at the end of three years of work, Friday confronts Robinson and tells him, "You're exploiting me. I only get a third of the produce. This year I should get 26/27th of it. And if we continue on in this way, I should get all of it eventually."

Robinson can't make anything out of this. He says, "But I provide the seed corn. Labor and seed corn are measured in different units. How can you make a fair claim on any portion of the output but what we have agreed to?"

Friday says, "It will take me a little while to explain." Robinson says, "Unless some pirates show up, we have time. Go on."

Friday says, "Each year we harvest 150 bushels corn using 1 year of labor and 50 bushels seed. We can see that any proportion of the harvest was due to the corresponding proportions of the labor and the seed corn. Here's some examples." And Friday draws the following table in the sand:

Table 1: Inputs and Outputs

Proportion	Seed Corn	Labor	Harvest
1	50 Bushels	1 Year	150 bushels
2/3	33 1/3 Bushels	2/3 Year	100 bushels
1/3	16 2/3 Bushels	1/3 Year	50 bushels
2/9	11 1/9 Bushels	2/9 Year	33 1/3 bushels
1/9	5 5/9 Bushels	1/9 Year	16 2/3 bushels

Robinson says, "That seems fairly obvious. I don't see where you are going with this." Friday says, "We can use these numbers to break down my work in each year to produce the output in the following years:"

Table 2: Reduction of Gross Output to Labor Inputs

Year	Work Torward Year 3 Harvest	Work Torward Year 2 Harvest	Work Torward Year 1 Harvest
1	5 5/9 Bushels seed & 1/9 year's labor produce 16 2/3 Bushels	11 1/9 Bushels seed & 2/9 year's labor produce 33 1/3 Bushels	33 1/3 Bushels seed & 2/3 year's labor produce 100 Bushels
2	16 2/3 Bushels seed & 1/3 year's labor produce 50 Bushels	33 1/3 Bushels seed & 2/3 year's labor produce 100 Bushels
3	50 Bushels seed & 1 year's labor produce 150 Bushels

Robinson says, "I guess that's fairly clever. If I add horizontally, I see that you have allocated each year's seed, labor, and output to your columns. That's good. But if I add the first column vertically, all I see is that our 150 bushels corn is the result of 1 4/9 year's of your work and 5 5/9 bushels of my initial seed corn. What's your point?"

Friday says, "Wasn't that seed corn the result of your work before I showed up?"

Robinson says, "Well, yes. I worked hard for it. And I was even generous enough to feed you at first."

Friday says, "That may be. But can't we say that the 150 bushels we have now embodies the sum of 1 + 1/3 + 1/9 + 1/27 and so on year's labor? And therefore that, the total labor embodied in this third year's harvest is 3/2 year's of effort?"

"I don't know."

"It's just arithmetic. My contribution to this year's harvest, as you saw, is 1 4/9 years of work. The 5 5/9 bushels you originally contributed represents the remaining 1/18 years needed to produce the harvest. Since [ 1 4/9 ]/[ 1/18 ] is 26, I should get 26 bushels for every one of yours in the harvest."

Robinson says, "Um..."

"In other words, I, Friday, should get 26/27ths of this year's produce as I said originally."

"Furthermore," Friday continues, "as long as we continue to follow your deal, your fair share should become smaller and smaller. In the limit, all of the annual harvest has been produced by me alone if you don't help out at all."

6.0 The Upshot

Robinson says, "Aren't you denying my capital is productive?"

Friday says, "We certainly need the seed corn. But how is your ownership of it productive?"

"Sure it is. You need me to make the decisions what to do with it."

"Maybe so. My labor's the horse, and your capital is the lash."

This comment seems subversive to Robinson, and he gets angry. "Look, your argument only works because of the simplicity of our island. Excess profits and losses indicate where investment can be directed most advantageously."

Friday says, "You are only arguing that the rate of profit be calculated, not that profits be paid out. That indicator is only one among several. We could have any of many different incentive schemes."

Frustrated, Robinson says, "A deal's a deal. Whatever comes out of our market transactions, that's what's fair. I refuse to do arithmetic, so I can continue to talk nonsense."

This blockheadedness on Robinson's part so angers Friday that he stages a revolution and kills Robinson. The island lives on in communism from that day forward.

7.0 Some Notes

This story is un-Marxist. According to Marx, capitalism did not arise through people rationally constructing capitalist institutions, property rights, markets, etc. Nor will it fall by convincing people of its unjustness by rational argument. Rather historical materialism describes beliefs as reflecting changes in productive forces as part of an historical process. My story is much too idealist for Marx. Also, my story does not contain money, and money is central to Marx's account of value.

The story can be made more realistic. We can add many workers and capitalists, and assume perfect competition. We can also assume continuously differentable production functions. For example, this parable is consistent with the Cobb-Douglas production function:

Q(L, X ) = 3 (50)^1/3 L^1/3 X^(2/3)

where Q is the corn harvested at the end of the year, L is the number of person-years of labor during the year, and X is the bushels of seed corn. Whatever wage comes out of the market will be equal to the value of the marginal product of labor. These assumptions and this equality of the wage and the value of the marginal product of labor are compatible with some such calculations as in the story. Unless the workers eventually get the entire product, they are exploited, as above.

While my parable is non-Marxist, the arithmetic for the concept of exploitation used in it is based on my understanding of some aspects of Marx's theory.

"...we must understand the importance which Marx attached to his distinction between 'labour' and 'labour-power': an importance essential for the context of exploitation as a key to understanding the bourgeois (or capitalist) mode of production. The role of the labour theory of value in relation to the theory of surplus value is frequently misunderstood. Often this is interpreted as embodying a Lockean 'natural right' principle, to the effect that the product of a man's labour belongs 'of right' to the labourer; whence it is held that the appropriation of part of this product by the capitalist is 'unnatural' and unethical. Hence exploitation is interpreted as a quasi-legal or ethical concept rather than a realistic economic description. If what we have said about labour and the labour process has been appreciated, it should be clear that this is an incorrect interpretation. What could be said, of course, is that the notion of labour as productive activity implicitly afforded the definition of exploitation as an appropriation of the fruits of activity by others - appropriation of those fruits by those who provided no productive activity of their own. But far from being an arbitrary or unusual definition of 'productive' and 'unproductive', this would surely meet with general aggreement as normal usage of these words. The problem for Marx was not to prove the existence of surplus value and exploitation by means of a theory of value: it was, indeed, to reconcile the existence of surplus value with the reign of market competition and of exchange of value equivalents. As he himself expressed it: 'To explain the general nature of profits, you must start from the theorem that, on an average, commodities are sold at their real values, and that profits are derived from selling them at their values ... If you cannot explain profit upon this supposition, you cannot explain it at all.'

The point of this can the better be appreciated if it is remembered that the school of writers to whom the name of the Ricardian Socialists has been given (such as Thomas Hodgskin, William Thompson and John Bray), who can be said to have held a 'primitive' theory of exploitation, explained profit on capital as the product of the superior bargaining power, lack of competition and 'unequal exchanges between Capital and Labour' (this bearing analogy with Duhring's 'force theory' which was castigated by Engels). This was the kind of explanation that Marx was avoiding rather than seeking. It did not make exploitation consistent with the law of value and with market competition, but explained it by departures from, or imperfections in, the latter. To it there was an easy answer from the liberal economists and free traders: namely, 'join with us in demanding really free trade and then there can be no "unequal exchanges" and exploitation.'" -- Maurice Dobb, "Introduction" in K. Marx, A Contibution to the Critique of Political Economy, Progress Publishers, 1970, pp. 12-13.

Interestingly enough, the great Austrian economist Eugen Böhm-Bawerk's account of capitalism arguably does not challenge Marx's claim that the workers are exploited.

"Whoever is the owner of a capital sum is ordinarily able to derive from it a permanent net income which goes under the scientific name of interest in the broad sense of the term.

This income is distinguished by certain notable characteristics.

It arises independently of any personal act of the capitalist. It accrues to him even though he has not moved a finger in creating it, and therefore seems in a peculiar sense to arise from capital, or, to use a very old metaphor, to be begotten by it...And, finally, it flows without ever exhausting the capital from which it arises, and therefore without any necessary limit to its continuance. It is, if one may use such an expression in mundane matters, capable of everlasting life.

And so the phenomenon of interest presents, on the whole, the remarkable picture of a lifeless thing, capital, producing an everlasting and inexhaustible supply of goods. And this remarkable phenomenon appears in economic life with such perfect regularity that the very concept of capital has often been founded on it. Thus Hermann, in his Staatswirtschaftiche Untersuchungen defines capital as 'wealth which produces a constant flow of income without suffering any diminution in exchange value.'

Whence and why does the capitalist receive this endless and effortless flow of wealth? -- Eugen von Böhm Bawerk, Capital and Interest, "Volume 1: History and Critique of Interest Theories", p. 1.

Notice that attempts to change the conditions don't attack the logic of the above story. I don't see how the ability for some workers to save to become capitalists or attempts to justify some highly paid personnel as being paid for the labor of supervision threatens the logic of the story. If you want to criticize the logic, show that it's not reasonable within its own assumptions. But this cannot be done. On the other hand, those that understand, say, the John von Neumann model of growth know how to generalize the story to make it much more realistic.

Prices Of Production Before Labor Values

1.0 Introduction

This post outlines an unoriginal argument against Marx's version of the Labor Theory of Value (LTV), if that is the right name. Somehow, this post was obliquely inspired by Fabio Petri's recent working paper.

Suppose technology, net output, and the real wage are given. Then the rate of profits and prices of production are determined.

Suppose that the technology provides a choice of technique. Then the determination of the choice of technique requires an analysis at the level of prices of production. One can do labor value accounting only after the determination of the technique in use.

Given the technique and the level of operation of each process, one can then determine the labor value embodied in the output of each industry. One can then use this labor value accounting in the overall system of labor values to calculate a supposed rate of profits. In general, this rate of profits is unequal to the rate of profits in the system of prices of production.

One can also use the technique in use to identify a commodity of an average organic composition of capital, in some sense. And one can calculate the rate of profits in the system of labor values for the industry producing this average commodity. And all of Marx's other volume 3 invariants hold in the production of Sraffa's standard commodity.

But the composition of the standard commodity also varies with the technique in use and, thus, depends on the real wage and an analysis at the level of prices of production.

Supply and demand, as conceptualized in marginalist economic theory, however, remains nonsense, not even wrong.

2.0 Givens

Suppose a capitalist economy is observed at a given point in time. The net output of the economy consists of a column vector d, in which each element is measured in physical units (kilotons, bushels, etc.)

Suppose the capitalists know of the processes comprising two techniques, Alpha and Beta, for producing the given net output. Each technique is characterized by a row vector of direct labor coefficients, a₀(α) and a₀(β) and a Leontief input-output matrix, A(α) and A(β). These vectors and matricies are given in physical units.

I assume constant returns to scale and, here, that all advanced capital is circulating capital. Both techniques must be able to produce the given net output, but different intermediate commodities may be produced. The economy must hang together, in some sense. That is at least one basic commodity exists in each technique, although the which commodities are basic may vary with the technique. Also, nothing like Sraffa's 'beans', in Appendix B of his book, exists in either technique.

One could articulate these assumptions more rigorously.

3.0 Prices of Production

Prices of production, for a competitive capitalist economy, are such that the same rate of (accounting) profits is obtained in each operated process. For the Alpha technique, prices of production must satisfy the following system of equations:

p(w, α) A(α) (1 + r(w, α)) + w a₀(α) = p(w, α)

If one takes net output as the numeraire, prices of production must be such that:

p(w, α) d = 1

Prices of production and the rate of profits can be found for a non-negative wage up to a certain maximum. Prices of production and the corresponding rate of profits can be found for each technique.

4.0 Choice of Technique

The determination of prices of production for each technique, at the given wage, allows for an analysis of the choice of technique.

If Alpha is the cost-minimizing technique at the wage w, supernormal profits cannot be obtained by operating Beta. The cost of operating each process in the Beta technique at Alpha prices cannot fall below the revenue obtained. The following must hold:

p(w, α) A(β) (1 + r(w, α)) + w a₀(β) ≥ p(w, α)

If the wage is not that at a switch point, a strict inequality must hold for at least one process in Beta. I suppose that prices of commodities only produced in Beta are zero for the above display and that prices for commodities only produced under Alpha do not appear in the price vector.

For the case of circulating capital, the above is equivalent to the rate of profits for Alpha exceeding the rate of profits for Beta:

r(w, α) ≥ r(w, β)

If Beta is the cost-minimizing technique, these conditions are reversed. In any case, which technique is cost-minimizing may vary with the wage.

5.0 Labor Values

Let a₀(w) be the row vector of direct labor coefficients and A(w) be the Leontief input-output matrix of the cost-minimizing technique at the wage w.

The labor embodied in each commodity produced for the cost-minimizing technique is found from the vector of direct labor coefficients and the Leontief inverse:

v = a₀(w) (I - A(w)^-1

One could go on to perform further calculations, including with the dominant eigenvalue and corresponding eigenvector for the input-output matrix A(w). As this notation emphasizes, the data for labor value accounting depends on the wage. The data also depend on the above analysis of prices of production.

6.0 Conclusion

One could respond to this argument by asserting that typically a single technique is dominant for any distribution of income. New techiques come about by innovation, replacing existing techniques.

This rebuttal does not work for, at least, some aspects of joint production. Extensive rent or differential rent of the first kind, for example, requires an analysis to identify which type of land pays no rent and is nevertheless cultivated. It is only after such an analysis at the level of prices of production that labor values can be calculated.

Supply and demand curves have not been drawn above. Nor has anything been said about utility maximization. As Laplace told Napoleon in a different context,"I have no need of that hypothesis."

References

• Fabio Petri. 2024. What remains valid of the first chapter of Marx's Capital?, Centro Sraffa Working Paper 65.
• Paul A. Samuelson. 1989. Revisionist findings on Sraffa. Essays in Honour of Piero Sraffa (ed. by K. Bharadwaj and B. Shefold).

Why Is Reswitching Empirically Rare?

Figure 1: Variation in the Economic Life of a Machine with Technical Progress

Exploration of the effects of perturbations of model parameters in the analysis of the choice of technique has suggested an answer to this question to me. I am not sure how well-developed the argument in this post is.

The question is raised by empirical results, particularly by Han & Schefold and by Zambelli. I have previous commented on Zambelli. Heinz Kurz has recently questioned the reliability of these results. The data come from economies in which fixed capital is widely used. One can expect old plants that would not be currently reproduced to be operated and to obtain quasi-rents. Nevertheless, empirical wage curves are surprisingly close to straight lines and reswitching and other 'perverse' phenomena seem to be rare.

Bertram Schefold took his empirical results seriously. He has been exploring what happens when the coefficients of input-output system are random in some sense. Reswitching is rare, but so is switching. For most of the range of feasible income distributions, one technique is dominant. If I recall correctly, he says this contrived problem. Most innovations replace one process with another, dominant process.

I get to the same result in another way. Figure 1 is from an example with fixed capital in which all coefficients of production decrease at an exponential rate. Reswitching occurs in Region 3. But that U-shape on its side is generic, in some sense. In models of the choice of technique with a single parameter varying or with parameters varying as a function of time, one will get the same sort of shape. Reswitching only occurs for a range of time. Before or after, no reswitching, at least of the same two techniques, occurs.

Figure 2: A Part of a Parameter Space

I also have considered how to partition parameter spaces based on fluke switch points. Figure 2 illustrates two parameters in a model of extensive rent. This example is written up in one of my publications. Regions 3 and 7 and their boundaries are also generic, in some sense. Reswitching occurs within these regions. The northeast boundary, in these cases, corresponds to a fluke switch point in which two wage curves are tangent at the switch point. Reswitching disappears over these boundaries.

These boundaries intersect, to the upper left, a boundary in which a fluke switch point occurs at a rate of profits of zero. At the intersection, the two wage curves are tangent at a rate of profits of zero. The reswitching pattern, on the other hand, intersects a boundary at the lower right at the maximum rate of profits. The region in which reswitching occurs can only be in a small part of the two-dimensional projection of the parameter space. Technical progress, in this example, is a movement from the upper right to the lower left in Figure 2.

I have been constructing or perturbing examples of 'perverse' phenomena. But the kind of structures outlined above are generic in some sense. I might think a bit about what regions with triple-switching and so on look like in the diagrams with two-dimensional projections of model parameters. It seems that technical progress is a matter of one technique becoming dominant, whatever the distribution of income. This change in dominance happens in secular time or in the very long-run. It is a matter of the wage frontier moving outward. Reswitching is a transient phenomenon, occurring in the long-run. I do not know how this impacts short-run dynamics or market prices.

References

• Z. Han and B. Schefold (2006) An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory", Cambridge Journal of Economics, V. 30: 737-765.
• Zambelli, Stefano. 2018. The aggregate production function is NOT neoclassical. Cambridge Journal of Economics 42: 383-426.

Communism Worked In Central New York Around 1500

A Beach On The East End Of Oneida Lake

The Iroquois are an example of primitive communism. This post includes lots of anachronisms, and I use current place names. I had never heard of the Haudenosaunee before, which apparently is the preferred term. I find I do not know much about my neighbors, the Oneidas. The Oneidas were one of the five nations in the Iroquois confederacy.

I am confused whether primitive capitalism is tied exclusively to hunter-gatherer societies, without a surplus product. Given the role of the three sisters, that is, corn, beans, and squash, in, say, the Oneida society, I guess they must have been an agricultural society. I gather that anthropologists have found the concept of a surplus product useful. Useful questions include who gets the surplus? What do they do with the surplus? Clark (1992) is an example of an institutionalist economist who questions whether a surplus can be conceptualized independently of its use and distribution. If primitive communism prevailed among many for much of prehistory, Marx and Engels are wrong in saying, "The history of all hitherto existing societies is the history of class struggles". Apparently, in later editions of the Communist Manifesto, Engels wanted to replace 'history' with 'recorded history'.

Anyways, as I understand it, extended families of Oneidas lived collectively in longhouses. Society was relatively egalitarian and matriarchal. They had a concept of personal property, but not of private property. In particular, land could not be owned. I gather land was periodically reallocated among families, as needed. Luxemburg, in the framents of her textbook on political economy, says that land was likewise reallocated in the German mark, where a mark is a village in ancient times. I guess some villages raided others, but, as a whole, the Iroquois lived under the great law of peace. Memorial day weekend is almost the only time one can see NCAA lacrosse on national television in the USA.

Lewis Henry Morgan was a nineteenth century anthropologist. I do not know much about him, how Marx and Engels built upon his studies, or current views by anthropologists of these ideas. I was surprised to find he was from New York State and extensively used the Iroquois as an example for his claims.

What happened to these working communist societies? My answer is very selective. The Sullivan expedition was a genocidal campaign ordered by George Washington during the U.S. revolution. The question of Oneida land claims in New York are a matter of recent current events.

References

• Charles M. A. Clark. 1992. An institutionalist critique of Sraffian economics. Journal of Economic Issues 16(2): 457-468.
• Rosa Luxemburg. 2013. The Complete Works of Rosa Luxemburg: Volume I, Economic Writings 1, Verso.
• Brian Moore. 1985. Black Robe
• Lewis Henry Morgan. 1877. Ancient Society or Researches in the Lines of Human Progress from Savagery through Barbarism to Civilization

David Champernowne

No book-length biography of D. G. Champernowne exists, as far as I can see. Even his Wikipedia page is quite terse. Yet he advised and participated in important twentieth-century intellectual developments.

From Hodges biography of Alan Turing, I learned that 'Champ' was a friend of his. Champernowne did early work in programming chess-playing algorithms, along with Turing and Claude Shannon. Game-playing is one of those disappointing applications of Artifical Intelligence. What seems to work best, like ChatGPT, uses lots of processing power, while ignoring what experts in the subject matter say. Anyways, Champernowne was in on the invention of the computer.

Champernowne (1953-1954) published an appreciation and explanation of the English translation of von Neumann's article on economic 'equilibrium'. This was in the same journal issue. Von Neumann's model is classical in inspiration. No agents are maximizing utility. The composition of capital goods is found as a solution of the model. Champernowne acknowledges conversations with Kaldor and Sraffa. in writing this article.

I had not previously known about Chamernowne's (1952, 1953, 1973, 1988) work on the Pareto distribution, in the context of income distribution. I find the Pareto distribution useful in the context of extreme events.

His commentary on Joan Robinson's article kicking off the Cambridge Capital Controversy (CCC) was published in the same journal issue as Robinson's article. He explicitly notes the possibility of capital-reversing and, if I understand correctly, provides a numerical example. And he develops chain-index measure of capital to enter in an aggregate production function when no such 'perverse' case exists.

Bibliography

• D. G. Champernowne. 1945-1946. A note on J. v. Neumann's article on 'A model of economic equilibrium'. The Review of Economic Studies 13(1): 10-18.
• D. G. Champernowne. 1952. The graduation of income distribution. Econometrica 20(4): 591-615.
• D. G. Champernowne. 1953. A model of income distribution. Economic Journal 63(250): 318-351.
• D. G. Champernowne. 1953-1954. The production function and the theory of capital: a comment. The Review of Economic Studies 21(2): 112-135.
• D. G. Champernowne. 1973. The Distribution of Income between Persons.
• D. G. Champernowne and Frank A. Cowell. 1998. Economic Inequality and Income Distribution.
• Andrew Hodges. 2015. Alan Turing: The Enigma, updated edition. Princeton University Press.

Future Papers For My Research Program?

I have sometimes written retrospectives about my research program. I have been exploring the results of perturbing parameters in models of the choice of technique. This is a bit more prospective.

• Illustrations of One-Dimension Pattern Diagrams: I have a selection of these written up.
• Independence of Economic Life of Machines and Capital-Intensity: I have the analytical results I want. I am being slow to read what I need to connect results up to Austrian capital theory. I have had a much different earlier version rejected by Metroeconomica.
• Illustrations of Partitions of Parameter Spaces by Fluke Switch Points: I have had a draft paper like this rejected by the Cambridge Journal of Economics.
• Extensive rent with perturbations of markups: I have had a paper based on this rejected by the Review of Radical Political Economics. I need to reach a more definite conclusion. I probably will not go further.
• Intensive rent with perturbations of markups: This is somewhat beyond me, and I probably will not develop this further.
• Extensive rent, intensive rent, and markup pricing: This, too, is somewhat beyond me, and I do not see that I will pursue it soon.
• The Choice of Technique with Harrod-Neutral Technical Progress: This is somewhat beyond me. I probably will not develop this.

I do not see if organizing my starts will inspire me to be more productive. Since I am working on my reading for the second suggestion above, maybe I should expect to be slow at this point.

Hayek In The Pure Theory Of Capital

This is more of my commonplace book, based on reading some of Hayek's The Pure Theory of Capital. Hayek rejects Böhm Bawerk's average period of production, a single number summarizing the capital intensity of a structure of production. He still strives to say that more capital-intensive techniques are longer in some non-aggregate sense. I probably will not finish this book. To compare and contrast this book with J. R. Hicks' Value and Capital would be of interest.

Hayek correctly takes issue with the treatment of capital as a homogeneous quantity and the explanation of interest by the supply and demand of capital:

"the attempts to explain interest, by analogy with wages and rent, as the price of the services of some definitely given 'factor' of production, has nearly always led to a tendency to regard capital as a homogeneous substance the 'quantity' of which could be regarded as a 'datum', and which, once it had been properly defined, could be substituted, for purposes of economic analysis, for the fuller description of the concrete elements of which it consisted." (Hayek 1941, p. 5)

and:

"As we shall see, it is more than doubtful whether the discussion of 'capital' in terms of some single magnitude, however defined, was fortunate even for its immediate purpose, i.e. the explanation of interest. And there can be no doubt that for the understanding of the dynamic processes it was disastrous. The problems that are raised by any attempt to analyse the dynamics of production are mainly problems connected with the interrelationships between the different parts of the elaborate structure of productive equipment which man has built to serve his needs." (Hayek 1941, p. 6)

Sraffa, of course, analyzes the structure of productive equipment in a different way.

Hayek is one of the originators of the notion of intertemporal general equilibrium

"An effective discussion of the problems of capital theory must, however, move precisely in that neglected field which deals with general equilibria that are not at the same time stationary states." (Hayek 1941, p. 6)

Hayek goes on to a discussion later built on by Lachmann and paralleling Robinson. At any point, the complex of capital equipment is unsuitable, inherited from the past in which the present was not completely foreseen. In equilibrium, the plans of all agents are adjusted. Equilibrium is not a state that an economy can get into in historical time. Nevertheless, equilibrium analysis has a logical use in a preliminary analysis. Hayek does not want to consider a temporary partial equilibrium, instead of a general intertemporal equilibrium. Furthermore, Hayek puts money aside, including the lending and borrowing of money in most of this preliminary study.

Hayek distinguishes between permanent and non-permanent resources and between producible and non-producible resources.

"The term capital itself, in so far as it is required to describe a particular part of the productive resources, will accordingly be used here to designate the aggregate of those non-permanent resources which can be used only in this indirect manner to contribute to the permanent maintenance of the income at a particular leve1." (Hayek 1941, p. 54, italics in original)

Both producible and non-producible resources can be capital. The latter include something like oil, which can be exhausted by drilling.

In his non-homogeneous concept to capital, Hayek still thinks a connection exists between capital-intensity and time:

"There are two main ways in which the productivity of investment shows itself ... the investment of any group of services of the permanent resources can be combined into one single 'process' of production in two ways. In the one case it is the duration of the actual process of production where the time factor enters, and in the other case is the durability of the product (or of the non-permanent resources used in production)." (Hayek 1941, Ch. 6, p. 65, italics in original)

Hayek was an early adopter of the distinction and terminology of point input, flow input, point output, and flow output:

"it is useful to construct ideal limiting cases which show their peculiarities in the purest form. The first case is best represented if we conceive of a continuous application of input through a period of time, leading to an output all of which matures at a moment of time at the end of the period. This has been described as the 'continuous input – point output' case. The second case is ideally represented if we imagine durable good which is produced at a moment of time and then rendes services continuously over a period of time. This case has correspondingly been described as the 'point input – continuous output' case." (Hayek 1941, p. 66-67, italics in original)

Hayek distinguishes the investment period from the length of the process and the period of production:

"The fundamental fact with which we are concerned is the change in the periods for which particular units of input are invested, that is, the interval between the application of a unit of input and the maturing of the quantity of output due to that input. This interval of time we shall describe as the investment period of that unit of input.” (Hayek 1941, p. 69, italics in original)

Hayek recognizes that an investment period requires a high degree of abstraction to identify and may not always exist.

Hayek is considering the choice of technique, in which many techniques are known for producing a given final output:

"The considerations advanced above - and it is important to remember this throughout the discussion - have nothing to do with technological progress in this sense. On the contrary, they refer to changes under conditions where knowledge is stationary. All that is assumed is that at any moment there are known possible ways of using the available resources which would yield a greater return than those actually adopted, but would not yield this return until a later date, and for this reason are not actually used.

Among the wide range of possible methods of production known at any one time there will be some which will yield their product after shorter periods of time and some which will not yield it until after longer periods. From among each group of methods involving the same 'amount of waiting' - if we may make provisional use of this vague term - the one that will be chosen will be the one which yields the greatest return from a given investment of factors. But so long as there is any limitation on the 'amount of waiting' for which people are prepared, processes that take more time will evidently not be adopted unless they yield a greater return than those that take less time. (Hayek 1941, p. 72-73)

Hayek uses 'process' synomously with what I usually call a technique. Hayek thinks longer processes, in some sense, support a greater division of labor and often the use of resources that were not used before. Perhaps the consumer good is different but satisfies the same needs.

Here Hayek is once again rejecting an average period of production:

"Before we can pass on to this problem it is necessary to return for a moment to the, difficulty of talking about changes in the length of the process of production. It will probably be fairly obvious by now that as the complete processes of production with which we have to deal become increasingly complex it becomes more and more difficult, and may in some cases be impossible, to say in any general way which of several, alternative processes under consideration is as a whole the shortest or the longest. The total length of time which elapses between the very beginning of the process and the completion of the product may be shorter in one process than in another, and yet by far the greater part of the input used may be applied very early in the first process and very late in the second process. Which of these two processes is to be regarded as the longer? It is impossible to answer this question at the present stage, and there is in fact no general answer to it. It is only mentioned at this point in order to warn the reader against any attempt to provide himself with an answer by introducing some concept of an 'average period' of production. Such a concept, as we shall see, is not only unnecessary but is also highly misleading." (Hayek 1941, p. 76)

The above does not get at reswitching, I do not think. He wants a process in which resources are applied at the start and the end, in contrast to when they are used mostly in the middle.

Somewhere around here, Hayek defines stages of production, much like in his triangles.

I think the following gets at the possibility of reswitching:

"... when we compare two different investment structures, it will not always be possible even to say, on purely technical grounds, which of them involves the greater amount of waiting. At one set of relative values for the different kinds of input and at one rate of interest, the one structure, and at a different set of values or a different rate of interest, the other structure will represent the greater amount of waiting, or will be 'longer' in the sense in which this term has commonly been used." (Hayek 1941, Ch. 11, p. 144)

There is also something suggestive of capital-reversing in Chapter XXI.

"We shall not follow up this point in detail. For the method adopted to give a general picture of the considerations involved is really not adequate for an exhaustive analysis. The reason for this is, of course, as in all other cases where productivity or demand curves for individual factors are regarded as given, that these curves cannot be regarded as simultaneously and independently valid. But to take account of the complicated relations of technological (and psychological) complementarity which are involved, requires another technique which has been evolved quite recently in closely related fields, and which will also have to be used in a more exhaustive investigation of our problems. Here all that we shall mention is that if we were to start from a complete statement of the substitution relationships between all the different resources concerned, all kinds of peculiarities and apparent anomalies in the behaviour of individual factors would appear to be quite consistent with the general tendencies which can be deduced from the cruder type of analysis. It is, for instance, quite possible that while a fall in the rate of interest will create a tendency for the services of most of the permanent factors to be invested for longer periods and for their prices to rise, in the case of some individual factor the effect may well be that it will be invested for shorter periods, or that its price will be lowered, or both." (Hayek 1941, Ch. 21, p. 191-192)

The earliest description of something like reswitching is due to Irving Fisher.

Hayek and other Austrian-school economists are, of course, wrong. In what sense, whether assessed by value measures or physical properties, do more well-chosen, roundabout techniques raise net output? Samuelson (1966) noted that reswitching is not consistent with "the simple tale told by Jevons, Bohm-Bawerk, Wicksell, and other neoclassical writers". Fratini (2019a, 2019b) shows that the adoption of techniques with an increased average period of production, as assessed by financial measures, is compatible with decreased net output per worker. Steedman (2020), in considering techniques associated with the operation of different types of machines, demonstrates that more durable machines can also yield less net output per worker. I know that the economic life of machines do not support Hayek's idea.

Technical Terms: Continuous (flow) input or point input, continuous (flow) output or point output, Intertemporal general equilibrium, Investment period, Period of production, Permanent and non-permanent resources, Producible and non-prodicable resources, Stages of production, Structure of production

Wages, Employment Not Determined By Supply And Demand

1.0 Introduction

I do not think I have presented an introductory example in a while in which an increased wage is associated with firms wanting to employ more labor, given the level of net output. This example is presented as a matter of accounting for a vertically integrated firm.

Exact calculations with rational numbers are tedious in this example. I expect that if anybody bothers to check this, they would use a spreadsheet. As far as I can tell, Microsoft Excel uses double precision floats.

2.0 Technology

The managers of a competitive, vertically-integrated firm for producing corn know of the four production processes listed in Table 1. Corn is a consumption good and also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. The first process produces iron, the second process produces steel, and the last two processes produce corn. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce the specified unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year. The data on technology are taken from a larger example.

Table 1: Technology

Input	Process
	a	d	e	f
Labor	1/3 person-year	7/20 person-year	1 person-year	3/2 person-year
Iron	1/6 ton	1/100 ton	1 ton	0 tons
Steel	1/200 ton	3/10 ton	0 tons	1/4 ton
Corn	1/300 bushel	0 bushel	0 bushels	0 bushels
Output	1 ton iron	1 ton steel	1 bushel corn	1 bushel corn

The managers of the firm have available two techniques for producing corn from inputs of labor, with intermediate inputs being constantly replaced. The iron-producing, steel-producing, and first corn-producing processes are operated in the Gamma technique. The second corn-producing process, as well as the iron and steel-producing processes, are operated in the Delta technique. Iron, steel, and corn all enter, either directly or indirectly, into the production of corn in both techniques. Vertically-integrated firms can also operate a linear combination of the Gamma and Delta technique.

3.0 Quantity Flows

One can consider various levels of operations in each of the processes for each of the technique. I consider two examples of snychronized production, in which inputs of labor simultaneously produce a net output of corn for consumption. A structure of production, consisting of specific capital goods, intervenes between the inputs and output. The labor input reproduces that structure, as well as producing the output.

3.1 Gamma Quantity Flows

Suppose 14,000/11,619 ≈ 1.205 tons iron are produced with the first process, 100/11,619 ≈ 0.0086 tons steel are produced with the second process, and 34,997/34,857 ≈ 1.004 bushels corn are produced with the third process. Then the quantity flows illustrated in Table 2 result. 14,000/11,619 tons iron are used as inputs among the three industries. These inputs are replaced by the output of the iron-producing process. 100/11,619 tons of steel are used as inputs among the three industries, and these inputs are replaced by the output of the steel-producing process. 140/34,857 bushels of corn are used as inputs among the three industries, leaving a net output of one bushel corn. In short, these quantity flows are such that 49,102/34,857 ≈ 1.409 person-years produce one bushel corn net. Obviously, I did not pick a very good set of coefficients for this example to support exact calculations in rational numbers.

Table 2: Vertically-Integrated Production with the Gamma Technique

Input	Process
	a	d	e
Labor	14,000/34,857 person-year	35/11,619 person-year	34,997/34,857 person-year
Iron	7000/34,857 ton	1/11,619 ton	34,997/34,857 ton
Steel	70/11,619 ton	30/11,619 ton	0 tons
Corn	140/34,857 bushel	0 bushel	0 bushels
Output	14,000/11,619 ton iron	100/11,619 ton steel	34,997/34,857 bushel corn

3.2 Delta Quantity Flows

Suppose 100/23,331 ≈ 0.00429 tons iron are produced with the first process, 25,000/69,993 ≈ 0.3572 tons steel are produced with the second process, and 69,994/69,993 ≈ 1.00001 bushels corn are produced with the fourth process. By the same logic as above, these quantity flows are such that 1807/1111 ≈ 1.626 person-years produce one bushel corn net.

Table 3: Vertically-Integrated Production with the Delta Technique

Input	Process
	a	d	f
Labor	100/69,993 person-year	1,250/9,999 person-year	34,997/23,331 person-year
Iron	50/69,993 ton	250/69,993 ton	0 ton
Steel	1/46,662 ton	7,500/69,993 ton	34,997/139,986 tons
Corn	1/69,993 bushel	0 bushel	0 bushels
Output	100/23,331 ton iron	25,000/69,993 ton steel	69,994/69,993 bushel corn

4.0 Prices

Which technique will the managers of the firm choose to adopt? By assumption, they take the price of corn and the wage as given on the consumer and labor markets. For simplicity, assume that price of a bushel corn is unity. That is firms treat the price of the consumer good as numeraire. At the end of the year, firms own a stock of iron, steel, and corn. They sell some of the corn to consumers. They retain the iron, steel, and enough corn to continue production the next year.

In a consistent accounting scheme, the price of iron and steel are such that:

• The same (accounting) rate of profits is obtained in all operated processes.
• The cost of the inputs, per bushel corn produced gross, for the corn-producing process not operated for a technique does not fall below that for the operated process.

The first condition specifies prices of intermediate goods and the rate of profits the accountants register. The second condition states that no pure economic profits can be obtained. Under these conditions, the managers of the firm can price their capital stock at the end of any year.

4.1 Prices at a Low Wage

Suppose the wage is w = 19,296/352,547 ≈ 0.05473 bushels per person-year. The accountants set the price of iron at p₁ = 6,860/27,119 ≈ 0.2530 bushels per ton iron and the price of steel at p₂ = 76,454/27,119 ≈ 2.819 bushels per ton steel. Table 4 shows the cost per unit output for each process and the resulting rate of profits obtained by operating each process. In constructing the tables for price systems, wages are assumed to be advanced. Under these assumptions, the rate of profits is 9/4, that is 225 percent, in each process comprising the Gamma technique. A lower rate of profits is obtained in the remaining corn-producing process, and it will not be operated. This is a consistent accounting system for the vertically-integrated firm, given the wage.

Table 4: Costs and the Rate of Profits at a Low Wage

Process	Cost	Rate of Profits
a	(1/6)p1 + (1/200)p2 + (1/300) + (1/3)w = 27,440/352,547	225 percent
d	(1/100)p1 + (3/10)p2 + (7/20)w = 305,816/352,547	225 percent
e	p1 + w = 2,308/7,501	225 percent
f	(1/4)p2 + (3/2)w = 554,839/705,094	≈ 27.1 percent

4.2 Prices at a Higher Wage with the Original Technique

Now suppose the wage is higher, namely w = 1,332/5,197 ≈ 0.2563 bushels per person-year. Consider prices of p₁ ≈ 0.2622 bushels per ton iron and p₂ ≈ 0.4167 bushels per ton steel. Table 5 shows cost accounting for these prices.

Table 5: Costs and the Rate of Profits at a High Wage (Incomplete)

Process	Cost	Rate of Profits
a	0.141 Bushels per ton iron	85.9 percent
d	0.2241 Bushels per ton steel	85.9 percent
e	0.5379 Bushels per bushel	85.9 percent
f	0.5178 Bushels per bushel	93.1 percent

Notice the same rate of profits is obtained in operating the first three processes. But the cost of producing a bushel corn with the last process is lower than in producing corn with process e. A larger rate of profits is obtained in operating that process. The managers of the firm will realize that their accounting implies that the Delta technique should be operated. If this firm were not vertically integrated and iron and steel were purchased on the market, a market algorithm would also lead to the Delta technique being adopted at this wage.

4.3 Prices at the Higher Wage with the Cost-Minimizing Technique

Continue to consider a wage of w = 1,332/5,197 ≈ 0.2563 bushels per person-year. The accountants report prices of p₁ = 1,420/5,197 ≈ 0.2732 bushels per ton iron and p₂ = 2,402/5,197 ≈ 0.4622 bushels per ton steel. Table 6 shows costs per unit output for the five processes under these prices.

Table 6: Costs and the Rate of Profits at a High Wage

Process	Cost	Rate of Profits
a	710/5,197	100 percent
d	1,201/5,197	100 percent
e	2,752/5,197	≈ 88.8 percent
f	1/2	100 percent

With this set of prices, the Delta technique is operated, and a rate of profits of 100 percent is obtained. The cost of operating the first corn-producing process exceeds the cost of operating the corn-producing process in the Delta technique. With a higher wage, the managers of a cost-minimizing firm will choose to operate a corn-producing process that requires more labor per bushel corn produced gross. (3/2 person-years is greater than 1 person-year.) More labor will also be hired per bushel corn produced net.

5.0 Conclusion

Table 7 summarizes these calculations. The ultimate result of a higher wage in the range considered is the adoption of a more labor-intensive technique. If this firm continues to produce the same level of net output and maximizes profits, its managers will want to employ more workers at the higher of the two wages considered. So much for the theory that, given competitive markets, wages and employment are determined by the interaction of well-behaved supply and demand curves on the labor market.

Table 7: A More Labor-Intensive Technique at a Higher Wage

Wage	Technique	Labor Intensity
0.05473 bushels per person-year	Gamma	1.409 person-years per bushel
0.2563 bushels per person-year	Delta	1.626 person-years per bushel

This example can be generalized in many ways. Different types of labor can be introduced. More intermediate produced capital goods can be included. Any number of processes can be available for producing each good, including an uncountable infinity. The use of fixed capital introduces more complications. The introductory marginalist textbook story about wages and employment in competitive markets is without foundation.

Why do so many economists teach nonsense?

Alienation And Commodity Fetishism

Marx, in Theories of Surplus Value, quotes James Stuart writing about 'profit upon alienation'. When one sells a good one owns, one has alienated it from oneself. In the typical work relation under capitalism, the managers of firms, that is, the representatives of capitalists, sell the product or services that workers produce. Workers do not own the goods they produce, for they have previously sold their labor-power. That is, they have agreed that their product is not owned by themselves, and neither is their labor.

But alienation means something more in Marx's Paris Manuscripts. The work of Ludwig Feuerbach is important background here. (By the way, this post is based mostly on secondary and tertiary literature, I forget which. I have not read most of the Marx and Engels' works cited here in some time.)

Feuerbach's criticism of Christianity is of some importance for Marx's concept of alienation. According to Feurbach, God's human-like qualities of knowledge, wisdom, and power are projections of extensions of human qualities. We impose them on God. This result of the projection of human qualities is then taken as ruling over us.

Capital goods are themselves the result of human labor. But, in capitalism, the alienated worker is then ruled by these products of human labor. In both cases, human do not usually understand that they are ruled by an entity created collectively by themselves.

The word 'alienation' never appears in the three volumes of Capital as I understand it. Instead, Marx writes about commodity fetishism. I guess the continuity I am claiming is debated among scholars of Marx. But the following sounds like alienation, as developed from the ideas of Feuerbach, to me:

"A commodity is therefore a mysterious thing, simply because in it the social character of men's labour appears to them as an objective character stamped upon the product of that labour; because the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour. This is the reason why the products of labour become commodities, social things whose qualities are at the same time perceptible and imperceptible by the senses... with commodities... existence of the things qua commodities, and the value relation between the products of labour which stamps them as commodities, have absolutely no connection with their physical properties and with the material relations arising therefrom. There it is a definite social relation between men, that assumes, in their eyes, the fantastic form of a relation between things. In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with the products of men's hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseparable from the production of commodities.

The religious analogy suggests, perhaps, that this supposed relation between things appears as a independent being. That is, capital is an entity with seeming agency and its own logic. Marx uses such metaphors as zombies, vampires, and table-turning for this spectral creature. "Capital comes dripping from head to foot, from every pore, with blood and dirt." In a longer exposition, I would also want to go the formal and real subsumption to capital.

It may seem odd to talk about capital as a creature with agency. Many human beings, following certain protocols, can implement a Turing machine, unbeknowest to themselves. The analogy of markets to a computer is harly novel. More prosaically, every manager or firm owner who justifies layoffs; the closure of factories, stores, and offices; or the abandoment of one line of business and the start up of another is appealing to some such logics of capital. Whatever you may think of such people, they are not wrong in claiming to be ruled by an overarching entity.

Capital is not the only supra-personel entity, discussed among Marxists, that seems to have agency. Hardt and Negri's Empire also seems to be such an entity.

I think that Marx condemns capitalism, inasmuch as he does, because he objects to the rule of capital as a supra-personel entity. This creature is constructed by human beings, and we should be able to rule ourselves without such illusions. The rule of this creature hardly seems consistent with a society in which "the free development of each is the condition for the free development of all."