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.

Markets As Automata, Theory Of Computation, Etc.

I do not expect this post to be well-posed. I suggest that the following researchers provide elements for an interesting approach to economics:

• Michel Callon: Applied Actor-Network Theory to financial markets. [I KNOW EVEN LESS ABOUT THIS.]
• Karin Knorr Cetina: the sociology of finance. Use of algorithms in financial markets.
• Donald MacKenzie: Edinburgh school for sociology of knowledge. Performativity and counter-performativity of financial markets.
• Philip Mirowski: Markets as automata. Parallels with Chomsky hierarchy. Economies as evoloving ecology of market automata.
• Kumaraswamy Vela Velupillai: Constructivism in economics, including in Sraffa's work.

The laws of supply and demand, as presented in neoclassical economics, are muddled and confused. Demand for consumer goods, for eample, is the result of households maximizing some non-existent utility subject to constraints. A market is an unanalyed entity, generally with no brokers who make markets, willing to trade on either side. Although not discussed, the market in neoclassical microeconomics is typically a posted price market, corresponding to the lowest level of the Chomsky hierarchy.

Those who specialize in finance might say they observe something like supply and demand in order books. But those curves are not the supply and demand curves presented in introductory economics and in neoclassical microeconomics. These financial markets are structured, with algorithmic rules for matching bids and offers. They often parallel future markets, capable of going into backwardation and contango.

A certain sort of mathematics is needed to fully analyze markets. I happen to be able to write computer code, in some languages to some extent. And I have been exposed to a perspective that computers should be designed to execute our algorithms, which are abstract mathematical entities independent of such implementation.

At one point, I was quite aware of IEEE 754-2019. IEEE Standard for Floating-Point Arithmetic. At one level of abstraction, I would think of my algorithms as applying to real numbers. I also worried about underflow and overflows and other details. (By the way, some editions of Numerical Recipes contain bugs. You have to read and think, not just copy the code.) I also worried about computational complexity. I probably did not worry about any more than whether or not an algorithm could be implemented in polynomial time and how a parallel implementation can provide speedup. From literature on algorithmetic game theory, I know that if P ≠ NP, complexity classes exist in-between.

So I do not adopt a constructivist approach to economics and mathematics. But I appreciate the provision of algorithms to solve economic problems. And I see that Sraffa does that. I do not know of any evidence that Sraffa and Wittgenstein talked about this, even given Wittgenstein's work on the foundations of mathematics.

Greg Mankiw Confusing Students About Money And Investment

"It was thenceforth no longer a question, whether this theorem or that was true, but whether it was useful to capital or harmful, expedient or inexpedient, politically dangerous or not. In place of disinterested inquirers, there were hired prize fighters; in place of genuine scientific research, the bad conscience and the evil intent of apologetic." -- Karl Marx

Suppose you run a restaurant. You think that you could expand if you paved your parking lot or put a deck up out back. You convince your local bank manager. The bank credits their own account with an asset and credits your account with a loan. That asset, for the bank, is a promise from you to pay off the loan, probably as a series of payments. You spend the money in your account by paying a paving or building contractor.

The bank has created money. No third party must first choose to increase their saving rate and deposit money in the bank. You are able to obtain resources to implement plans for increased production.

The author of a prominent introductory textbook for economics has another, confused story:

Financial intermediaries are financial institutions through which savers can indirectly provide funds to borrowers. The term intermediary reflects the role of these institutions in standing between savers and borrowers. Here we consider two of the most important financial intermediaries: banks and mutual funds.

Banks If the owner of a small grocery store wants to finance an expansion of his business, he probably takes a strategy quite different from that of Intel. Unlike Intel, a small grocer would find it difficult to raise funds in the bond and stock markets. Most buyers of stocks and bonds prefer to buy those issued by larger, more familiar companies. The small grocer, therefore, most likely finances his business expansion with a loan from a local bank.

Banks are the financial intermediaries with which people are most familiar. A primary job of banks is to take in deposits from people who want to save and use these deposits to make loans to people who want to borrow. Banks pay depositors interest on their deposits and charge borrowers slightly higher interest on their loans. The difference between these rates of interest covers the banks' costs and returns some profit to the owners of the banks." -- Greg Mankiw. 2018. Principles of Economics, 8th edition p. 545.

Mankiw then goes on with archaic nonsense about loanable funds and government spending crowding out private investment.

Why do economists teach balderdash?

I have been reading J. W. Mason and Arjun Jayadev's new book, Against Money. I have pointed out Mankiw's confusion and foolishness before.

Competing Ballot Propositions

I have occasionally written about vote-counting protocols.

Onondaga County is to the west of me. Syracuse, NY, is their major city. Members of the county legislature currently have term limits of 12 years. Twelve years is three terms. They are currently arguing about term limits for the County Executive, of 12 or 16 years. The Democrats support the former, and the Republicans support the latter. The County Executive is currently a Republican.

The County Executive has proposed a curious set of ballot initiatives, leaving it up to the voters. One initiative will set a term limit of twelve years. Another will set a term limit of sixteen years. If neither initiative gets a majority of votes, the County Executive will continue to serve without a term limit. If both pass, the one with more votes will prevail.

I do not know if any precedent exists in New York State for dueling ballot initiatives, and, apparently, some argument exists among the county legislature about this question. I suspect the results of votes on California ballot initiatives have posed some such challenge of interpretation.

How to draw district lines and how to count votes is an interesting mathematical question. This question is often entangled with racism in the United States, both in ensuring white supremacy and in fighting it.

Was There A Communist State In Paraguay In The Seventeenth And Eighteenth Century?

People have been organized in diverse ways in many societies across time and space. A communist state existed for a century and a half in Paraguay in the seventeenth and eighteenth century. I doubt many socialists today want this degree of regimentation. This state extended into Argentia and Brazil.

The Jesuits, formally named the Society of Jesus, is a religious order in the Catholic church. The Guarani are an indigenous people in South America.

The Jesuits agreed with the Spanish king, in 1609, to found communities along the Parani River. These communities, called 'reductions', were each organized around a mission. Each was ruled by a cacique, that is, a Guarani chief, under the direction of the Jesuits. Collectively, these missions were eventually called the Rio de Plata missions. They reached a population of almost 150,000 in 30 missions in 1732.

Life in these reductions was regimented under the 1689 General Rules of the Missions. Land was farmed communally, with crops and cattle introduced by the Jesuits. There were also individual fields, albeit with inefficient farming. As with life in a monastery, mornings began with hymns and mass, and many feast days were celebrated. Meals were communal. The Jesuits provided education to the children, as you might expect.

I note above that the population under Jesuit guidance grew to a large extent. Original contact between Europeans and the indigenous people resulted in the spread of deadly, contagious diseases. The Jesuits moved a good portion of the population in the missions twice. The Jesuits armed the population to fend off neighbors who tried to kidnap people to force into slavery. The Guarani thereby had militias. Eventually, the Jesuits moved some communities to more remote areas. Portugal gained territory in Brazil in the Treaty of Madrid in 1750. The Jesuits moved some communities out of Portuguese territory.

This experiment in a theocratic communism came to an end in 1767. Spain expelled the Jesuits from the Americas. This expulsion had more to do with European politics than anything going on in these missions.

Naturally, Jesuits put this history in a good light.

References

• Massimo Livi-Bacci and Ernesto J. Maeder 2004. The missions of Paraguay: the demography of an experiment. Journal of Interdisciplinary History xxxv(2): 185–224.
• Philip Caraman. 1976. The Lost Paradise: The Jesuit Republic in South America. [I have not read this. The title is evocative.]
• Paraguay: The Noble Ruins of Paradise.

Two Ways To Think About Fixed Capital

1.0 Introduction

This post presents two approaches to fixed capital. The first emphasizes power and convention. It emphasizes that the 'money world', as Mason and Jayadev (2026) put it, is not a direct reflection of physical properties of production. The second is much closer to a determined model, with one degree of freedom.

I have at least one previous post, more abstractly on these themes

2.0 Depreciation as Accounting Conventions and Mediated by the Exercise of Power

Robert Paul Wolff points out that how overhead costs are allocated is a political exercise in many firms. Two managers on the same level might each be in charge of the production of a specific product. Suppose these products are produced in the facility. Each manager wants upper management to see that they are making the most profits for the company. In is in the interest of each to see that as much of possible of the overhead for running the facility is applied to their rival's department.

A given machine might be used in multiple production processes, resulting in the production of different products. The allocation of overhead costs here follows the above logic.

Sometimes (many times?), no fact of the matter exists for how to allocate costs. As I understand it, the Generally Accepted Accounting Principles (GAAP) includes different conventions for depreciation. Some models I have seen assume radioactive decay so to speak. Tax law specifies what can be allowed.

3.0 Depreciation and the Economic Life of Machines as an Aspect of Prices of Production

Another way of thinking about fixed capital is as in Sraffa (1960). Enough equations are given for prices to be determined, corresponding to a given wage or rate of profits. The data include inputs and outputs, in disaggregated physical terms, for all combinations of ages of machines. These detailed specifications are not based solely on the age, but the entire history of each machine.

Alessandro Roncaglia showed, back in the 1970s, that a countable infinity of equations can arise when production processes can require inputs of combinations of machines. The theory of pure fixed capital includes assumptions that rule out this possibility.

Sraffa derives the formula for an annuity from his treatment of a machine of constant efficiency. But the analysis generalizes. This approach is in tension with the first approach.

4.0 Conclusion

I will continue exploring mathematical puzzles. I like to think that Sraffa presents the elements of an alternative theory, not just an immanent critique of 'neoclassical' theory. The analysis points outside itself.

Reference

• Mason, J. W. and Arjun Jayadev. 2026. Against Money. University of Chicago.

Jack Birner On The Cambridge Capital Controversy

I have been rereading Jack Birner's 2002 book, The Cambridge Controversies in Capital Theory. Birner is an economist of the Austrian school. He probably generally disagrees with me on lots of matters. Torward the start of the introduction, he writes:

"Four decades ago the best minds in economics were engaged in a confrontation which the entire profession followed in the pages of the leading journals almost as if it were a soccer match. It has become customary to distinguish two opposing groups of economists to the debate..." -- Jack Birner (2002: 1)

And he expresses astonishment that the results of this dispute are ignored:

"What I do want to draw attention to is that the conclusions reached in that debate constitute a rare example of a set of formally proven, uncontestable, undeniably true and reliable results in economics... They can be summarized by saying that the K of the production function that modern economists so confidently and fully rely on for their theoretical and empirical work can only be used in conditions where there is only a single, homogeneous capital good. One does not need to have a degree in economics to know that in reality this is not the case. The economy consists of a bewildering variety of buildings, machines, software, skills and ways of organizing production. And as everyone who has filed a corporate tax declaration knows, it is not even possible to give more than a rather inexact estimate of their value. In other words, not only is there no intuitive justification for the use of aggregate, homogeneous K, we have proofs by Nobel-calibre economists assisted by 100 per cent certain mathematical techniques that demonstrate without a shred of doubt that this K cannot and should not be used for the objectives it is currently used for. Nevertheless, economists go about their business as if these proofs did not exist. That some of them are the very same people who produced these proofs earlier makes things even more curious. The fact that production functions with the same aggregate K figure prominently in all current textbooks of macroeconomics is worse than curious: it is deeply worrying." -- Jack Birner (2002: 1-2)

I do not think the situation is different today. I agree with Birner that the overall point of the CCC is not at all clear from the details of the match. The participants were worrying about local details. I think more was at stake than an aggregate theory. I like to emphasize the labor 'market' in my expositions. Fabio Petri, among others, emphasizes mistakes in what the early marginalists thought could be consistently taken as given in their theory.

Birner considers the role of idealizing assumptions in mathematical models. He considers the relations of such ideal models to models that more 'factual', that is, closer to being able to be applied empirically.

The trend, for decades, in the philosophy of science is to be descriptive, to try to understand how specialists in specific disciplines become convinced of their ideas. The CCC poses a problem for the methodologist.

I'm am doubtful about Birner's methodology at points. He draws upon some scholars I like. For example, he draws on Arthur Koestler's The Sleepwalkers: A History of Man's Changing Vision of the Universe. Koestler points out that Copernicus was focused on narrow points. One of the virtues of a geocentric model, for him, was that it got rid of equants. An equant is a circular orbit that has uniform velocity around a point displaced from its center.

Likewise, economists in the CCC were focused on narrow points about, say, Samuelson's surrogate capital and Robinson's pseudo-production function. For Birner, Sraffa and Garegnani were about the only ones awake.

In some sense, Birner does not resolve his problem. He concludes most economists are still asleep.

Socialism Succeeding In Emilia-Romagna

Emilia-Romagna is a region in Italy, north of Tuscany. I have written about its capital, Bologna, before.

About a third of the gross domestic product of Emilia-Romagna is produced by co-operatives. About two thirds of those who reside in Emilia-Romagna participate in co-ops in some ways. (See this article from John Duda.) Apparently, co-ops in Italy go back to the nineteenth century, surviving through the fascists in the twentieth century.

Article 45 of the 1947 Italian constitution promotes co-ops. It states:

The Republic recognises the social function of co-operation of a mutually supportive, non-speculative nature. The law promotes and encourages co- operation through appropriate means and ensures its character and purposes through appropriate checks.

The law safeguards and promotes the handicrafts.

A capability for a worker to take unemployment benefits at once to set up a co-op is one of the provisions of the 1985 Macora law.

A society with a large co-operative segment will have related institutions. Co-ops will market to each other. Scholars, such as Vera Zamagni at the University of Bologna, will study them. Competition among co-ops might be less cut-throat. The study of management and administration at academic institutions will have curriculum supporting co-ops. Mutual banks might be set up to loan to co-ops, and other financial institutions will have more practice in making such loans. Co-ops might set up institutes to perform research into processes and products improving their technology.

The 1986 book, The Second Industrial Divide: Possibilities for Prosperity, by Michael J. Priore and Charles Sabel, is supposed to be of interest on this topic.

Anomalous Switch Points

I have a new working paper at the Centro Sraffa. The abstract follows:

Abstract: This article presents examples of models of rent with decreasing wage frontiers; with unique, square cost-minimizing techniques at a given rate of profits; but without the wage maximization property. Anomalous switch points are highlighted, where an anomalous switch point has properties that contrast with generic switch points in models of circulating capital. This article presents a numeric example of a switch point along a single wage curve, with no other wage curve intersecting at the switch point. Other numeric examples are of switch points in which only the scale, not the operated processes, vary between the cost-minimizing techniques at the switch point. A fake switch point is presented in which prices vary only for goods which are not commodities under the non-cost minimizing technique, also known as ghost commodities.

The Roosevelt Dime And Fluoridated Water: Communist Plots

Franklin Delano Roosevelt died in 1945, and World War II ended with the Japanese surrender in August. Germany had surrendered in May. The Roosevelt dime was introduced in 1946. John Sinnock, an artist at the mint, designed the obverse. His initials are under Roosevelt’s head.

The Soviet Union was the ally of the United States in fighting the fascists. This quickly changed. Somehow anti-communists became convinced that the J. S. on the Roosevelt dime stand for Joseph Stalin. I don't know what advantage the communists were supposed to get out of this plot.

When I first saw Dr. Strangelove, I thought the idea that fluoridated water was a communist plot was quite comic. I did not realize that Kubrick did not make this up. Anti-communists believe this. I do not know if they talk about, "Sapping our precious bodily fluids," as General Jack D. Ripper does in the movie.

I have documented some other stupid stuff anti-communists and anti-Marxists have said.

On Building On Pasinetti's Lectures On The Theory Of Production

I have been re-reading Pasinetti's 1977 book. I claim I am original in partitioning parameter spaces with fluke switch points, concrete numerical examples, certain diagrams for visualizing certain analyses, and extending the capital critique to non-competitive markets. I have noted that participants in the 1966 QJE symposium, including Pasinetti, explicitly noted the possibility of fluke switch points.

Pasinetti’s Lectures contain:

• The algebra repeated in my derivation of Hayek's triangle (p. 91, p. 118).
• An explanation of how a switch point can occur along a single wage curve. The numeraire is a basic good. Two techniques differ in the method or process for producing a non-basic good (p. 161).
• A fluke case with three or more wage curves intersecting at a switch point (p. 164).

The first is an elaboration of Sraffa's reduction to dated labor quantities. I do not feel obligated to cite Newton when I take a derivative. This reduction is close to that. I do not see others linking up this analysis to Hayek's triangles, though,

Pasinetti does not provide a figure or numeric example illustrating the second point. Land is non-basic. Perhaps I should note this in my example with fixed capital and rent.

Pasinetti does provide a figure with three wage curves intersecting in a single switch point. But citing articles from 1966 is sufficient.

C129.4r: Harcourt on Translation Of Sraffa (1925)

This letter is from G. C. Harcourt to Piero Sraffa. As I understand it, Sraffa later refused permission for this translation to be published while he was alive. The translation now available is from Alessandro Roncaglia and John Eatwell.

Adelaide, South Australia 5001
Telephone: 23 4333

Department of Economics
14th April 1970.

Piero Sraffa, Esq.,
Trinity College,
CAMBRIDGE, U.K.

Dear Piero,

Just a short note to say how delighted I was that you will let Mario Nuti translate the Italian version of your 1926 article for Australian Economic Papers. We will, of course, honour strictly your conditions. It really is very generous of you and I personally am extremely grateful.

I hope to be in Cambridge next January for 4 – 6 weeks and hope very much that we may meet then. I hear from Vincent from time to time, he seems to be flourishing. I have just come back from three marvellous months in Japan. I wrote a book on capital theory while there, expanding the assertions of my survey article into, I hope, persuasive arguments.

With all good wishes,

Yours ever,
Geoff. [Handwritten]
G. C. HARCOURT
Professor of Economics

Some Cambridge Controversies in the Theory of Capital is the book Harcourt mentions writing while visiting Japan. I do not know who Vincent is.

Elsewhere

John Conway on Besicovitch

• Abram Besicovitch was friends with Sraffa and gave him advice on mathematics.
• Clara Mattei defines capitalism.
• A documentary, "Amazon created the socialist dream". I think the narrator does not know about linear programming. But maybe deep learning is better for some applications.
• Pol Antràs explores capital theory:
• An 'Austrian' model if international specialization, working paper, 2026, with Adrian Kulesza.
• Measuring the average period of production, AEA Papers and Proceedings, 2025, with Vitalii Tubdenov. As far as I can see, this paper defines the APP to be Bohm Bawerk's obsolete average with simple, not compound, interest.
• Interest rates and world trade: an 'Austrian' perspective, AEA Papers and Proceedings, 2023.
• Bob Murphy interviews Pol Antràs.
• Arin Dube has a substack.
• Paul Krugman interviews Arin Dube.

Instability, A Problem For The Theory Of Supply And Demand

General Equilibrium Theory (GET) is the most rigorous and most developed version of the theory of supply and demand. More than half a century ago, economists discovered that GET does not support the just so stories many economists still tell. (Experimental economists have validated Scarf's example of instability.)

Franklin Fisher was an authority on this topic.

"Yet the very power and elegance of equilibrium analysis often obscures that it rests on a very uncertain foundation. We have no similarly elegant theory of what happens out of equilibrium, of how agents behave when their plans are frustrated. As a result, we have no rigorous basis for believing that equilibria can be achieved or maintained if disturbed. Unless one robs words of their meaning and defines every state of the world as an 'equilibrium' in the sense that agents do what they do instead of doing something else, there is no disguising the fact that this is a major lacuna in economic analysis.

Nor is that lacuna only important in microeconomics. For example, the Keynesian question of whether an economy can become trapped in a situation of underemployment is not merely a question of whether underemployment equilibria exist. It is also a question of whether such equilibria are stable. As such, its answer depends on the properties of the general (dis)equilibrium system which macroeconomic analysis attempts to summarize. Not surprisingly, modern attempts to deal with such systems have been increasingly forced to treat such familiar macroeconomic issues as the role of money." -- Franklin M. Fisher. 1987. Adjustment processes and instability. In J. Eatwell, M. Milgate, P. Newman, The New Palgrave: A Dictionary of Economics. Macmillan.

As far as I know, although some interesting work has been done, this gap still exists.

Reswitching In A Model With Exhaustible Resources?

1.0 Introduction

Part of my program is to construct numeric examples of the reswitching of techniques and of other capital-theoretic 'paradoxes' in a variety of models. Models of exhaustible resources, under some interpretation, provide another opportunity.

2.0 Background

A dispute exists on how compatible the existence of exhaustible resources is with the long period method. An excessively simple analysis is to treat payments for exhaustible resources like rent paid for 'the original and indestructible powers of the soil' (Ricardo 1951: 67). At a given point in time, the cost of mining a resource varies among deposits, and rent varies among mines in use. More than one mine is typically operated for an exhaustible resource because of constraints on the capacity at which mine can be operated. This, arguably, is Ricardo's approach in Chapter III, on the rent of mines, in his Principles. Sraffa (1960), too, groups 'land and mineral resources' together, under the heading of natural resources. Kurz & Salvadori (2009, 2015) read both Ricardo and Sraffa as having a somewhat more sophisticated approach

Parrinello (1983) and Schefold (1989) consider exhaustible resources as such. Bidard & Erreygers (2001, 2020), with the corn-guano model, argue that exhaustible resources are inconsistent with the long period method. The story associated with the model is about an island which was populated by dodos. Manure increases the yield of corn. But, since the dodo is extinct, no more guano is being made in the story. Eventually, capitalist farmers must adopt the backstop technology. They argue that a royalty for an exhaustible natural resource will vary over time, in accordance with the Hotelling rule. All prices will vary over time, as long as exhaustible resources are used in production

Parrinello (2004) and Kurz & Salvadori (2009, 2011, 2015) argue that when the resource will be exhausted is not well-enough known for the Hotelling rule to fully apply. In Kurz & Salvadori's models, a constraint on mines limits how much of each exhaustible resources can be brought above ground in each production period. The price of unmined exhaustible resources increases in accordance with the Hotelling rule, but the rent on mines can decrease in parallel, leaving the price of mined resources unchanged over time. Even though this is an intertemporal model, the prices of produced commodities do not vary over time.

For Ravagnani (2008), the royalty for an exhaustible resource provides another degree of freedom and is set as a percentage of production by conventions and social norms, much like the natural wage in Ricardo and Marx. Huang (2018) builds on Kurz & Salvadori and treats exhaustible resources by introducing processes to search for resources.

3.0 Parameters

Tables 1 and 2 specify a technology that extends an example from Kurz & Salvadori (2011) to include the production of iron. Iron and corn are basic commodities in the sense of Sraffa. Each column in Table 1 specifies the inputs needed to operate the process at a unit level. Each column in Table 2 specifies the corresponding outputs for the process, when operated at a unit level. All processes exhibit constant returns to scale (CRS).

Table 1: Inputs for The Technology

Output	Process
	I	II	III	IV	V	VI	VII	VIII
Labor (Person-Yrs.)	a0,1	a0,2	a0,3	a0,4	a0,5	a0,6	-	-
Iron (Tons)	a1,1	a1,2	a1,3	a1,4	-	-	-	-
Corn (Bushels)	a2,1	a2,2	a2,3	a2,4	-	-	-	-
Oil Underground (Barrels)	-	-	-	-	a3,5=1	-	a3,7=1	-
Menthane Underground (K-Litres)	-	-	-	-	-	a4,6=1	-	a4,8=1
Extracted Oil (Barrels)	-	-	a5,3=1	-	-	-	-	-
Extracted Menthane (K-Litres)	-	-	-	a6,4=1	-	-	-	-

Table 2: Outputs for The Technology

Output	Process
	I	II	III	IV	V	VI	VII	VIII
Iron (Tons)	b1,1 = 1	-	-	-	-	-	-	-
Corn (Bushels)	-	b2,2=1	b2,3=1	b2,4=1	-	-	-	-
Oil Underground (Barrels)	-	-	-	-	-	-	b3,7=1	-
Menthane Underground (K-Litres)	-	-	-	-	-	-	-	b4,8=1
Extracted Oil (Barrels)	-	-	-	-	b5,5=1	-	-	-
Extracted Menthane (K-Litres)	-	-	-	-	-	b6,6=1	-	-

The first process produces iron. The next three processes produce corn. The first corn-producing process is part of a backstop technology. The other two use oil and menthane as fertilizer, respectively. Processes V and VI are extraction processes. Processes VII and VIII are conservation processes.

The extraction processes, V and VI, are constrained not to produced more than a maximum output in any year. I let t_o be the maximum output for oil extraction in a year. Let t_m be the maximum output for menthane extraction in a year. The data also includes the specification of q_uo, the initial quantity of unexextracted oil, and q_um, the initial quantity of unextracted menthane.

Final demand, y₁ and y₂ for iron and corn, are the last parameters needed to specify this model.

4.0 Selected Price Variables

I need to specify techniques and quantity flows for each technique. The amount of unextracted oil and methane will vary over time. Depending on the parameters, only some techniques will be feasible.

Table 3 defines the price variables that will be found by solving the price equations. Rent on mines and the prices of unextracted exhaustible resources vary over time, as reflected in the notation.

Table 3: Selected Price Variables

Variable	Definition
p1	Price of a ton iron.
p2	Price of a bushel corn.
po	Price of a barrel of extracted oil.
pm	Price of a kilo-litre of extracted methane.
puo(t)	Price of a barrel of unextracted oil at the end of the tth year.
pum(t)	Price of a kilo-litre of unextracted menthane at the end of the tth year.
rhoo(t)	Rent per barrel oil extracted in a year.
rhom(t)	Rent per kilo-litre methane extracted in a year.
w	The wage.
r	The rate of profits.

6.0 Conclusion

My problem is to find numeric values for model parameters such that reswitching results. This reswitching might be analogous to the reswitching of the order of efficiency. Perhaps for some ranges of the rate of profits, the backstop technology is operated along with the extraction of oil. And, at other ranges, the backstop technology is operated along with the extraction of methane.

Or maybe the solution will be that corn is produced with process III, without the backstop technology, at some ranges of the rate of profits. And, at other ranges, corn is produced with process IV, also without the backstop technology.

This post only poses a problem. I do not think it do difficult to see that capital-theoretic 'paradoxes' can appear in Kurz and Salvadori's approach to exhaustible resources. I suppose it would be good to have concrete examples.

References

• Bidard, C. and G. Erreygers. 2001. The corn-guano model. Metroeconomica 52(3): 243-253.
• Bidard, C. and G. Erreygers. 2020. Exhaustible resources and classical theory. History, Methodology, Philosophy 10(3): 419-446.
• Huang, B. 2018. An exhaustible resources model in a dynamic input-output framework: A possible reconciliation between Ricardo and Hotelling. Journal of Economic Structures, 7(1): 1-24.
• Kurz, H. D. and N. Salvadori. 2009. Ricardo on exhaustible resources and the Hotelling rule. In Aiko Ikeo and Heinz D. Kurz (eds), A History of Economic Theory: Essays in Honour of Takashi Negishi. London: Routledge.
• Kurz, H. D. and N. Salvadori. 2011. Exhaustible resources: Rents, profits, royalties and prices. In Volker Caspari (ed.), The Evolution of Economic Theory: Essays in Honour of Bertram Schefold. London: Routledge, 39-52.
• Kurz, H. D. and N. Salvadori. 2015. The 'classical' approach to exhaustible resources. Parrinello and the others. In Heinz D. Kurz and Neri Salvadori (eds), Revisiting Classical Economics. Studies in Long-Period Analysis. London: Routledge, 304-316.
• Parrinello, Sergio. 1983. Exhaustible natural resources and the classical method of long-period equilibrium, in J. Kregel (ed.), Distribution, Effective Demand and International Economic Relations, London: Macmillan, pp. 186–99
• Parrinello, Sergio. 2004. The notion of effectual supply and the theory of normal prices with exhaustible resources. Economic Systems Research, 16(3): 311-322.
• Ravagnani, Fabio. 2008. Classical theory and exhaustible natural resources: notes on the current debate. Review of Political Economy, 20(1).
• Ricardo, David. 1951. The Works and Correspondence of David Ricardo: Volume 1: On the Principles of Political Economy and Taxation. Cambridge: Cambridge University Press.
• Schefold, Bertram. 1989. Mr. Sraffa on Joint Production and Other Essays, Routledge.
• Sraffa, Piero. 1960. The Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory. Cambridge: Cambridge University Press.

The Production Of Commodities And The Structure Of Production

I have a working paper at the Munich Personal RePEc Archive (MPRA). MPRA does not have a peer-review process. Here is the abstract:

Abstract: Consider a model of the production of commodities by means of commodities. This article illustrates how to construct a Hayekian triangle with such a model, in the case with circulating capital. Capital-theory paradoxes, specifically the reswitching of techniques, have implications for such triangles. The use of such triangles to tell the stories that Austrian economists want to tell cannot be sustained. The switch point that is normal in a reswitching example, from a mainstream neoclassical perspective, has perverse Hayekian triangles. The switch point that is perverse from a mainstream perspective has Hayekian triangles consistent with the Austrian story about how a decreased time preference rotates the triangle to lengthen the structure of production.

The History Of The Soviet Union Is Inconsistent With Marxism

1.0 Introduction

You can tell a history of the Union of Soviet Socialists Republics in which events are inconsistent with Marx's theory of history.

2.0 Bolshevik Revolution

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 start successful in either country.

I have some caveats. Marx's 1881 letter to Vera Zasulich speculates on the possibility of socialism in Russia. I am aware that Lenin had an argument about how socialism can start with the weakest link in the age of imperialism. But he still expected his revolution to be supported by revolutions in advanced capitalist countries. And, for a moment he seemed to be right, what with the Spartacist revolution in Germany, the Bavarian Socialist Republic, and Hungary.

3.0 Socialism In One Country

Stalin came up with the idea of socialism in one country. That country was still quite backward, not an advanced capitalist country. Is the championing of the Soviet Union by communists in advanced capitlist countries what Marxists would wnat? The Soviet Union presented an alternative. But shouldn't their priority be building socialism at home? And their cause was weakened when the Soviet Union behaved like other great powers in Hungary in 1956 and in Czechoslovakia in 1968.

4.0 Khrushchev's Secret Speech

Khrushchev denounced Stalin in his 'secret' speech of 25 February 1956. He came up with the concept of the cult of personality. What is that from a Marxist perspective? History is supposed to be determined, ultimately, by contradictions in material conditions. How can the mistakes of one leader be so important?

5.0 Gorbachev's Voluntarism

I do not understand the collapse of the Soviet Union. I think of the fall of the Berlin Wall in 1989 and the dissolution of the Soviet Union in 1991.

As I understand it, Gorbachev and other members of the Politburo acquiesced in the dismantling of the Soviet Union. Poor performance pointed out the need for reforms. Nevertheless, I find it strange that political leaders can decide that the system they preside over has no legitimacy like that.

Steve Paxton provides an account of how the fall of the Soviet Union was a triumph for Marx's theory of history.

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.

Reswitching And Other Capital-Theoretic Paradoxes In A Variety Of Models

Apparently, it is part of my project to construct explicit numeric examples of the rewitching of techniques and capital-theoretic paradoxes in a range of models. Here are some examples I have produced:

• The reswitching of techniques in a capitalist economy with non-competitive markets.
• The reswitching of the orders of efficiency and of rentability in a model with extensive rent.
• The reswitching of techniques in a model with extensive rent.
• The complete reversal of the orders of efficiency and rentability in a model with extensive and intensive rent (See region 11 in the example).
• The reswitching of techniques in a model with extensive and intensive rent and with multiple (two) agricultural commodities.
• The recurrence of truncation and reverse labor substitution without the reswitching of techniques.
• Capital-reversing in an example with fixed capital and scarce land.

This post is one of my summary posts.

I Did Not Invent The Concept Of Fluke Switch Points

I find myself writing about generic switch points, fluke switch points, anomalous switch points, fake switch points, normal switch points, and 'perverse' switch points. I do not seem to have definitions with the precision of those in mathematical analysis.

A switch point is a fluke when any perturbation of some parameters, such as coefficients of production, destroys defining features of the switch point. The concept of a fluke goes back to the 1966 symposium on capital theory in the Quarterly Journal of Economics:

"If, by a fluke more than one switch of technique happened to take place at exactly the same point, the nonzero columns [of the matrix formed by the difference of two Leontief matrices] would be more than one" (Pasinetti 1966: 511).

Other participants recognize this fluke case in which four wage curves intersect at a switch point, with processes replacing one another in two industries:

"'Adjacent" techniques on two sides of a switching point of a switching point will usually differ from each other only with respect to one activity" (Bruno, Burmeister, Sheshinski 1966: 542).

Two wages curves tangent at a switch point is another fluke case. A perturbation leads to either the reswitching of techniques or of one cost-minimizing technique around the rate of profits at which the switch point formerly existed. Other fluke cases arise when a switch point exists at the maximum wage or the maximum rate of profits:

"Cases with multiple roots or cases in which the curves cross only at end points... These ... are cases which one technique can be ignored since it is dominated" (Bruno, Burmeister, Sheshinski 1966: 534).

Pierangelo Garegnani recognizes the possibility of the fluke case with two wage curves tangent:

"The possibility that, at r^* and r^**, the two wage curves touch without intersecting is excluded...” (Garegnani 1966: 567).

Fluke switch points exist in both models of single and joint production. Vienneau (2021) examines fluke switch points in pure fixed capital models, while Vienneau (2022) partitions a parameter space, with fluke switch points, in a model of extensive rent. Vienneau (2024) looks at fluke switch points in a model of non-competitive markets with single production. The characterization of fluke switch points is useful for analyzing structural economic dynamics with a choice of technique.

References

Bruno, Michael, Edwin Burmeister, and Eytan Sheshinski. 1966. The nature and implications of the reswitching of techniques. Quarterly Journal of Economics 80(4): 526-553.

Garegnani, P. 1966. Switching of techniques. Quarterly Journal of Economics 80(4): 554-567

Pasinetti, Luigi L. 1966. Changes in the rate of profit and switches of technique. Quarterly Journal of Economics 80(4): 503-517.

Vienneau, Robert L. 2021. Fluke switch points in pure fixed capital systems. Centro Sraffa working papers n. 48.

Vienneau, Robert L. 2022. Reswitching in a model of extensive rent. Bulletin of Political Economy 16(2): 133-146.

Vienneau, Robert L. 2024. Characteristics of labor markets varying with perturbations of relative markups. Review of Political Economy 36(2): 827-843.