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.

Surveys Of The Cambridge Capital Controversy

'Neoclassical' economists accepted, in the third quarter of last century, that the theories they teach and apply have no rigorous foundation. They are illogical and incoherent. Why does that not matter? This presents a puzzle.

Many have surveyed or responded to the Cambridge Capital Controversy. Here are some surveys and responses:

• Jack Birner. 2002. Cambridge Controversies in Capital Theory: A Methodological Analysis. Routledge.
• Mark Blaug. 1974. The Cambridge Revolution: Success or Failure?. London: Institute of Economic Affairs. (I stumbled upon this negative review in the History of Political Economy.)
• Christopher Bliss. 1975. Capital Theory and the Distribution of Income. Elsevier North-Holland.
• Edwin Burmeister. 1982. Capital Theory and Dynamics. Cambridge University Press.
• Avi J. Cohen and G. C. Harcourt. 2003. Whatever happened to the Cambridge capital theory controversies. Journal of Economic Perspectives 17(1): 199-214.
• Avinash Dixit. 1977. The accumulation of capital theory. Oxford Economic Papers 29(1): 1-29.
• Roger W. Garrison. 2006. Reflections on reswitching and roundaboutness. In Money and Markets: Essays in Honor of Leland B. Yeager (ed. by Roger Koppl). Routledge.
• G. C. Harcourt. 1969. Some Cambridge controversies in the theory of capital. Journal of Economic Literature 7(2): 369-405.
• G. C. Harcourt. 1972, 2022. Some Cambridge Controversies in the Theory of Capital. Cambridge University Press.
• Daniel Hausman. 1981. Capital, Prices and Profits. Columbia University Press.
• Andrés Lazzarini. 2011. Revisiting the Cambridge Capital Theory Controversies: A Historical and Analytical Study. Pavia University Press..
• Joseph E. Stiglitz. 1974. The Cambridge-Cambridge controversy in the theory of capital: a view from New Haven. Journal of Political Economy 82(4): 893-903.
• Leland B. Yeager. 1979. Capital paradoxes and the concept of waiting. In Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (ed. by M. J. Rizzo). Lexington Books.

Harcourt (1972) is my favorite of these surveys - an utterly conventional view. I disagree with much in many of these surveys and responses. But those who have never been exposed to the CCC will learn something from any of them.

To Read Adorno's Minima Moralia Requires Understanding Of Marx

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

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

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

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

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

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

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

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

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

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

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

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

Numerical Examples Of The Reswitching Of Techniques In Spatial Economics?

It is my custom to work through, with graphs, example of the reswitching of techniques and other capital-theoretic 'paradoxes' in various models. Sometimes I have created numeric examples, and perturbed them too.

Reswitching examples exist in the literature on spatial, regional, and urban economics. Nowhere have I worked through them.

I think of regional economics as having two traditions for building theoretical models. One is the the Von Thunen model, with a central city and concentric rings of land uses. Transport costs are of importance. Reswitching is manifested by non-adjacent rings being used to produce the same commodities, with other commodities being produced in between. Barnes & Sheppard (1984) have graphs suggesting that they have a concrete numerical example. But they do not present parameter values. Their text suggests that an example can be created based on the example in Metcalfe & Steedman (1979).

Walter Isard invented regional economics in the middle of the twentieth century. This approach has different countries or regions described by individual Leontief matrices. Imports and exports show interactions between the regions.

Pavlik (1990) has a numeric example for this second tradition, reproduced, I think, in section 5.1 of Sheppard & Barnes (1990). They have the production distributed among regions, as I understand it, like in 'gravity models'. And its solution requires an application of an iterative algorithm. I think this implies the eample does not necessarily have a technique that is cost-minimizing across all regions, as opposed to within each region. I suppose it would be good to replicate this example and produce some graphs. (I realize that computers these days provide capabalities that were not also easily available decades ago.)

Perhaps Zaffari & Sbrenna (2024) provide a model on which I should concentrate. This model seems to be in the Isard tradition, with improvements. Their modeling includes transportation costs, the spatial capacity of regions in space, and the endogenity of various variables. I can make various simplifications in developing a concrete numerical example.

Can I work through existing numerical examples in the literature? Can I find numerical values for the parameters in the model in Zaffari & Sbrenna (1984), perhaps simplified, for a reswitching example? I suppose techniques might differ in which regions, processes are run to capacity. Or, perhaps, one region specializes in manufacturing one set of commodities and the other in making manufacturing another set. I do not know how far I will get.

References

• Barnes, Trevor & Eric Sheppard. 1984. Technical choice and reswitching in space economies. Regional Science and Urban Economics 14: 345-362.
• Metcalfe, J. Stanley & Ian Steedman. 1979. Reswitching and primary input use. In Fundamental Issues in Trade Theory (ed. by I. Steedman) New York: St. Martin's Press.
• Pavlik, C. 1990. Technical reswitching: a spatial case. Environment and Planning A 22:1025-1034.
• Sheppard, Eric & Trevor Barnes. 1990. The Capitalist Space Economy: Geographical Analysis after Ricardo, Marx and Sraffa. London: Unwin Hyman.
• Zaffari, Gabriel & Giacomo Sbrenna. (2024) Sraffa goes to space: spatial elements of political economy. Review of Political Economy DOI: 10.1080/09538259.2024.2434532

'Neoclassical' Economists On The Lack Of Foundation For Some 'Neoclassical' Economics

1.0 Introduction

Last century and into this one, 'neoclassical' economists noted the lack of theoretical foundation for certain widely used models in economics. They noted that the interest rate is generally not equal to the marginal product of capital. This post quotes three prominent 'neoclassical' economics, over decades, noting the lack of theoretical foundation for such an equality.

For the purposes of this post, I have little to say about my disagreements with these authors. I will note that Sraffians have something to say about microeconomics too. I also do not want to go into here why empirical work with these unfounded models is almost always a kind of humbug.

2.0 Frank Hahn

Frank Hahn attacks my favorite school of thought. He says:

"Sraffa ... confined himself to the remark that the [missing] equation cannot be one which demands the equality of the marginal product of 'capital' and the rate of profit. ... the neoclassical economist has the same view but his reasons are not those given by Sraffa." -- Frank Hahn (1982) The neo-Ricardians. Cambridge Journal of Economics. 6(4): 362.

And again:

"The Sraffian picture of neoclassical theory is this. At any moment of time we can observe something physical called the stock of capital (K) as well as the amount of labor (L). There is a concave production function

Y = F(K, L)

where Y is output. In a neoclassical equilibrium all inputs are used and must be paid their marginal products. The latter are known once (K, L) are known. Hence the rate of profit of capital, the real wage and the distribution of income are all known once F(), K and L are known. The concavity of F further implies that the rate of return on capital is non-increasing (generally decreasing) in K. This construction, to be called the parable, Sraffians claim not to be watertight except in the single good economy. In this they are generally correct." -- Frank Hahn (1982: 370)

3.0 Edwin Burmeister

This is from a standard reference work:

"Imposing some set of conditions on the technology T() should be sufficient to ensure that the real Wicksell effect is always negative. Such conditions would be of interest - especially if they could be empirically tested - since they would validate the qualitative conclusions derived from the one-good model often used in macroeconomics without any theoretical justification for ignoring aggregation problems. Moreover, Burmeister (1977, 1979) has proved that a negative real Wicksell effect is a necessary and sufficient condition for an index of capital, k, and a neoclassical aggregate production function F(k) defined across steady-state equilibria such that (i) c = F(k), (ii) r = F’(k), and (iii) F’’(k) < 0. Unfortunately, no set of such sufficient conditions is known, but the literature on capital aggregation suggests that they would impose severe restrictions on the technology." -- Edwin Burmeister (1987). Wicksell effects. The New Palgrave.

That index is Champernowne's chain index measure of capital.

4.0 Emmanuel Farhi

Here is Emmanuel Farhi giving a lecture in 2018 agreeing with the above authors. His history of the CCC is in the first half hour. There is an accompanying paper (working paper version here). Farhi's co-author, David Rezza Baqaee, seems to be pursuing this approach.

5.0 Conclusion

Economics presents a problem for the sociology of 'knowledge'.