Wednesday, January 01, 2025


I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Friday, January 27, 2023

Engels To Mehring On False Consciousness

The following is from Friedrich Engels' letter to Franz Mehring of 14 July 1893:

London, 14 July 1893

Dear Mr. Mehring,

It has taken me until today to get round to thank you for the Lessing-Legende you were so kind as to send me. I did not wish merely to send you a formal note acknowledging receipt of the book, but also and at the same time to say something about it - its contents. Hence the delay.

Let me begin at the end - with the appendix, 'II ber den historischen Materialismus' in which you have brilliantly collated the essentials in a manner that must convince any impartial reader. If I have any criticism to make, it is that you accord me more merit than I deserve, even if one takes account of what I may, perhaps, have found out for myself - in course of time - but which Marx, with his swifter coup d'oeil and greater discernment, discovered much more quickly. If one has been fortunate enough to spend forty years collaborating with a man like Marx, one tends, during one's lifetime, to receive less recognition than one feels is due to one; when the greater man dies, however, the lesser may easily come to be overrated - and that is exactly what seems to have happened in my case; all this will eventually be put right by history, and by then one will be safely out of the way and know nothing at all about it.

Otherwise only one point has been omitted, a point which, however, was never given sufficient weight by Marx and myself in our work, and in regard to which we are all equally at fault. For we all of us began, as we were bound to do, by placing the main emphasis on the derivation of political, legal and other ideological conceptions, as of the actions induced by those conceptions, from economic fundamentals. In so doing we neglected the formal in favour of the substantial aspect, i.e. the manner in which the said conceptions, etc., arise. This provided our opponents with a welcome pretext for misinterpretation, not to say distortion, Paul Barth being a notable case in point.

Ideology is a process which is, it is true, carried out consciously by what we call a thinker, but with a consciousness that is spurious. The actual motives by which he is impelled remain hidden from him, for otherwise it would not be an ideological process. Hence the motives he supposes himself to have are either spurious or illusory. Because it is a mental process, he sees both its substance and its form as deriving solely from thought - either his own or that of his predecessors. He works solely with conceptual material which he automatically assumes to have been engendered by thought without inquiring whether it might not have some more remote origin unconnected therewith; indeed, he takes this for granted since, to him, all action is induced by thought, and therefore appears in the final analysis, to be motivated, by thought.

The historical ideologist (here historical is used as an omnibus term for political, legal, philosophical, theological, in short, for all spheres appertaining to society and not merely to nature) - the historical ideologist, then, possesses in every sphere of science a material which has originated independently in the thought of previous generations and has undergone an independent course of development of its own in the brains of these successive generations. True, external facts appertaining to one sphere or another may also have helped to determine that development but according to what has been tacitly assumed, those facts, themselves are merely the fruits of a mental process, and thus we still find ourselves in the realm of pure thought which would appear to have succeeded in assimilating even the most recalcitrant facts.

What has above all deluded the majority of people is this semblance of an independent history of political constitutions, legal systems and ideological conceptions in each individual sphere. When Luther and Calvin ‘overcome' the official Catholic faith, when Hegel 'overcomes' Fichte and Kant, or when, with his republican Contrat social, Rousseau indirectly 'overcomes' the constitutionalist Montesquieu, the process is one which remains within the confines of theology, philosophy and political science, which represents a stage in the history of these spheres of thought and never emerges from the sphere of thought. And since the advent of the bourgeois illusion of the eternity and ultimacy of capitalist production, even the overcoming of the Mercantilists by the Physiocrats and Adam Smith has come to be regarded merely as a victory of the concept, not as the conceptual reflection of changed economic facts, but as the correct perception, now at last achieved, of actual conditions as they have always and everywhere existed. If Richard Coeur-de-Lion and Philip Augustus had introduced free trade instead of becoming involved in the Crusades, we should have been spared five hundred years of misery and folly.

We have all, I believe, neglected this aspect of the matter, which I can only touch on here, to a greater extent than it deserves. It's the same old story - initially, form is always neglected in favour of substance. As I have said, I, too, have done this, never realising my mistake until after the event. Far be it from me, therefore, to reproach you on that score - as the senior culprit I am in no way entitled to do so, quite the contrary - but rather I would draw your attention to this point with a view to future occasions.

Hand in hand with this goes the ideologists' fatuous conception that, because we deny independent historical development to the various ideological spheres which play a role in history, we also deny them any historical efficacy. Underlying this is the ordinary, undialectical conception of cause and effect as rigidly opposite poles, quite regardless of any interaction. The gentlemen forget, often almost deliberately, that an historical element, once it is ushered into the world by other, ultimately economic, causes, will react in its turn, and may exert a reciprocal influence on its environment and even upon its own causes. Cf. Barth, for example, on the priestly caste and religion, your p. 475. 1 was delighted by the way you dismissed this quite incredibly superficial Johnnie. And they go and make the chap professor of history at Leipzig! Old Wachsmuth used also to be there; he too was not a little shallow-pated but he had a tremendous feeling for facts - a very different sort of chap.

For the rest I can only remark of this book what I said more than once about the articles when they appeared in the Neue Zeit, namely that it is by far the best account of the genesis of the Prussian state that exists, indeed I might even say the only good one, being in most cases an accurate and minutely detailed exposition of correlations. One can only regret that, while you were about it, you did not feel able to include the whole course of events up till Bismarck; nor can one help hoping that you may some day do so and present the whole picture, from the Elector Frederick William to old William, in context. You have, after all, already done the preliminary studies which you have all but completed at any rate so far as the essentials are concerned. And, after all, it has got to be done some time, before the rickety contraption collapses. The exploding of the monarchist-patriotic myths, if not exactly a necessary prerequisite for the elimination of that bulwark of class rule, the monarchy (a purely bourgeois republic in Germany having already become an anachronism before it has ever existed) is nevertheless one of the most effective means to that end.

You would then also be better off as regards space and opportunity when you come to depict local Prussian history as part of the whole German misère. This is a matter upon which my views differ here and there from your own, notably as regards the conditions responsible for the dismemberment of Germany and the failure of the German bourgeois revolution in the 16th century. If I get round to revising the introduction to my Peasant War, as I hope to do next winter, I shall be able to enlarge on the points in question. Not that I consider those you adduce to be incorrect, but I should include some others and marshal them rather differently.

I have always found, when studying German history - which is one long, continuous misère - that a true perspective can only be obtained by comparing it with the same periods in France, because what happens there is the exact opposite of what happens in Germany. There we have the establishment of the national state from the disjecta of the feudal state at the very time of our worst decline. There, a rare kind of objective logic permeates the whole course of events; in our case, a barren and ever more barren haphazardness. There, the English conqueror of the Middle Ages, who intervenes in favour of the Provençal nationality as opposed to North French nationality, represents foreign intervention; the English wars are, as it were, the equivalent of the Thirty Years' War which, however, ended with the ejection of foreign intervention and the subjection of the South by the North. Next comes the struggle between the central power and its Burgundian vassal, supported by his foreign possessions and playing the part of Brandenburg-Prussia, a struggle which, however, ends in victory for the central power and puts the seal on the establishment of the national state. And at the selfsame time in Germany, the national state (in so far as the 'German Kingdom' within the Holy Roman Empire can be called a national state) collapses completely, and the wholesale plundering of German territory begins. It is a comparison that is exceedingly humiliating to Germans, but all the more instructive for that, and now that our working men have again placed Germany in the van of the historical movement, it may be somewhat easier for us to swallow the ignominy of the past.

But what is of particular significance so far as developments in Germany are concerned is the fact that the two member states, which eventually partitioned the whole of the country between them, were neither of them purely German but were colonies on captured Slav territory - Austria a Bavarian, and Brandenburg a Saxon, colony; also the fact that they acquired power in Germany only with the support of foreign, non-German possessions - Austria with that of Hungary (not to mention Bohemia), Brandenburg with that of Prussia. Nothing of the kind happened on the western frontier, more at risk than anywhere else; on the northern frontier it was left to the Danes to protect Germany against the Danes, while in the South there was so little to protect that the frontier guards, the Swiss, were actually able to detach themselves from Germany!

But I am divagating - my loquacity can, at any rate, serve you as proof of the extent to which your book has stimulated me.

Once again, many thanks and warm regards from


F. Engels

Monday, January 23, 2023

Martin Luther King, Jr., Was A Democratic Socialist

I was prompted to write this post by Matthew Yglesias's post from Martin Luther King Day.

"[A. Philip] Randolph, of course, continued as a major leader in the struggle until his death in 1979. When I became deeply involved in the civil rights movement in the fifties and sixties, I was a conscious Randolphite, dedicated to the program of an integrated class struggle against both exploitation and racism. And when I began to work with Martin Luther King, Jr., I discovered that he, too, had much the same view. After the first time that we were able to talk together at length - which was over several days in Los Angeles in 1960 when we were hiding him in a hotel room so that the representatives of the various Democratic presidental candidates could not pester him for endorsements - I concluded that he was a democratic socialist, like Randolph.

It did not even occur to me to ask King to proclaim publicly those beliefs since I understood he had troubles enough without adding to them an ideological commitment, which would be inevitably misunderstood. Bit I was delight when Bearing the Cross, David Garrow's brilliant biography of King, recently documented the truth of my conviction about him, revealed that King actually called himself a democratic socialist in private conversation." -- Michal Harrington, The Long-Distance Runner: An Autobiography, Henry Holt and Company (1988): 41-42.

For me, democratic socialism was, for many decades in the United States, whatever Michael Harrington said it was. The Socialist International is also an authoritative source for much of this time.

Saturday, January 21, 2023

CCC Does Not Depend On Reswitching

The logical possibility of the reswitching of techniques is a devastating challenge to marginalism. But the Cambridge capital controversy does not depend on the presence of reswitching. I suppose I should have links for the possibilities listed below. None of these possibilities are fluke cases.

One might make a distinction between the reswitching of techniques and the recurrence of techniques. In both cases a technique is cost-minimizing at two non-overlapping ranges of the wage. If only one technique is cost-minimizing at wages between these ranges, that is reswitching. If more than one technique is cost-minimizing between, then one should talk about the recurrence of techniques. I forget where I have seen this not very common and not very useful distinction.

Capital reversing can occur with neither the reswitching of techniques nor the recurrence of techniques occurring on the wage frontier. Reswitching and the recurrence of techniques, however, imply the existence of a switch point in which capital reversing occurs. With capital reversing, a lower rate of profits around a switch point is associated with a switch to a technique with a lower capital intensity and a lower net output per labor input. Capital intensity is measured by either the capital-labor ratio or the capital-output ratio, with capital valued at prices of production. Net output is of a given physical composition. I like to express the logical possibility of capital reversing by noting that around such a switch point, firms want to hire a greater quantity of labor at a higher wage, given net output.

A production process can be in cost-minimizing techniques at two non-overlapping ranges of the wage, with techniques not operating this process being cost-minimizing at intermediate wages. The recurrence of techniques implies process recurrence, but process recurrence can exist without the recurrence of techniques.

The reverse substitution of labor can occur without the recurrence of techniques, capital reversing, or process recurrence. The reverse substitution of labor occurs when around a switch point, the technique that is cost-minimizing at a higher wage results in the adoption of a process in some industry in which more direct labor is hired per unit of gross output in that industry.

The presence of fixed capital creates the possibility of additional effects. The analysis of the choice of technique includes the analysis of the economic life of machines. The recurrence of truncation occurs when the economic life of a machine in the cost-minimizing technique is the same at two non-overlapping ranges of the wage. Some other economic lifetime is in the cost-minimizing technique at intermediate wages.

In the theory of fixed capital, the adoption of a cost-minimizing technique around a switch point with an increased economic life of a machine can be associated with the choice of a less capital-intensive technique of production. I do not have a name for this phenomenon. As far as I know, nobody has explicitly pointed out this possibility before me, although I will not be surprised if somebody points out some text in Pasinetti (1980) or some work by Schefold.

I next turn to the theory of extensive rent, another special case of the theory of joint production. The order of fertility, also known as the order of efficiency, is the order of types of land, given the wage, from a high rate of profits downwards among wage curves. Alternatively, one can take the rate of profits as given and order lands downward by wages. These orders are not necessarily the same. The order of fertility shows the order in which lands will be cultivated as requirements for use expand. Anyways the order of fertility can vary with distribution.

The order of rentability is the order of types of land from high rent per acre to low rent per acre. The order of rentability can vary with distribution.

The order of fertility need not match the order of rentability. Whether or not these orders of types of land match can vary with distribution.

One can have the reswitching of the order of fertility. Given requirements for use, the order of fertility can be the same at two non-overlapping ranges of the wage. Some other order of fertility occurs at intermediate wages. One might note this possibility does not require any variation in the cost-minimizing technique. The same processes can be operated for industrial commodities, and the same types of land can be fully cultivated. The type of land that is only partially cultivated can be cultivated at the same level with these variations with distribution.

One can also have the reswitching of the order of rentability. Given requirements for use, the order of rentability can be the same at two non-overlapping ranges of the wage. Some other order of rentability occurs at intermediate wages. This possibility also does not require any variation in the cost-minimizing technique. As far as I know, I am the first to point out the possibility of the reswitching of the order of fertility and of the reswitching of the order of rentability.

The above descriptions of various results from the analysis of the choice of technique have all been about how cost-minimizing techniques vary around switch prices. I have not considered variations in prices of production for a single technique as distribution varies. Such variations are known as price Wicksell effects. Nor have I considered the general theory of joint production or the special case of intensive rent.

Prices of production reflect a different vision of political economy than marginalist theory.

Friday, January 20, 2023

Translation Between The Language Of Classical Economists And Marginalists

Lately, when trying to write up my results I use terminology from classical political economy. The table below maps some terms from classical political economy to terminology for marginalists.

Use valueUtility
SupplyQuantity supplied
DemandQuantity demanded
(Normal) profitsInterest
Extra profits(Pure) economic profits
Supernormal profits
Market pricesShort run prices
Natural pricesLong run prices
Prices of production

I probably am leaving some important mapping out. Nuances, at least, exist to distinguish between entries in rows in the tables. And maybe it depends on which classical or marginalist economist you read, and which of their works. I think the first row is the most questionable.

Monday, January 16, 2023

Reswitching Of The Order Of Fertility

Figure 1: An Example of the Reswitching of the Order of Fertility
1.0 Introduction

Nobody has ever pointed out the possibility highlighted by this post, as far as I know. This post can be contrasted with this one. Talk of "switch points" and "reswitching" for the wage curves on the left pane in Figure 1 above is, arguably, an abuse of terminology. Quantity flows do not change around the switch points. The same lands are fully farmed, and the same land that is partially farmed has the same quantity left fallow.

This post presents a numerical example of extensive rent in which the order of rentability does not vary with distribution. Rent curves do not intersect. Yet the ranking of lands by fertility varies with distribution. The same order of fertility appears at low and high rates of profits, with a different order arising for intermediate rates of profits.

2.0 Technology

The analysis of the choice of technique in models of extensive rent can be based on the construction of wage curves, even though the outer envelope does not represent the cost-minimizing technique. The orders of fertility and rentability are emphasized here. The order of fertility is defined for specified techniques, in which multiple qualities of land are used in each technique, and a single quality of land pays no rent. At a given rate of profits, the qualities of land are ordered by wages, with the most fertile land paying the highest wage. The order of rentability specifies the sequence of different qualities of lands from high rent per acre to low rent per acre. Both orders may vary with the wage or the rate of profits. Table 1 presents coefficients of production for an example.

Table 1: The Coefficients of Production
InputIron IndustryCorn Industry
Type 1 Land049/10000
Type 2 Land0059/1000
Type 3 Land0009/20

The amount of corn that can be produced is constrained by the available quantities of each type of land. Endowments of land and requirements for use must be among the givens to analyze the choice of technique in this example. Suppose the quantities of the different types of land and net output is such that all three types of land must be farmed. One type will be only partially farmed. The iron-producing process must be operated in each of the three economically viable techniques. Table 2 describes which type of lands are fully cultivated and which type of land is left partially fallow in each of the Alpha, Beta, and Gamma techniques.

Table 2: Techniques of Production
Type 1Type 2Type 3
AlphaFully farmedFully farmedPartially farmed
BetaPartially farmedFully farmedFully farmed
GammaFully farmedPartially farmedFully farmed

3.0 Prices of Production

Prices of production are specified by a system of equations with one degree of freedom. Suppose a bushel corn is the numeraire. Let p be the price of a ton of iron; r the rate of profits; w the wage; and ρ1, ρ2, and ρ3 the rent per acre on Type 1, Type 2, and Type 3 lands. Prices of production satisfy the following system of equations:

((9/20) p + 2)(1 + r) + 1 w = p
(a1,2 p + (6/125))(1 + r) + (49/100) ρ1 + a0,2 w = 1
((9/10000) p + (27/100))(1 + r) + (59/100) ρ2 + (91/250) w = 1
((67/1000) p + (3/20))(1 + r) + (9/20) ρ3 + (67/100) w = 1

The following equation specifies that at least one type of land obtains no rent:

ρ1 ρ2 ρ3 = 0

Consider a solution of the above system of four equations with non-negative prices, rents, wage, and the rate of profits. Either the wage or the rate of profits is taken as given from outside this system. Such a solution defines prices of production, given, say, the rate of profits.

One can solve for prices of production for each technique. The left pane in Figure 1 depicts wage curves for each technique, as functions of the rate of profits.

4.0 The Choice of Technique

The managers of firms choose among techniques on the basis of cost, where the prices must be such that no land pays a negative rent.

At a given rate of profits, order the wage curves on the left pane in Figure 1 from high wages to low wages. This is the order of fertility, also known as the order of efficiency. In this example, the Alpha technique is always cost-minimizing. Given the rate of profits, one works down among wage curves from high wages to low wages until one finds the wage curve for a technique at which requirements for use can be satisfied by cultivating only lands that obtain a non-neagtive rent. In the example, in which all three types of land must be cultivated, at least somewhat, the inner frontier is the wage curve for the cost-minimizing technique.

For the parameters illustrated in Figure 1, the order of fertility is Type 2, Type 1, and Type 3 lands for low and high rates of profits. The order of fertility is Type 1, Type 2, and Type 3 lands for intermediate rates of profits. This is a numerical example of the reswitching of the order of fertility.

The order of rentability, as illustrated by the right pane in Figure 1, is Type 1, Type 2, and Type 3 lands for all rates of profits. Type 3 lands pay no rent. The order of fertility matches the order of rentability at intermediate rates of profits, but not outside the range defined by the switch points.

5.0 Perturbation of Selected Parameters

Figure 2 shows a partition of part of the parameter space around the example illustrated in Figure 1. The rent curves do not intersect for any regions in this small two-dimensional slice of the parameter space. The order of rentability is such that Type 1 land pays more rent per acre than Type 2 land for any income distribution. Type 3 land pays no rent.

Figure 2: A Portion of the Parameter Space

The example illustrated is for parameters in the central region in Figure 2. Here, the order of fertility varies from the order of rentability at low and high rates of profits, but not for intermediate rates of profits. This intermediate region disappears at the partition between this central region and the region to the northeast. The two upper wage curves on the left in Figure 1 become tangent at a single rate of profits for points along this partition. Consequently, the order of fertility deviates from the order of rentability for any parameters in the region to the northeast.

Fluke cases partition the parameter space into regions among which the order of fertility varies. To the southwest in Figure 2, one switch point between the wage curves for Beta and Gamma has vanished over the wage axis, and the other is at a rate of profits exceeding the maximum rate of profits for Alpha. The order of fertility matches the order of rentability. The northwest and southeast also illustrate parameters for which the order of fertility varies with the rate of profits. The order of fertility varies from the order of rentability at one or the other extreme, as indicated.

6.0 Conclusion

The order of fertility can vary with the wage or the rate of profits. The order of rentability can also vary with the wage or the rate of profits. And they can vary from one another with distribution. The rate of fertility may vary with distribution, while the order of rentability stays constant, as in this post.

The reswitching of the order of fertility is not a fluke case. I do not think this example would surprise, for example, Heinz Kurz, Neri Salvadori, or Fabio Petri. Nevertheless, I think nobody has explicitly pointed out this possibility. Is this example "perverse" from the viewpoint of obsolete marginalist economics?

Saturday, January 14, 2023

John Barkley Rosser, Jr. (1948-2023)

Barkley Rosser's professional contributions include the study of complex dynamics in economic models, development and transition economics, observations on the sociology of economists, and editorship. I knew him through Internet discussions and his editing of one of my articles. Peter Dorman has an obituary.

Rosser's major book on complexity economics went through two editions. I am not sure I ever made it totally through his book. I think of him as building on, in the Post-Keynesian tradition, some work by Nicholas Kaldor and Richard Goodwin, for example. Plenty of work on mainstream models can also display complex dynamics. I find particularly intriguing Rosser's work connecting the reswitching of techniques to a cusp catastrophe. The one aspect of his comparison and contrast of complex dynamics with dialectics I recall is that it is a principle of dialects is that a sufficient quantitative change can be qualitative. This make sense to me in terms of bifurcations of dynamical systems and the exploration of perturbations in parameter spaces.

Rosser also looked at the sociology of economics. With David Colander and Richard Holt, he distinguished between the dichotomy between mainstream and non-mainstream economics and the dichotomy between orthodox and (traditional) heterodox economics. Traditional heterodox economics is a grouping of schools of thought such as Austrian, (old) institutional, Post-Keynesian and Marxist economics. This way of thinking ends up with the possibility of mainstream heterodox economics, which might include behavioral economics, complexity economics, agent-based economics, and complexity economics. These three also argued that cutting edge mainstream economics is more pluralist and open than traditional economists say. I hadn't thought this before, but maybe Rosser was open to this because he personnally straddled Post-Keynesian and mainstream economics.

Rosser was a professor at James Madison University. He was a long-time and successful editor of the Journal of Economic Behavior and Organization (JEBO). He stepped down as editor-in-chief in 2010 and later founded a new journal, the Review Of Behavioral Economics (ROBE).

I want to mention a couple of times his personal life intersected with history. His father, John Barkley Rosser, Sr. was a great logician, one of the first to appreciate and extend Kurt Gödel's incompleteness theorem. He showed that Gödel could dispense with omega inconsistency and stick with just inconsistency in the statement in the theorem. Apparently his father was an able academic administrator. In 1970, he was director of the Army Mathematical Research Center (AMRC), in Sterling Hall at the University of Wisconsin. I believe that Rosser, the son, was opposed to the Vietnam world. On 24 August 1970, some radicals blew up Sterling Hall, killing one. This resulted in some tension between father and son at the time, as he has blogged about. Yeah, if some of your son's crowd blow up your office, you might have an issue.

Rosser married Marina Rostislavovna Vcherashnaya. His marriage involved overcoming the refusal of the Soviet Union to live up to the Helsinki accords. I believe that this was an important case.

  • David Colander, Richard P. F. Holt, and J. Barkley Rosser. 2004a. The changing face of mainstream economics. Review of Political Economy. 16(4):
  • David Colander, Richard P. F. Holt, and J. Barkley Rosser. 2004b. The Changing Face of Economics: Conversations with Cutting Edge Economists. University of Michigan Press.
  • John Guckenheimer and Philip Holmes. 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Spring-Verlag.
  • Yura A. Kuznetsov. 1998. Elements of Applied Bifurcation Theory, second edition. Springer.
  • J. Barkley Rosser. 1983. Reswitching as a cusp catastrophe. Journal of Economic Theory. 31(1): 182-193.
  • J. Barkley Rosser. 2000. Aspects of dialectics and non-linear dynamics. Cambridge Journal of Economics. 24(3): 311-324.
  • J. Barkley Rosser. 2013. From Catastrophe to Chaos: A General Theory of Economic Discontinuities 2nd editions. Springer.
  • Peter Schmitt and Doug Erickson. 2020. The blast that changed everything. On Wisconsin