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, March 17, 2023

The Reswitching Of The Orders Of Fertility And Rentability Revisited

Figure 1: A Part of a Parameter Space

This post revisits my numerical examples in which I demonstrate the possibility of the reswitching of the order of fertility and of the reswitching of the order of rentability. Each of those posts presents a numeric example. In each, different ranges of the coefficients of production a0,2 and a1,2 are considered. This post combines those ranges, while still not considering the full parameter space, even for the slice for these coefficients.

In the example, reproduction of a capitalist economy requires the production of two commodities, iron and corn. Managers of firms know one process for producing iron and three processes for corn. Each corn-producing processes operates on a different quality of land. The given endowments of land and the requirements for use are such that all three types of land must be farmed. In each of three techniques of production, Alpha, Beta, and Gamma, the decisions of managers of firms result in two types of land being completely farmed. The third type of land is only partially farmed. Being in excess supply, it pays no rent (the rule of free goods). Which type of land pays no rent varies among the three techniques.

I consider the analysis of the choice of technique in this example. Following Sraffa, I assume wages and rents are paid out of the surplus product after the harvest. In this analysis of prices, extra profits cannot be obtained at prices of production by operating any available process. The difference between the revenues and wages and charges on capital goods for processes that produce agricultural goods are compensated for the rents obtained by landlords.

Figure 1, at the top of the post, illustrates, a part of a slice of the parameter space. Reswitching of the order of rentability occurs in region 3. Reswitching of the order of fertility occurs in region 7. Table 2 summarizes the result of the analysis of the choice of technique in each section. For this range of paramters, the Alpha technique, in which type 3 land pays no rent, is always cost-minimizing. The maximum rate of profits is the maximum rate of profits for the Alpha technique. The range of the rate of profits is partitioned into intervals where either the order of fertility or the order of rentability do not vary. And these orders are also listed.

Table 2: Techniques of Production
RegionRange of Rate of ProfitsOrder of FertilityOrder of Rentability
10 ≤ rr1Type 2, 1, 3Type 1, 2, 3
r1rrα,maxType 2, 1, 3
20 ≤ rrα,maxType 2, 1, 3Type 2, 1, 3
30 ≤ rr1Type 2, 1, 3Type 2, 1, 3
r1rr2Type 1, 2, 3
r2rrα,maxType 2, 1, 3
40 ≤ rrα,maxType 2, 1, 3Type 1, 2, 3
50 ≤ rr1Type 2, 1, 3Type 2, 1, 3
r1rrα,maxType 1, 2, 3
60 ≤ rr1Type 1, 2, 3Type 1, 2, 3
r1rrα,maxType 2, 1, 3
70 ≤ rr1Type 2, 1, 3Type 1, 2, 3
r1rr2Type 1, 2, 3
r2rrα,maxType 2, 1, 3
80 ≤ rrα,maxType 1, 2, 3Type 1, 2, 3
90 ≤ rr1Type 2, 1, 3Type 1, 2, 3
r1rrα,maxType 1, 2, 3

Technical progress can be seen as a reduction in coefficients of production. For this example and the chosen coefficients of production, technical progress is a movement from the northeast to the southwest in the figure at the top of the post. Initially, the order of rentability is the same as the order of fertility, and neither order varies with the rate of profits (region 2). At some point, the order of rentability has reversed, for lands that pay a rent (region 4). Even later, the order of fertility has reversed, so the orders of fertility and rentability once again match, whatever the rate of profits (region 8). The reswitching of these orders appear at intermediate regions of time between each reversal.

This example is another example showing why biotechnological determinism is unfounded. One can see that one type of land is simultaneously more and less fertile than another type, depending on the rate of profits or the wage. And this ranking can be reversed and then switched back with, say, an increase in the rate of profits. Furthermore, owning the more fertile type of land need not allow its owner to obtain a larger rent per acre than a less fertile type of land that pays a rent. And whether or not these orders match also varies, possibly non-monotonically, with the distribution between wages and profits.

It is meaningless to claim that economic agents earn the worth of the contributions (of the goods that they own) to production.

Saturday, March 11, 2023

Georgists Should Study Post-Sraffian Economics

1.0 Introduction

Here are some attempts to step back, but not very far, from some of the details in my numeric examples.

2.0 Henry George and Piero Sraffa

Henry George's book Progress and Poverty misrepresents classical political economy. I cannot justify this claim, since I read George's book more than a decade ago. But George and his followers are absolutely correct on a couple of points.

Marginalism developed by extending the theory of intensive rent, as in David Ricardo's Principles for example, to capital. This mistake results in the conflation of capital and land. And the acceptance of this mistaken approach was politically motivated to cover over the conflict between classes evident in classical political economy. It was an attempt to ignore the social question.

Henry George was also correct in thinking economists give good reason to tax rent on unimproved land. I think Quesnay and Ricardo each provide evidence that George was correctly understanding this aspect of classical political economy.

Piero Sraffa generalized interesting properites of land to the distinction between basic and non-basic goods. As I recall, he suggests a definition of non-basic goods, in the case of joint production, as those goods whose price of production is changed by a tax but in which that change has no wider impact on the prices of all goods.

I think a study comparing some aspects of the economics of George and and Sraffa might be a good research prospect for others.

3.0 Marginalism as an Illegimate Generalization of Ricardo's Theory of Intensive Rent

Part of the point of my numeric examples is demonstrating that marginalisms attempt to treat capital and land by the same theory fails. Capital (goods?) cannot coherently be considered as a given quantity to be allocated among alternative uses. Jevons, Menger, Walras and their fellow marginalists were mistaken.

The marginalists also had a utility theory of consumer demand. Amazingly, the human psyche and production follow the same laws.

I have thought, not very hard, about how appending demand functions for consumer goods might impact my exposition of numeric examples of rent theory. An additional fluke case would arise. This edge case would be between a case where a certain type of land is partially farmed and pays no rent and a case where this type of land is fully farmed and pays a rent. In the edge case, this type of land needs to be fully farmed to meet requirements for use. Rent on this type of land can range from zero to the rent it would pay if net output were increased by an infinitetesimal amount. In the edge case, prices of production are indeterminate. I guess payments to factors of production are still not rewards to physical contributions to production.

4.0 Fixed Capital and Extensive Rent

Models of single production (circulating capital) have some nice propeties that do not hold in general joint production. Given the rate of profits, prices of production are uniquely defined. Given a higher rate of profits, the wage is lower.

These properties hold in models of pure fixed capital and in models of extensive rent. I suspect they do hold in a model that combines fixed capital and extensive rent.

One might consider a model in which an industrial good, a tractor, is produced in a process that does not use land. It can be run for several years in processes that produce agricultural goods on different types of land. The analysis of the choice of technique would consider the economic life of the tractor, as well as which lands are fully or partially farmed. It seems to me this model would have at least some of the properties of the theory of intensive rent.

Monday, March 06, 2023

An Example Of Non-Uniqueness In A Model Of Extensive And Intensive Rent

Figure 1: Wage and Rent Curves for a Numeric Example
1.0 Introduction

This post continues, with some repitition, my exposition of a model of extensive and intensive rent.

In the example, the cost-minimizing technique is non-unique at a low enough wage or rate of profits. One cost-minimizing technique, Epsilon, illustrates a case of extensive rent. The other cost-minimizing technique, Iota, illustrates a case with both extensive and intensive rent. In this technique, a kind of absolute rent arises on a land that is only partially farmed, and, thus, in excess demand. The rule of free goods does not seem to apply. (I am not sure how well thought out this idea is.) I also note the existence of what I am calling a 'semi-fake' switch point.

The conflicts among workers, landlords, and capitalists are complicated in this example. At a given rate of profits, workers get a lower wage if landlords can get more rent. At a given wage, the rate of profits is lower if landlords can get more rent

Economists demonstrated over a half-century ago that a theory of supply and demand functions is a kind of nonsense.

2.0 Technology

Table 1 presents coefficients of production for the example. Here, two types of land exist. Only one agricultural commodity, corn, can be produced on the processes in which land is used. For the second type of land, two processes can be operated on land. Only one process is known for producing the industrial commodity.

Table 1: The Coefficients of Production
Labora0,1 = 1a0,2 = 9/10a0,3 = 91/250a0,4 = 1/2
Type I Land0c1,2 = 100
Type II Land00c2,3 = 13/10c2,4 = 1
Irona1,1 = 2/5a1,2 = 1/50a1,3 = 9/10,000a1,4 = 67/1000
Corna2,1 = 2a2,2 = 6/125a2,3 = 27/100a2,4 = 3/20

I assume 300 acres of Type 1 land and 200 acres of Type 2 land are available. Requirements for use, that is, required net output, consists of 90 tons iron and 60 tons steel. This commodity basket is also the numeraire.

Table 2 lists the available techniques of production. Not all are feasible. Feasibility depends on requirements for use (that is, required net output) and how much of each type of land is available. Rent is zero for the Alpha, Beta, and Gamma techniques, since neither type of land is fully used. That is, land is not scarce. Techniques Delta, Epsilon, Zeta, and Eta are examples of extensive rent since only one process is operated on each type of land. The Theta technique resembles an example of intensive rent. Finally, if the Iota technique is adopted, one will observe both extensive and intensive rent.

Table 2: Techniques of Production
TechniqueProcessesType 1 LandType 2 Land
AlphaI, IIPartially farmedFallow
BetaI, IIIFallowPartially farmed
GammaI, IVFallowPartially farmed
DeltaI, II, IIIFully farmedPartially farmed
EpsilonI, II, IIIPartially farmedFully farmed
ZetaI, II, IVFully farmedPartially farmed
EtaI, II, IVPartially farmedFully farmed
ThetaI, III, IVFallowFully farmed
IotaI, II, III, IVPartially farmedFully farmed

Under these assumptions, the Delta, Epsilon, Zeta, Eta, and Iota techniques are feasible. The processes in the Alpha, Beta, Gamma, and Theta techniques cannot be operated at any level in which requirements for use are satisfied. Both types of land must be farmed to meet requirements for use.

3.0 The Choice of Technique

A system of price equations is associated with each technique. Wage curves for the Alpha, Beta, Gamma, and Theta techniques are shown in the left pane of Figure 1 at the top of this post. I only consider, in the analysis of the choice of technique, ranges of the rate of profits in which neither rent nor the wage is negative. This criterion rules out the Delta technique, always. Which type of land is fully farmed varies with which process is chosen for operation on type 2 land.

Under Epsilon, process III is operated; Type 2 land is fully farmed; and Type 1 land pays no rent. The Epsilon technique is, in some sense, a combination of the Alpha and Beta techniques. The wage curve for Beta is further out than the wage curve for Alpha wage curve for the full range of profits. The wage curve for Epsilon is the Alpha wage curve, that is the further inward of the Alpha and Beta wage curves. The left pane in Figure 2 shows that Epsilon is cost-minimizing for the full range of the rate of profits in which the wage curve for Alpha is in the first quadrant; extra profits cannot be obtained by operating process IV, the only process not in the Epsilon technique, at Epsilon prices. Thus, the intersections of the Alpha and Gamma wage curves and of the Epsilon and Zeta rent curves are not switch points.

Figure 2: The Epsilon Technique Is Cost-Minimizing; The Zeta and Eta Techniques Are Never Cost-Minimizing

The Zeta and Eta techniques are a combination of the Alpha and Gamma techniques. The intersections of the Alpha and Gamma wage curves and the Eta and Zeta rent curves, at a rent of zero, relate to the range of the rate of profits at which they can enter into the analysis of the choice of technique. These intersections occur at the same rate of profits. The wage curves for Zeta and Eta are the innermost frontier of the Alpha and Gamma wage curves. For a rate of profits less than at the semi-fake switch point, Alpha is the frontier. Type 1 land pays no rent, and the Zeta technique cannot be operated with a non-negative rent. For a higher rate of profits, Gamma is the frontier, and Type 2 land pays no rent. Since only two types of land exist in this example, the order of fertility cannot deviate from the order of fertility. The right pane in Figure 2 shows that neither the Zeta nor the Eta technique is ever cost-minimizing.

The Iota technique is, in some sense. a combination of the Alpha and Theta techniques. The price equations for Theta determine, at a given rate of profits, the wage, the prices of corn and iron, and the rent on Type 2 land. Type 2 land is fully farmed under Theta. A linear combination of the price equations for processes III and IV eliminates rent from these equations. One ends up with a system of two price equations, for iron and corn, with one degree of freedom, given the numeraire. But the Theta technique cannot satisfy requirements for use. The price equation for process II, which operates on Type 1 land, can only be satisfied if rent on Type 1 land is positive. It does not matter for this solution whether or not Type 1 land is fully farmed. The wage frontier for Iota is the innermost of the Alpha and Theta wage curves, that is, the Theta wage curve. Since all processes in the example enter into the Iota technique, no extra profits can be obtained by operating any process at Iota prices. Iota is always cost minimizing, up to the maximum rate of profits for the Theta technique. What do you think of this absolute rent on Type 1 land?

So the above presents my rationale for saying this is an example, at low rates of profits, of non-unique cost-minimizing techniques. Prices, including the wage and rents per acre, are also non-unique. And I am able to apply a theory of prices, in an open model, without ever deriving supply and demand functions.

4.0 An Aside on Multiple Agricultural Commodities

I do not know if, for example, the possibility of absolute rent, with some land of a specified quality left uncultivated has been noticed before.

I also think the following claim, from the chapter on rent in Piero Sraffa's PofCbyMofC, has not been justified or falsified in non-fluke cases:

"89. More complex cases can generally be reduced to combinations of the two that have been considered. The main type of complication arises from the multiplicity of agricultural products.

Thus, suppose that in the first case land of one quality was so exceptionally well-suited for one particular crop, that such a crop was grown on the whole of that land and on no other land; under these circumstances there would be room for two different methods of producing the crop in question on that land, and its rent would be determined independently of that of the other lands becoming in effect an instance of the second case.

Or consider the more general case in which each of several qualities of land can be used for several alternative crops; although none of the crops is grown on land of all qualities; while on the other hand none of the lands is sufficiently specialised to have its rent determined independently of the others. What is required in any case is that the number of separate processes should be equal to the number of qualities of land plus the number of products concerned; and, moreover, that the links or overlaps between the various products and the various lands on which they are grown should be sufficient for the determination of the rents and the prices. The type of link required may be sufficiently indicated by the consideration that the above condition were such as to make possible the construction of a Standard commodity from which were excluded all the lands as well as any non-basics among the products.

In the case of a single quality of land, the multiplicity of agricultural products would not give rise to any complications. It may however be noted that only for one of the crops would two separate methods of production be compatible; for the rest, the number of processes would have to be equal to the number of products." Sraffa (1960)

Sraffa certainly does not justify that claim in his book. I suppose I could work through the example problems at the end of Chapter 10 of Kurz and Salvador (1995) and look up the authors from which these examples are drawn. These authors include Antonio D'Agata, Guido Erreygers, Giuseppe, Alberto Quadrio-Curzio, and Philippe Saucier. Unfortunately, a lot of this work seems to be languages I cannot read.

Saturday, March 04, 2023

Direct And Indirect Methods, Axioms And Algorithms For The Choice Of The Technique

1.0 Introduction

Kurz and Salvadori (1995) explain prices of production with two methods of analysis: the direct method and the indirect method. The indirect method, for the circular capital case, involves the creation of the wage frontier, the most well-known diagram to come out of Sraffa (1960). The direct method characterizes a system of prices of production by axioms, while the indirect method suggests algorithms for finding cost-minimizing techniques.

2.0 The Direct Method

In both methods, the given technology is characterized as a set of processes. A process is specified as the quantities of inputs and the quantities of outputs for a given level of operation. In the case of reproducible natural resources, that is, land, the quantity available of each quality of land should be specified. I do not think that non-reproducible natural resources fit comfortably in this model; some work has been done on the corn-guano model exploring this.

I find it useful to assume constant returns to scale. I understand why Sraffa does not need this assumption in the first two sections of his book. He does not consider the choice of technique there or how a state can be reached in which the same rate of profits is obtained for each operated process. He considers which process is operated and the level of operation of each process as given. Sraffa explicitly says that his assumption, that no question of the returns to scale arises, does not apply to the last section, analyzing the choice of technique. I find it difficult to understand how the theory of joint production can be set out without considering the choice of technique.

Informally, the following six axioms characterize quantities and prices for a capitalist economy undergoing smooth reproduction:

  1. The levels of operation of the processes comprising the technology are such that, after replacing commodities used up in production and those needed for accumulation at the given rate of growth, requirements for use can be satisfied by net output.
  2. The levels of operation of the processes comprising the technology are such that one unit of labor is employed throughout the economy.
  3. No pure economic profits can be made by operating any process. That is, for each process, the revenues obtained from operating it do not exceed its costs, including charges for the rate of profits, rent, and wages.
  4. The price of the numeraire is unity.
  5. The rule of free goods: The price of a good in excess supply (that is, with a level of production strictly exceeding its requirements for use) is zero.
  6. The rule of non-operated processes: If the costs of operating a process, including charges for the rate of profits, strictly exceeds the revenues obtained from that process, it is not operated.

Kurz and Salvadori set out these axioms for specific models, along with non-negativity conditions. In models of rent, one discards the second axiom; scale matters. The most general model, I guess, is that of full joint production. What can be deduced from the axioms varies among these models.

3.0 The Indirect Method

One can set out the indirect method by applying combinatorics, in which one looks at all possible techniques that can be constructed from the processes comprising the technology. Discard those techniques that cannot satisfy requirements for use. In the circulating capital case, each technique yields a system of equations with one degree of freedom. These equations can be solved. So each technique has a wage curve, in which the wage is lower, the higher the rate of profits. All these curves can be graphed on the same graph, and the outer wage frontier shows which technique is cost-minimizing at any given wage or rate of profits.

How can a combinatorial explosion be avoided in this analysis? By applying certain algorithms which do not require one to consider every technique. Christian Bidard champions the Lemke algorithm for the case of fixed capital. As in the case of the simplex method for linear programs, one does not need to consider every feasible technique in finding the cost-minimizing technique for a given wage or rate of profits.

4.0 Questions

Different, but related questions, arise for the two methods. For the direct method, one asks, what conditions must technology satisfy such that a solution of quantities and prices exist? When is this solution unique? For the case of circulating capital, one looks at the Hawkins-Simon condition, the Perron-Frobenius theorem, and the misleadingly-named non-substitution theorem. In the case of general joint production, the special case in which the rate of profits is equal to the rate of growth is of interest. I suppose research questions might still revolve about how many of the nice properties of circulating capital carry over to models that are intermediate between this case and full joint production. For example, has any work been done on combining a fixed capital model with a model of extensive rent? Biao Huang recently found that revisiting the fixed capital model was worthy of research. Relaxing the assumption of free disposal is important for investigating environmental concerns.

For the indirect method, I ask on what platforms are these algorithms executing? When I apply numerical methods for finding fluke switch points, I am definitely not making any claims about how markets work. I think my application of linear programming and duality theory in my 2005 Manchester School article is another case of an external analyst examining an economic model. But sometimes, as in my 2017 ROPE article, an algorithm is described that can be executed by an abstract market. At least this seems to be Bidard's view. And these algorithms might even be able to be executed in parallel by, say, accountants working for different firms in different industries. What I would like to see, however, is how market structures, how bids and asks are resolved, for example, enters into these algorithms. Be that as it may, one can ask which algorithms converge. How fast? Is the point to which they converge unique and independent of the initial condition?

  • Christian Bidard. 2004. Prices, Reproduction, Scarcity. Cambridge University Press.
  • Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis. Cambridge University Press.
  • Keiran Sharpe. 1999. Note and comment: on Sraffa's price system. Cambridge Journal of Economics 23(1): 93-101.
  • Piero Sraffa. 1960. The Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory. Cambridge University Press.
  • K. Vela Velupillai. 2021. Definitions, assumptions, propositions and proofs in Sraffa's PCMC. In A Reflection on Sraffa's Revolution in Economic Theory (ed. by Ajit Sinha). Palgrave
  • Ludwig Wittgenstein. Remarks on the Foundations of Mathematics, revised edition.
  • J. E. Woods. 1990. The Production of Commodities: An Introduction to Sraffa. Macmillan.

Thursday, March 02, 2023

Antonio Labriola On The Philosophy Of Praxis

I think of Gramsci or Lukacs as the authors to read for understanding why Marxism might be called a "philosophy of praxis". Apparently, that phrase was first used by Antonio Labriola. His collection of letters to Georges Sorel was published as Socialism and Philosophy. In the following letter, "praxis" is translated as "practice" in the last two paragraphs.

Rome, May 14, 1897

To return to my first argument, it seems to me that the following question is uppermost in your mind: By what means, and in what manner, would it be possible to inaugurate a school of historical materialism in France? I don't know whether I am at liberty to answer this question, without running the risk of being numbered among those journalists of the old school who, with imperturbable assurance, gave good advice to Europe at the imminent peril of being almost never heeded. As a matter of fact, they never were. I shall try to be modest. In the first place, it ought not to be so very difficult to find editors and publishers in France who should be willing to publish and spread accurate translations of the works of Marx, Engels, and others that may be desired. That would be the best way to make a start. I am aware of the fact that in the art of translating one comes across some queer difficulties. I have been reading German for more than thirty-seven years, and I have always noted that we people of the Latin tongue get into strange linguistic and literary byways, whenever we attempt to translate from the German. That which seems alive, clear, direct, in German, becomes often enough, when translated into Italian, cold, pointless, and even outright jargon. In such translations as are commonly current the convincing effect is lost with that of the meaning. In such a vast work of popularization as that which I have in mind, it would be desirable, aside from the faithful interpretation of the original text, to supply in the prefaces, foot-notes, and comments of the translated writings the materials for that easy assimilation which is already in process or prepared in the writings grown on native soil.

Languages are not accidental variations of universal speech. They are even more than simple external means of communication expressing thought and mind. They are the conditions and limits of our internal activity, which for this reason, among many others, is not indebted to accident for the various national modes and forms. If there are any internationalists who ignore this, they should rather be called confusionists and ignorers of form. Of such are those who get their information, not from the ancient apocalyptics, but from that specious Bakunin who proclaimed even the equalization of the sexes. The assimilation of ideas, of lines of thought, of definite tendencies, of plans, which have found mature expression in the literature of a foreign language, is a rather difficult case of social pedagogy.

Since this last expression has slipped from my pen, permit me also to confess that it is not the continuous growth of success at elections which fills me more than anything else with admiration and vivid hope, when I closely examine the previous history and present condition of the German Social-Democracy. Instead of speculating over the vote as a measure of the future, according to the often erroneous calculations of inference and statistical combination, I feel a special admiration for this truly new and imposing case of social education. This is the great point that in such a vast number of men, especially of laborers and little bourgeois, a new consciousness is in process of formation, to which the direct influence of economic conditions, which cause them to struggle, and the propaganda of socialism as a means and aim of development, equally contribute. This digression calls to my mind a recollection. I was either the first, or certainly one of the first, in Italy to call the attention of those of our laborers, who were and are able to move along the line of the modern proletarian class struggle, to the example of Germany. But it never entered my mind to assume that the imitation of Germany should relieve us in any way from spontaneous action. It never occurred to me to follow the example of those monks and priests, who were for centuries almost the exclusive educators of an already disintegrating Italy, and who blithely taught the art of poetry by ordering their pupils to learn Horace's Art of Poetry by heart. It would be queer, if you, Bebel, with your merits, activity, and wisdom, were introduced among us in the garb of another Horace! It would surprise even my friend Lombroso, who hates Latin worse than the starvation fever.

In short, there are still other difficulties, of a greater scope and weight. Even if able and experienced writers and editors, not only in France, but also in the other civilized countries, undertook to spread translations of all the works on historical materialism, it would only stimulate, but not form and keep alive in the various nations those creative energies which produce and nourish vigorously a certain intellectual movement. To think is to produce. To learn means to produce by reproduction. We do not really and truly know a thing, until we are capable of producing it ourselves by thought, work, proof, and renewed proof. We do this only by virtue of our own powers, in our social group and from the point of view which we occupy in it.

And now think of France, with its great history, with its literature, which was so dominant for centuries, with its patriotic ambitions, and with its very peculiar ethnological and psychological differentiation, which shows itself even in the most abstract products of the mind! It would not become me, an Italian, very well to pose as the defender of your chauvinists, upon whom you heap so much well-deserved opprobrium. But let us remember what happened in the eighteenth century. The revolutionary thought came from more than one part of the civilised world, from Italy, England, Germany, but it was not European unless it assumed the guise of French spirit. And the European revolution was at bottom the French revolution. This imperishable glory of your nation weighs, like all glories, upon the people. It burdens you with a deep-rooted prejudice. But are not prejudices likewise forces, at least impediments of progress, if nothing else? Paris will no longer be the brain of the world, if for no other reason but that the world has no brain, except in the imagination of some shallow sociologists. Neither is Paris to-day, nor will it ever be in the future, that sacred Jerusalem of revolutionists from all parts of the world which it seemed to be once upon a time. At all events the future proletarian revolution will have nothing in common with an apocalyptic millennium. And in our day, special privileges are doomed for nations as well as for single individuals. So Engels observed, justly. By the way, it would be worth the while of you French to read what he wrote in 1871 concerning the Blanquists who were trying to foment a violent revolution, so shortly after the catastrophe of the Commune. But when all is said, when the peculiar conditions of French agriculture and industry are taken into account, which retarded so long the concentration of the labor movement, and when the proper blame is recorded against the various petty leaders and heads, who kept French Socialism so long split and divided, then the fact always remains that historical materialism will not make any headway among you, so long as it gives the impression of being simply a mental elaboration of two Germans of great genius. By this expression Mazzini intensified the national resentment against these two authors, who, being communists and materialists, seemed made to order for the purpose of routing the idealistic formula of Patriotism and God.

In this respect, the fate of the two founders of scientific socialism was almost tragical. They were often regarded as the two Germans by so many who were jingoes even though revolutionaries. And Bakunin, whose mind inclined so strongly toward invention, to put it mildly, accused them of being champions of Pan-Germanism, although these two Germans, who left their country as exiles from the days of their young manhood, were received with studied silence by those professors for whom servility is an act of patriotism. As a matter of fact these professors avenged themselves. For Capital, whose entire presentation is rooted in the traditions of classic economy, not excluding the ingenious and often talented writers of Italy in the 18th century, speaks only with sovereign contempt of such men as Roscher and others like him. Engels, who devoted himself with so much ability to the amplification and popularisation of the results of researches made by the American Morgan, had the settled conviction that the thing which he justly called classic philosophy had reached its dissolution with Feuerbach. And when he wrote his Anti-Dühring, he showed a frank unconcern for the philosophers of that time, the neocriticism of his countrymen, an unconcern which is explicable, even if not excusable, in his case, but which is ridiculous in other socialists who affect to imitate him. Their tragic fate was, so to say, inherent in their mission. They had given themselves heart and soul to the cause of the proletariat of all nations. And for this reason their scientific work finds in every nation only that reading public which is capable of a similar intellectual revolution. In Germany, where Social Democracy stands firmly in serried ranks, owing to historical conditions, among them above all the fact that the capitalist class has never been able to break its ties with the old regime (look at that emperor who speaks with impunity in the language of a vice-god and who is nothing but a Frederick Barbarossa acting as a commercial traveler for goods made in Germany), it was quite natural that the ideas of scientific socialism should find a favorable soil for their normal and progressive diffusion. But none of the German socialists - at least I hope not - will ever think of looking upon the ideas of Marx and Engels from the simple point of view of the rights and duties, merits and demerits, of comrades of the party. Here is what Engels wrote not so very long ago: "It will be noticed that I do not call myself a social-democrat in these articles, but a communist. I do this for the reason that the name of social-democrats was given in those days to many who had not written upon their banners the demand for the socialization of all the means of production. By a social-democrat people understood in France a republican democrat, who had genuine, but indefinite, sympathies for the working class men like Ledru-Rollin in 1848, and like the socialist radicals in 1874, who were tainted with Proudhonism. In Germany, the Lasalleans called themselves social democrats. Although the great majority of these gradually recognised the necessity of the socialization of the means of production, nevertheless one of the essential points of their public program remained productive associations with state help. It was, therefore, quite impossible for Marx and myself to choose such an elastic term for the designation of our specific point of view. To-day it is different and this term may pass muster. Nevertheless it will always be ill-fitting for a party whose program is not generically socialistic, but directly communistic, and whose ultimate political aim is to do away with all forms of state, and therefore also with democracy."

It seems to me that the patriots - I do not use this term derisively – have good ground for consolation and comfort. For there is no foundation for the conclusion that historical materialism is the intellectual patrimony of one sole nation, or that it was to become the privilege of any clique, circle, or sect. Its objective origins belong equally to France, England, and Germany. I shall not repeat at this place what I said in another letter concerning the form of the thought which developed in the minds of our two authors under the conditions created by the intellectual culture of Germany in their youth, especially by philosophy, while Hegelianism either lost itself in the walks of a new scholasticism, or gave way to a new and more ponderous criticism. But at the same time there existed the great industries of England with all their accompanying miseries, with the ideological counterbalance of Owen and the practical counteraction of the Chartist agitation. There were furthermore the schools of French socialism, and the revolutionary traditions of the West, out of which were just developing the forms of a truly proletarian communism. What else is Capital but the critique of that political economy which, as a practical revolution and its theoretical expression, had reached full maturity only in England, about the sixties, and which had barely begun in Germany? What else is the Communist Manifesto but the conclusion and explanation of that socialism which was either latent or manifest in the labor movements of France and England? All these things were continued and brought to the point of critique, not excluding the philosophy of Hegel, by the immanent critical character of dialectic advance and its transformations. That is the process of that negation which does not consist in the contentious and oppositional discussion of one concept with another, of one opinion with another, but which rather verifies the things which it denies because that which is made negative by it either contains the material conditions or the intellectual premise for the continuation of the process. [

France and England may resume their parts in the elaboration of historical materialism without seeming to commit an act of mere imitation. Should the French never write truly critical books on Fourier and Saint Simon, showing that they were, and to what extent they were, the precursors of contemporaneous socialism. Isn't there enough occasion to devote literary work to the events of 1830 to 1848, so that one may see that the theory of the Communist Manifesto was not their negation, but rather was their outcome and solution. Isn't there a demand for an exhaustive work on the coup d'état of Louis Napoleon, as a counterpart for the Eighteenth Brumaire of Marx which, though a work of great genius and insuperable in its aim, is nevertheless largely a work of the hour and colored by publicist methods? Does not the Commune still await its final critical treatment? Has the great revolution of the 18th century, whose literature is colossal so far as its general history goes, but very small when it comes to details, ever been thoroughly treated with an insight into the class movements of which it consisted, and as a typical illustration of industrial history? To be brief, does not the whole modern history of France and England offer to the students of those countries a far greater scope for the illustration historical materialism than that afforded until recently by the conditions of Germany? The conditions of Germany were, since the Thirty Years' War, greatly complicated through obstacles to progress and remained almost always enveloped in the mists of various speculations in the heads of those who lived under them and observed them. The Florentine chroniclers of the 14th century would be moved to merriment by those misty ideas.

I have dwelt upon these particulars, not in order to assume the airs of a counsellor of France, but in order to wind up with the statement that, with the present bent of Latin minds, it is not an easy thing to get them imbued with new ideas, if one undertakes to approach them merely with abstract forms of thought. But they will assimilate new ideas quickly and effectively, when offered in the shape of stories or essays which have some of the elements of art about them.

I return for a moment to the question of translating. Engels' Anti-Dühring is that work which ought to get an international circulation before any other. I know of few books which are equal to it in compactness of thought, multiplicity of view-points, and effectiveness in bringing home its points. It may become mental medicine for young thinkers, who generally turn with vague and uncertain touch to books which are said to deal with socialism of some kind. This was what happened when this book appeared, as Bernstein wrote about three years ago in the Neue Zeit, in an article commemorating the event. This work of Engels remains the unexcelled book in the literature of socialism.

Now, this book was not written for a thesis, but rather for an anti-thesis. With the exception of some detachable portions which were made into a book by themselves and in this shape made a tour of the world (Socialism, Utopian and Scientific), this book has for its guiding thread the criticism of Eugene Dühring, who had invented a philosophy and a socialism of his own. But what person not living in the circles of professed scientists, and how many readers of other than German nationality, should take an interest in Mr. Dühring? Well, unfortunately every nation has too many Dührings. Who knows what book against some other know-it-all an Engels of some other nationality might have written, or might still write? The effect of this work on the socialists of other countries should be, in my opinion, to supply them with those critical aptitudes which are required for writing all other Anti-Somethings needed for the rebuttal of those who try to thwart or infest the socialist movement in the name of so many confused notions in sociology. The weapons and methods of critique will, of course, vary from country to country according to the requirements of local adaptation. The point is to cure the patient, not the disease. That is the method of modern medicine.

To try to act differently would be to invite the fate of those Hegelians who came to the fore in Italy from 1840 to 1880, especially in the South, for instance in Naples. Most of them were mere followers, but a few were strong thinkers. On the whole they represented a revolutionary current of great importance, owing to their traditional scholasticism, their French esprit, and their philosophy of the so-called common sense. This movement became somewhat known in France. For it was one of these Hegelians, Vera by name, and not the profoundest and strongest of them, who supplied France with the most readable translations of some of the fundamental works of Hegel and accompanied them with copious comments. Now every trace, and even the memory, of this movement has passed away among us after the lapse of but a few years. The writings of these thinkers are not found anywhere but in the shops of antiquarians and second rate book dealers. This dissolution into nothing of an entire scientific school of no mean account is not due solely to the often unkind and little praiseworthy vicissitudes of university life, nor to tile epidemic spread of positivism which gathers here and there fruits of a rather demi-monde science, but to deeper causes. Those Hegelians wrote, and taught, and held disputations among themselves, as though they mere living in Berlin, or in Utopia, instead of Naples. They held mental converse with their German comrades. They replied from their pulpits, or in their writings, only to such criticisms as were made by themselves, so that they carried on a dialog which appeared as a monolog to their audience and readers. They did not succeed in molding their treatises and dialectics into books which looked like new intellectual conquests of the nation. This unpleasant and unattractive recollection came to my mind when I began writing the first of my two essays on historical materialism, and there is now no reason why I should not follow them up with others. But then I asked myself quite often: How shall I go about it to say things which will not appear hard, foreign, and strange to Italian readers? You tell me that I succeeded, and perhaps it is so. Would it not be a singular case of discourtesy, if I should be my own judge and discuss the praise which you bestow upon me?

About five years ago I wrote to Engels: "In reading the Holy Family I remembered the Hegelians of Naples, among whom I lived in my earliest youth, and it seems to me that I understood and appreciated that book more than others could who are not familiar with the peculiar inside facts of that queer satire. It seemed to me that I had personally seen that quaint circle in Charlottenburg at close range, whom you and Marx satirised so funnily. I saw before my mind's eye, more than any one else, a certain professor of esthetics, a very original and talented man, who explained the romances of Balzac by deduction, made a construction of the cupola of the Church of Saint Peter, and arranged the musical instruments in a genetic series; and who by degrees, from negation to negation, by way of the negation of the negation arrived ultimately at the metaphysics of the unknowable which he, although unfamiliar with Spencer, but in a way himself an unglorified Spencer, called the unnameable. I, also, lived in my young days, as it were, in such a training hall, and I am not sorry for it. For years my mind was divided between Hegel and Spinoza. With youthful ingenuity I defended the dialectics of the former against Zeller, the founder of neo-kantianism. The writings of Spinoza I knew by heart, and with loving understanding I gave expositions of his theory of affections and passions. But now all these things seem as far away in my recollection as Primeval history. Shall I, too have presently my negation of the negation? You encourage me to write on communism. But I have always misgivings when it comes to doing things which are beyond my strength and which have little effect in Italy."

Whereupon he replied... But I shall make a period here. It seems almost impolite to reproduce the private letters of a man, especially so soon after his death, unless the public interest urgently demands it. At all events, compared with writings which are purposely written for publication, quotations from private letters carry little conviction and little weight, even if they refer to current topics and are limited to questions of theory and science. With the growth of the interest in historical materialism, and in the absence of a literature which would illustrate it generally and specifically, it came about that Engels, during the last years of his life, was asked, and even tormented with endless questions, by many who enrolled themselves as voluntary and free students in the adventurous and outlawed university of socialism, of which Engels was a professor without a chair. This accounts for his published letters, and for many of them which have not been published. From those three letters, which were recently reproduced by Le Devenir Social from a Berlin review and a Leipzig paper, it appears that he was somewhat afraid lest Marxism might presently develop into a sort of cheap doctrinarism.

To many of those who profess to be scientists, not in the adventurous university of the coming people, but in that of present official society, it happens that they are caught on the wing by students and seekers of information and that, with one foot lifted, they answer every question as though they had the explanation for everything stamped upon their brains. The most conceited of the professors, not wishing to deprive science of its priestly saintliness and pretending that it consists wholly of materialised knowledge instead of being mainly a skill in directing the formation of knowledge, give offhand answers and thereby frequently succeed in satirising themselves, after the manner of that delightful Mephistopheles in the guise of a master of all four faculties. Few have the Socratic resignation to reply: I don't know, but I know that I don't know, and I know what might be known, and what I might know, if I had made those efforts, or accomplished those labors, which are necessary in order to know; and if you will give me an infinite number of years, and an infinite capacity for methodical work, I might extend my knowledge almost indefinitely.

This is the substance of the practical mental revolution of the theory of understanding implied by historical materialism.

Every act of thinking is an effort, that is to say, new labor. In order to perform it, we need above all the material of mature experience and the methodical instruments, made familiar and effective by long handling. There is no doubt that an accomplished task, or a finished thought, facilitates the production of new thought by new forces. This is so, first, because the products of yesterday remain incorporated in the writings and other representative arts of to-day, and in the second place, because energies accumulated by us internally penetrate and endow labor, thereby keeping up a rhythmic movement. And it is precisely this rhythmic process which constitutes the method of memory, of reasoning, of expression, of communication. and so forth. But nevertheless this is not saying that we ever become thinking machines. Every time that we set about producing a new thought, we need not only the external materials and impulses of actual experience, but also an adequate effort in order to pass from the most primitive stages of mental life to that superior, derived and complex stage called thought, in which we cannot maintain ourselves, unless we exert our will-power, which has a certain determined intensity and duration beyond which it cannot be exerted.

So here we have arrived once more at the philosophy of practice, which is the path of historical materialism. It is the immanent philosophy of things about which people philosophize. The realistic process leads first from life to thought, not from thought to life. It leads from work, from the labor of cognition, to understanding as an abstract theory, not from theory to cognition. It leads from wants, and therefore from various feelings of well-being or illness resulting from the satisfaction or neglect of these wants, to the creation of the poetical myth of supernatural forces, not vice-versa. In these statements lies the secret of a phrase used by Marx, which has been the cause of much racking for some brains. He said that he had turned the dialectics of Hegel right side up. This means in plain words that the rhythmic movement of the idea itself (the spontaneous generation of thought!) was set aside and the rhythmic movements of real things adopted, a movement which ultimately produces thought.

Historical materialism, then, or the philosophy of practice, takes account of man as a social and historical being. It gives the last, blow to all forms of idealism which regard actually existing things as mere reflexes, reproductions, imitations, illustrations, results, of so-called a priori thought, thought before the fact. It marks also the end of naturalistic materialism, using this term in the sense which it had up to a few years ago. The intellectual revolution, which has come to regard the processes of human history as absolutely objective ones, is simultaneously accompanied by that intellectual revolution which regards the philosophical mind itself as a product of history. This mind is no longer for any thinking man a fact which was never in the making, an event which had no causes, an eternal entity which does not change, and still less the creature of one sole act. It is rather a process of creation in perpetuity. (Emphasis added -- RLV)

I have been point out private letters in which some concepts important to the intellectual history of socialism were first formulated. Or, at any rate, in which certain turns of phrase first apear. For example, I have noted some letters from Engels describing historical materialism, false consciousness, and the law of value. As I understand it, though, Engels' book Anti-Dühring was of great importance in creating and spreading orthodox Marxism throughout the second international, in general, and the German social democratic party, in particular. I think here we can find here the claim that dialectical materialism applies even to the natural sciences. Engels re-issued three chapters as the pamphlet Socialism: Utopian and Scientific. It would not surprise me that Engels' book was more discussed than the first volume of Capital between Marx's death and the first world war.

Monday, February 27, 2023

Prices Of Production For A Model Of Extensive And Intensive Rent

This post continues the treatment of this model.

A number of conditions must be satisfied by quantity flows and prices to allow the economy to undergo smooth reproduction. The net output of each produced commodity meets the requirements for use:

(B - A) q = d

The amount of each quality of land that is farmed cannot exceed the available quantity:

C qt

A vector is greater than or equal to another if each element of the vector is greater or equal to the corresponding element of the other vector. The level of operation of each process is non-negative:

qi, i = 1, 2, ..., n + m - 1

The costs of each process cannot fall below the revenues for that process:

p A (1 + r) + ρ C + w a0p B

In other words, no process returns supernormal profits. The required net output is the numeraire:

p d = 1

The price of each produced commodity is non-negative:

pj ≥ 0; j = 1, 2, ..., n

The rent on each type of land is nonnegative:

ρj ≥ 0; j = 1, 2, ..., k

The specification of prices of production includes a duality condition, the rule of non-operated processes. The following display shows the application of this rule to this model:

[p B - p A (1 + r) - ρ C - w a0] q = 0

According to the fourth display above, the quantity in parenthesis above is non-positive. Thus, if costs exceed revenues in a process, that process is not operated.

Consider a non-trivial solution to the price and quantity systems, with a given rate of profits, that also satisfies the rule of non-operated processes. The first three equations specify the quantity system. The next four equations specify the price system. Such a solution consists of a cost-minimizing technique, the wage, and prices of production. The prices of production include the rents on each type of land. Kurz and Salvadori (1995) prove an existence theorem for a more general model of rent that encompasses this model.

The next step in my development of this model would be to find some interesting numerical examples. I do not expect to be fast about doing this.