Sunday, September 25, 2022

Sowell, Kolakowski, Baumol, Schumpeter: Böhm Bawerk Was Mistaken

Empirically, prices are fairly close to proportional to labor values. But that is neither here nor there as far as the correctness of Marx's theory of value. To see that, you have to get to the last footnote in chapter 5 of Capital. (Most "refutations" of Marx are based on ignorance of the first few pages of chapter 1.)

From the foregoing investigation, the reader will see that this statement only means that the formation of capital must be possible even though the price and value of a commodity be the same; for its formation cannot be attributed to any deviation of the one from the other. If prices actually differ from values, we must, first of all, reduce the former to the latter, in other words, treat the difference as accidental in order that the phenomena may be observed in their purity, and our observations not interfered with by disturbing circumstances that have nothing to do with the process in question. We know, moreover, that this reduction is no mere scientific process. The continual oscillations in prices, their rising and falling, compensate each other, and reduce themselves to an average price, which is their hidden regulator. It forms the guiding star of the merchant or the manufacturer in every undertaking that requires time. He knows that when a long period of time is taken, commodities are sold neither over nor under, but at their average price. If therefore he thought about the matter at all, he would formulate the problem of the formation of capital as follows: How can we account for the origin of capital on the supposition that prices are regulated by the average price, i. e., ultimately by the value of the commodities? I say 'ultimately', because average prices do not directly coincide with the values of commodities, as Adam Smith, Ricardo, and others believe.

-- Karl Marx. 1887. Capital, first english edition.

Only volume 1 was published in Marx's lifetime. But the question of the validity of Marx's theory, say, the value theory of labor, cannot be discussed without looking at volume 3, unpublished in Marx's lifetime.

Wicksteed had an early discussion of the validity of Marx's theory from a marginalist standpoint. Eugen von Böhm Bawerk's Karl Marx and the Close of his System is problably better known. His book is definitely important from a historical perspective. But its content is not all that insightful. Some anti-Marxists agree with me.

"The classic 'refutation' of Capital was made by a leading figure in the new economics, Eugen von Bohn-Bawerk. His refutation repeatedly misunderstood what it was refuting, and unknowingly repeated criticisms that Marx had made of Ricardo in manuscripts still unpublished at that time. Bohm-Bawerk also made the claim, often echoed since then, that in his discussion of value Marx had attempted 'a stringent syllogistic conclusion allowing of no exception,' that Marx attempted 'a logical proof, a dialectical deduction.' As already noted, Marx considered the idea of proving a concept to be ridiculous. Moreover, Engels had asserted, long before Bohm-Bawerk, that one only proves one's ignorance of dialectics by thinking of it as a means by which things can be proved. This was typical of a tragi-comedy of errors that has plagued the interpretation of Marx ever since.

Contrary to some interpretations, Marx did not change his mind about value and price between volumes of Capital. He explicitly worked out the analysis to be followed in Volume III in a letter to Engels written several years before publication of Volume I."

-- Thomas Sowell. 1985. Marxism: Philosophy and Economics, Routledge.

Sowell refers to Marx's letter of 2 August 1962. I have all sorts of disagreements with Sowell, which I forget. In some, I am probably critical of Marx than Sowell. One should probably ignore the final chapter of this book.

My next example is not from an economist:

"Marx of course knew that prices are determined in practice by various factors, including labour productivity, supply and demand, and the average rate of profit. If he disregarded these in the first volume of Capital, it was for methodological reasons and not because he thought value and price were the same thing; thus he cannot be reproached with inconsistency as between Volume I and Volume III, which deals inter alia with the average rate of profit."

-- Leszek Kolakowski. 1978. Main Currents of Marxism: The Founders (Book 1), Chapter XIII, Section 6.

I turn back to an economist:

"Writers on 'the transformation problem' since L. Bortkiewicz have focussed on an issue that is largely periperal; and others like E. Bohm-Bawerk have asserted that there is a contradiction between the analyses of Volumes I and III which is certainly not to be found there unless one reads into them an interpretation different from that which Marx repeatedly emphasized."

-- William J. Baumol. 1974. The transformation of values: what Marx 'really' Meant (An Interpretation). Journal of Economic Literature 12 (1): 51-62.

Even one of his students was not too impressed by Böhm Bawerk on Marx:

"As it was, most critics felt no hestitation in convicting him of having by the third volume flatly contradicted the doctrine of the first. On the face of it that verdict is not justified. If we place ourselves on Marx's standpoint, as it is our duty in a question of this kind, it is not absurd to look upon surplus value as a 'mass' produced by the social process of production considered as a unit and to make the rest a matter of distribution of that mass

Joseph A. Shumpeter, Chapter III. Marx the Economist, Capitalism, Socialism, and Democracy. Third Edition, New York: Harper and Brothers, 1942, 1947, 1950.

Valid, non-outdated criticisms of Marx exist. Böhm Bawerk does not have one.

Saturday, September 24, 2022

Saul Kripke (1940 - 2022)

I want to write an inadequate appreciation of Saul Kripke, a great analytical philosopher. The Guardian has an obituary.

I start from an example of a pratical use of his work. Chin and Older (2011) use modal logic to specify and reason about the security properties of (computer) systems. One wants to be able to assert who (or what) has access to certain data and who can grant access. Certain states of a system should never arrive.

A Kripke structure, as presented in Chin and Older (2011), is a three-tuple consisting of:

  • A set W, known as the set of all possible worlds.
  • An interpretation I, that maps each proposition to a subset of W. Informally, I(p) is the set of worlds in which the proposition p is true.
  • A function J that maps the name of each principal to a set of ordered pairs of possible worlds. Consider J(A), the set of ordered pairs (W1, W2) mapped to by this function. This is intended to be such that if the current world is W1, A believes the world might be W2.

For the above definition to be completely formal, one needs to specify the language for propositions p. In propositional logic, operators such as "and", "or", and "not" combine atomic propositions. Predicate calculus introduces such notions as "for all" and "there exists". Model theory is used to characterize semantics, to specify models in which a set of sentences is true. I guess a Kripke structure is a kind of structure, as structures are defined in model theory. Modal logic uses the apparatus of model theory to characterize propositions as "necessarily true", "possibly true", and so on. The textbook I have available for model theory, which I cannot get very far into, does not go into this.

Misleading talk, some of that by Kripke, about possible worlds raises the question of "transworld identification". Consider a proposition p(a) about an individual a. How do we identify a across possible worlds? If one uses the name Nixon to identify the winner of the 1968 U.S. presidential election, are we not requiring one to call Humphrey "Nixon" in some possible worlds? Amusingly, Kripke also raises the question of why we might say that 9 is necessarily greater than 7, but be unwilling to say that the number of planets is neccessarily greater than 7. In the current world, the number of planets is now eight. Pluto is now, by stipulation, not a planet. Kripke argues, in Naming and Necessity that Frege and Russell had mistaken theories about reference.

I will probably not be able to wrap my head around the idea of necessary contingent truths in a couple of weeks. Consider the length of a certain rod in Paris back when that was the definition of a meter. It was a necessary truth that a meter is that length. In some possible worlds, the room it is stored in might possibly be hotter. A meter would still be a meter in all possible worlds, according to Kripke, but the length of the standard meter might possibly be different.

I find Kripke (1982) to be easier to understand, maybe. I know that Kripke says that he is presenting an argument from Wittgenstein, not his own. If I try to orally summarize it, I tend to bring in Goodman's "grue" and "bleen", Putnam's "twater" on twin earth, or Wittgenstein's beetle in a box. The topic seems to be how words mean, not epistemology or ontology. How do you know that when talking to people they do not mean "grue" when they say "green"? Even more troublesome, how do you know you did not mean "grue" every time you said "green" in the past? By postulation in the argument, there does not seem to be any empirical fact one can point to. Meaning is not in an individual's mind.

  • Shiu-Kai Chin and Susan Older. 2011. Access Control, Security, and Trust: A Logical Approach. CRC Press.
  • Nelson Goodman. 1983. Fact, Fiction, and Forecast, 4th ed. Harvard University Press.
  • Wilfrid Hodges. 1997. A Shorter Model Theory. Cambridge University Press.
  • Saul A. Kripke. 1980. Naming and Necessity, 2nd ed. Harvard University Press.
  • Saul A. Kripke. 1982. Wittgenstein on Rules and Private Language: An Elementary Exposition. Harvard University Press.
  • Hilary Putnam. 1983. Reason, Truth, and History. Cambridge University Press.

Tuesday, September 20, 2022

Karl Marx To Abraham Lincoln On His Re-Election

Apparently, Lincoln responded to this congratulations from the International Workingmen's Association:


We congratulate the American people upon your re-election by a large majority.

If resistance to the Slave Power was the reserved watchword of your first election, the triumphant warcry of your re-election is, Death to Slavery.

From the commencement of the Titanic-American strife the working men of Europe felt instinctively that the star-spangled banner carried the destiny of their class. The contest for the territories which opened the dire epopee, was it not to decide whether the virgin soil of immense tracts should be wedded to the labour of the emigrant, or prostituted by the tramp of the slave-driver?

When an oligarchy of 300,000 slave-holders dared to inscribe, for the first time in the annals of the world, "slavery" on the banner of Armed Revolt; when on the very spots where hardly a century ago the idea of one great Democratic Republic had first sprung up, whence the first Declaration of the Rights of Man was issued, and the first impulse given to the European revolution of the 18th century; when on those very spots counter-revolution, with systematic thoroughness, gloried in rescinding "the [...] ideas entertained [...] at the time of the formation of the old Constitution", and maintained "slavery to be a beneficent institution", indeed the only solution of the great problem of "the relation of labour to capital", and cynically proclaimed property in man "the cornerstone of the new edifice", then the working classes of Europe understood at once, even before the fanatic partisanship of the upper classes for the Confederate gentry had given its dismal warning, that the slave-holders' rebellion was to sound the tocsin for a general holy crusade of property against labour, and that for the men of labour, with their hopes for the future, even their past conquests were at stake in that tremendous conflict on the other side of the Atlantic. Everywhere they bore therefore patiently the hardships imposed upon them by the cotton crisis, opposed enthusiastically the pro-slavery intervention, importunities of their betters - and, from most parts of Europe, contributed their quota of blood to the good cause.

While the working men, the true political power of the North, allowed slavery to defile their own republic; while before the Negro, mastered and sold without his concurrence, they boasted it the highest prerogative of the white-skinned labourer to sell himself and choose his own master; they were unable to attain the true freedom of labour or to support their European brethren in their struggle for emancipation, but this barrier to progress has been swept off by the red sea of civil war.

The working men of Europe feel sure that, as the American War of Independence initiated a new era of ascendancy for the middle class, so the American Anti-Slavery War will do for the working classes. They consider it an earnest of the epoch to come that it fell to the lot of Abraham Lincoln, the single-minded son of the working class, to lead his country through the matchless struggle for the rescue of an enchained race and the reconstruction of a social world.

Signed on behalf of the International Working Men's Association

The Central Council

I have noted before parallels between Marx and an American creed.

Friday, September 16, 2022

Three Quotations: Rousseau, Adam Smith, Engels

Here is Jean Jacques Rousseau:

"...whether those who command are necessarily better than those who obey, and if strength of body or of mind, wisdom or virtue are always found in particular individuals, in proportion to their power or wealth: a question fit perhaps to be discussed by slaves in the hearing of their masters, but highly unbecoming to reasonable and free men in search of the truth." -- Jean Jacques Rousseau, Discourse on Inequality (1755).

Early developers of political economy were not slavish. Here is Adam Smith explaining that returns to capital and land are the result of value added by labor not paid out in wages.

"In the early and rude state of society... the whole produce of labour belongs to the labourer; and the quantity of labour commonly employed in acquiring or producing any commodity, is the only circumstance which can regulate the quantity of labour which it ought commonly to purchase, command, or exchange for.

As soon as stock has accumulated in the hands of particular persons, some of them will naturally employ it in setting to work industrious people, whom they will supply with materials and subsistence, in order to make a profit by the sale of their work, or by what their labour adds to the value of the materials. In exchanging the complete manufacture either for money, for labour, or for other goods, over and above what may be sufficient to pay the price of the materials, and the wages of the workmen, something must be given for the profits of the undertaker of the work, who hazards his stock in this adventure. The value which the workmen add to the materials, therefore, resolves itself in this case into two parts, of which the one pays their wages, the other the profits of their employer upon the whole stock of materials and wages which he advanced. He could have no interest to employ them, unless he expected from the sale of their work something more than what was sufficient to replace his stock to him; and he could have no interest to employ a great stock rather than a small one, unless his profits were to bear some proportion to the extent of his stock...

...As soon as the land of any country has all become private property, the landlords, like all other men, love to reap where they never sowed, and demand a rent even for its natural produce. The wood of the forest, the grass of the field, and all the natural fruits of the earth, which, when land was in common, cost the labourer only the trouble of gathering them, come, even to him, to have an additional price fixed upon them. He must then pay for the licence to gather them, and must give up to the landlord a portion of what his labour either collects or produces. This portion, or, what comes to the same thing, the price of this portion, constitutes the rent of land, and in the price of the greater part of commodities, makes a third component part." -- Adam Smith, The Wealth of Nations, Book I, Chapter VI (1776).

Many read the above as an account of how labor is exploited under capitalism. I find something similar in an essay a young Engels wrote before his life-long partnership with Marx:

"We have seen that capital and labour are initially identical; we see further from the explanations of the economist himself that, in the process of production, capital, the result of labour, is immediately transformed again into the substratum, into the material of labour; and that therefore the momentarily postulated separation of capital from labour is immediately superseded hy the unity of both. And yet the economist separates capital from labour, and yet clings to the division without giving any other recognition to their unity than by his definition of capital as "stored-up labour". The split between capital and labour resulting from private property is nothing but the inner dichotomy of labour corresponding to this divided condition and arising out of it. And after this separation is accomplished, capital is divided once more into the original capital and profit-the increment of capital, which it receives in the process of production; although in practice profit is immediately lumped together with capital and set into motion with it. Indeed, even profit is in its turn split into interest and profit proper. In the case of interest, the absurdity of these splits is carried to the extreme. The immorality of lending at interest, of receiving without working, merely for making a loan, though already implied in private property, is only too obvious, and has long ago been recognised for what it is by unprejudiced popular consciousness, which in such matters is usually right. All these subtle splits and divisions stem from the original separation of capital from labour and from the culmination of this separation- the division of mankind into capitalists and workers-a division which daily becomes ever more acute, and which, as we shall see, is bound to deepen. This separation, however, like the separation already considered of land from capital and labour, is in the final analysis an impossible separation. What share land, capital and labour each have in any particular product cannot be determined. The three magnitudes are incommensurable. The land produces the raw material, but not without capital and labour. Capital presupposes land and labour. And labour presupposes at least land, and usually also capital. The functions of these three elements are completely different, and are not to be measured by a fourth common standard. Therefore, when it comes to dividing the proceeds among the three elements under existing conditions, there is no inherent standard; it is an entirely alien and with regard to them fortuitous standard that decides— competition, the cunning right of the stronger. Rent implies competition; profit on capital is solely determined by competition; and the position with regard to wages we shall see presently." -- Friedrich Engels, Outlines of a Critique of Political Economy (1844).

I think one can discard the conjectural history and moral overtones of the above and freely play in the mathematics of Leontief matrices. But many academic economists nowadays are imposing mind-forged manacles onto another generation.

Saturday, September 10, 2022

Marx On The Transformation Problem In 1847

This is the start of Section 5, "Strikes and combinations of workers", in the second chapter of The Poverty of Philosophy:

"'Every upward movement in wages can have no other effect than a rise in the price of corn, wine, etc., that is, the effect of a dearth. For what are wages? They are the cost price of corn, etc.; they are the integrant price of everything. We may go even further: wages are the proportion of the elements composing wealth and consumed reproductively every day by the mass of the workers. Now, to double wages ... is to attribute to each one of the producers a greater share than his product, which is contradictory and if the rise extends only to a small number of industries, it brings a general disturbance in exchange; in a word, a dearth.... It is impossible, I declare, for strikes followed by an increase in wages not to culminate in a general rise in prices: this is as certain as that two and two make four.' (Proudhon, Vol. I, pp. 110 and 111)

We deny all these assertions, except that two and two make four.

In the first place, there is no general rise in prices. If the price of everything doubles at the same time as wages, there is no change in price, the only change is in terms.

Then again, a general rise in wages can never produce a more or less general rise in the price of goods Actually, if every industry employed the same number of workers in relation to fixed capital or to the instruments used, a general rise in wages would produce a general fall in profits and the current price of goods would undergo no alteration.

But as the relation of manual labour to fixed capital is not the same in different industries, all the industries which employ a relatively greater mass of capital and fewer workers, will be forced sooner or later to lower the price of their goods. In the opposite case, in which the price of their goods is not lowered, their profit will rise above the common rate of profits. Machines are not wage-earners. Therefore, the general rise in wages will affect less those industries, which, compared with the others, employ more machines than workers. But as competition always tends to level the rate of profits, those profits which rise above the average rate cannot but be transitory. Thus, apart from a few fluctuations, a general rise in wages will lead, not as M. Proudhon says, to a general increase in prices, but to a partial fall - that is a fall in the current price of the goods that are made chiefly with the help of machines.

The rise and fall of profits and wages expresses merely the proportion in which capitalists and workers share in the product of a day's work, without influencing in most instances the price of the product. But that 'strikes followed by an increase in wages culminate in a general rise in prices, in a dearth even' - those are notions which can blossom only in the brain of a poet who has not been understood." -- Karl Marx

You can see why after this, Marx and Proudhon were no longer drinking buddies. Anyways, Marx here considers a rise in wages. Echoing Ricardo, Marx argues that some prices drop and others rise. So even though the labor embodied in commodities does not alter, relative prices of production vary because of a variation of wages. I take this to be a statement of the so-called transformation problem.

An early statement of Marx's solution can be found in his 2 August 1862 letter to Engels.

I see in the above an idea Marx takes over from Ricardo. Think of the yearly net output of a capitalist economy as produced by the labor employed during that year. The 'real wage', in Ricardo's terminology, is the proportion of that labor that goes to produce the commodities purchased and thereby consumed by the workers. Suppose productivity increases, and total employment does not change. The workers can thereby obtain a greater quantity of 'necessaries and luxuries', while the real wage declines, depending on how the results of this increased productivity are divided among the classes making up society. The current usage among mainstream economists of the term 'real wage' is an obstacle to reading Ricardo, if one is not careful.

By the way, in a comment on one of my posts on the Temporal Single System Interpretation, Hedlund recommends Robert A. Bryer's "Marx's accounting solution to the 'transformation problem'". This is a chapter in his book Accounting for Value in Marx's Capital: The Invisible Hand

Wednesday, September 07, 2022

Standards Organization As Partly A Non-Capitalist Logic

This post draws attention to the existence of a vast web of existing organizations that, perhaps, operate partly outside and partly inside a capitalist logic. These standards organizations define technologies vital to keeping our society running. I think I would find it interesting for some scholar interested in council communism or syndicalism to look into these. The examples I list are perhaps idiosyncratic, out-of-date, and reflect my personal history with computing.

Here is a list of some of the organizations I have in mind:

  • American National Standards Institute (ANSI)
  • International Electrotechnical Commission (IEC)
  • Institute of Electrical and Electronics Engineers (IEEE)
  • Internet Engineering Task Force (IETF)
  • International Standards Organization (ISO)
  • International Telecommunications Union (ITU)
  • National Institute for Standards and Technology (NIST)

The IEEE is a professional organization that provides an umbrella for a wide range of specialized societies. They publish academic journals, organize conferences, define certain certification programs, and have a professional code of ethics. IEEE-STD-754 is an example of a standard I am often conscious of. It defines how floating point numbers are stored in your computer, where floating point numbers are a finitary representation, in some sense, of real numbers. This standard was developed and is maintained by a committee of academics, representatives of companies, etc. under the auspices of the IEEE. The original standard and each update is circulated for comment and for voting by the wider membership.

Sometime a standard is developed and maintained by such a committee under the auspices of a government agency. For example, consider the Interplanetary Overlay Network (ION), a delay-tolerant network (DTN), implementing an interplanetary internet. As I understand it, ION was developed by the Interplanetary Networking Special Interest Group, a committee set up by the National Aeronautics and Space Administration (NASA) and chaired by Vincent Cerf.

Sometimes a standard is replaced by another one. The Perry memo, issued under Bill Clinton, directed the Department of Defense to prefer commercial standards to their own military standards, where feasible. For example, MIL-STD-2167A was replaced by ISO/IEC 12207 Information Technology – Software life cycle processes. This standard describes documentation to be produced during software development lifecycles, such as design documentation, user manuals, and test plans.

Sometimes a single corporation develops a standard. For example, Java was developed by Sun, now by Oracle. As those who develop enterprise systems know, a vast set of tools are available for Java, including integrated development environments (IDEs), application servers, deployment tools such as Ant and Gradle, and even other languages that compile to execute on the Java Virtual Machine (JVM).

Corporations have an interest in having their internal developments recognized by a standards body. I am not sure that this is a good example, but C was developed by Bell Labs before becoming ANSI C.

Sometimes, a standard is developed as a contest. (Dean Baker might find this of interest.) The Ada programming language (ANSI/MIL-STD-1815A) had four qualifiers for the first round: CII Honeywell Bull (green), Intermetrics (red), Softech (blue), and SRI International (yellow). Eventually, the U.S. Department of Defense decided "green is Ada". More recently, NIST developed the Advanced Encryption Standard (AES) with a contest.

The technical feasibility of a standard is sometimes in question, and a reference implementation is often developed alongside the standard. For some reason, I associate the term "reference model" with the Open Systems Interconnection (OSI) layered model for the Internet. A standards body might impose some control on who can claim to have implemented the standard. Ada was accompanied with, for example, test suites for verifying implementations.

Even in a society of hierarchical organizations, a need exists for people to cooperate across such organizations.

Thursday, September 01, 2022

On Sraffian Subsytems And Labor Values

1.0 Introduction

I recently stumbled across McKiernan (2017), an Austrian response to Sraffa's book. This is a weird working paper. He works through Sraffa, with apparently no knowledge of all the textbooks explaining the book. McKiernan correctly notes that Sraffa provides little context about his points. And the mathematics is not always explicit. Naturally, McKiernan makes mistakes. If he ever revisits this, I think he would want to break it up into several papers. (Fabra (1991) is the strangest published response to Sraffians of which I know.)

I only want to focus on one point, Sraffian subsytems. But before doing that, let me at least point out something insightful in McKiernan's paper. He points out one of what I later call a fluke case:

However, Sraffa makes no note of cases in which a scarcity of land is offset by using a more expensive method of production, and that employment meets present desire for the product exactly when applied to all available land, so that only one method is used. In this case, two variables, pcorn and ρ, correspond to one equation. (p. 22)

I think I could also construct a fluke case with intensive rent, which is closer to his point.

2.0 A Criticism Of Subsystems

McKieran mistakenly asserts:

But consider the pricing of a commodity that were not produced in surplus, as could happen in these models with a purely infrastructural commodity. A sub-system for this commodity would have a net production of 0, but these models have all presumed a need for active renewal, so there would be an expenditure of labor. If returns to scale were co-incident, so that the sub-system might be embodied, that sub-system standing alone would produce a wage of 0, but wages are presumed to be shared across sub-systems (else Sraffa’s argument falls apart). Hence, it appears that prices of commodities of this infrastructural sort must be whatever one makes of division by 0. (p. 8)

(If McKieran ever revisits this, I wish he would give a more explicit and formal definition of co-incident returns. I think I get his point, but I do not think I have ever seen this notion in the economics literature.)

Anyways, if the net output of a commodity is zero, the decomposition of the given quantity flows into Sraffian subsytems, with nothing left over, will result in no labor being directed towards producing a net output of that commodity. So one rather gets a quotient of zero divided by zero, not a division of a positive quantity of zero. Nevertheless, one can still find a Sraffian subsystem for producing that commodity.

3.0 A Decomposition of One Set of Quantity Flows

I take an example from my FAQ on the Labor Theory of Value. Consider an economy with the observed quantity flows shown in Table 1. In this little model economy, wheat, iron, and labor are used to produce a net output of 500 quarters of wheat and 8 tons iron. From the postulated observations, one cannot tell whether iron is somehow consumed or whether this economy is undergoing steady growth. Given, say, the real wage, one can calculate prices of production. But many questions are not adressed here.

Table 1: Given Quantity Flows
74 qr. wheat & 37 t. iron & 592 worker.->592 qr. wheat
18 qr. wheat & 3 t. iron & 48 workers->48 t. iron

I find Leontief coefficients of production useful. Table 2 results from dividing the first of Table 1 by 592 qr. wheat and the second row by 48 t. iron.

Table 2: Leontief Coefficients
1/8 qr. & 1/16 t. & 1 workers->1 qr. wheat
3/8 qr. & 1/16 t. & 1 workers->1 t. iron

Suppose these coefficients of production are used to calculate inputs when gross outputs of are approximately 588.2 quarters wheat and 39.2 tons iron. Table 3 results. The net output of the wheat subsytem is 500 quarters wheat, produced from an input of 32000/51 workers. That is 64/51 ≈ 1.25 workers are embodied in each quarter of wheat.

Table 3: Wheat Subsystem
1250/17 ≈ 73.5 qr. & 625/17 ≈ 36.8 t. & 10000/17 ≈ 588.2 workers10000/17 qr. wheat
250/17 ≈ 14.7 qr. & 125/51 ≈ 2.5 t. & 2000/51 ≈ 39.2 workers2000/51 t. iron

Table 4 shows the iron subsystem. In this subsystem, 640/51 ≈ 12.5 workers produce a net output of 8 tons iron. In other words, 80/51 ≈ 1.57 workers are embodied in each ton iron.

Table 4: Iron Subsystem
8/17 ≈ 0.5 qr. & 4/17 ≈ 0.2 t. & 64/17 ≈ 3.8 workers64/17 qr. wheat
56/17 ≈ 3.3 qr. & 28/51 ≈ 0.5 t. & 448/51 ≈ 8.8 workers448/51 t. iron

The quantity flows shown in Tables 3 and 4 add up to the quantity flows in Table 1. In these subsystems are thought of as operating side-by-side, total quantity flows are as in the observed economy. No assumptions on returns to scale are needed for this decomposition into subsystems.

4.0 A Decomposition of Another Set of Quantity Flows

I now want to consider another set of quantity flows that might be observed. Suppose these quantity flows are as in Table 5. The net output of this economy consists of 500 quarters wheat. For ease of calculation, I have used the same coefficients of production as in Table 2. They very well could be different since gross outputs vary from those in Table 1. If coefficients of production vary, so do returns to scale. Anyways, in this example, the net output of iron is zero. But even so, one can find here a subsystem for producing iron.

Table 5: Another Set of Quantity Flows
1250/17 ≈ 73.5 qr. & 625/17 ≈ 36.8 t. & 10000/17 ≈ 588.2 workers10000/17 qr. wheat
250/17 ≈ 14.7 qr. & 125/51 ≈ 2.5 t. & 2000/51 ≈ 39.2 workers2000/51 t. iron

Consider the quantity flows shown in Table 6. The net output is 500 quarters wheat and -8 tons iron. This is not a Sraffian subsystem. It is unbalanced. But these quantity flows are constructed from the same coefficients of production as manifested in Table 5.

Table 6: Unbalanced Quantity Flows
1242/17 ≈ 73.1 qr. & 621/17 ≈ 36.5 t. & 9936/17 ≈ 584.5 workers9936/17 qr. wheat
194/17 ≈ 11.4 qr. & 97/51 ≈ 1.9 t. & 1552/51 ≈ 30.4 workers1552/51 t. iron

Now consider what quantity flows result from subtracting those in Table 6 from those in Table 5. Table 7 results. This is the same subsystem for producing iron as shown in Table 4. Even though the net output of iron in the observed quantity flows in Table 5 is zero, one can still find in them an iron subsystem.

Table 7: The Iron Subsystem Again
8/17 ≈ 0.5 qr. & 4/17 ≈ 0.2 t. & 64/17 ≈ 3.8 workers64/17 qr. wheat
56/17 ≈ 3.3 qr. & 28/51 ≈ 0.5 t. & 448/51 ≈ 8.8 workers448/51 t. iron

5.0 Results

No assumptions on returns to scale are made in analytically decomposing the observed quantity flows into subsystems.

Given observed physical quantity flows, one can ask how much more labor would be employed if net output of the economy was increased by a small quantity of a specified commodity. In other words, each commodity has an employment multiplier, to use the jargon of Leontief analysis. If non-constant returns to scale do not prevail, the error in this calculation will become more pronounced as the specified quantity increases. An insight behind the differential calculus is that, for continuous functions, a small enough variation has an approximately linear effect.


Friday, August 26, 2022

Reminder: Wages, Employment Not Determined By The Supply And Demand Of Labor

1.0 Introduction

Over a half-century ago, economists reached a consensus. The model in which employment and real wages are explained by the intersection of a downwards-sloping labor demand function and a supply function is incoherent, not even wrong. This incoherence was demonstrated under the assumptions of perfect competition and of firms that have adjusted their plant and other capital inputs. I do not know what Greg Mankiw and Jonathan Gruber are doing, but it certainly is not education.

Anyways, I have not recently gone through a simple example, without some of my innovations. Maybe I will repost this some time with graphs and more references.

2.0 Technology

Consider a very simple vertically-integrated (representative) firm that produces a single consumption good, corn, from inputs of labor, iron, and (seed) corn. All production processes in this example require a year to complete. The managers of the firm know of two processes for producing corn and two processes for producing iron. The processes A and B, for producing corn, require the tabulated inputs to be available at the beginning of the year for each bushel corn produced and available at the end of the year. Similarly, process C, for example, requires one person-year, 1/40 bushels corn, and 1/10 tons iron to be available at the beginning of the year for each ton of iron produced by this process. This is an example of circulating capital; all inputs of corn and iron are used up during the year in producing the gross output.

Table 1: Coefficients of Production
Labora0, 1(A) = 1a0, 1(B) = 1a0, 2(C) = 1a0, 2(D) = 275/464
Corna1, 1(A) = 2/5a1, 1(B) = 3/5a1, 2(C) = 1/40a1, 2(D) = 0
Irona2, 1(A) = 2a2, 1(B) = 1/2a2, 2(C) = 1/10a2, 2(D) = 113/232

Apparently, inputs of iron and corn can be traded off in producing corn outputs. Likewise, inputs of corn and iron can be traded off in producing iron. The iron-producing process that uses less iron and more corn, however, also requires a greater quantity of labor input.

2.0 Techniques

A technique consists of a process for producing corn and a process for producing iron. Thus, there are four techniques in this example. They are defined in Table 3.

Table 2: Techniques of Production
TechniqueCorn ProcessIron Process

3.0 Quantity Flows

I want to consider a couple of different levels at which this firm can operate the processes comprising the techniques. First, consider the quantity flows in Table 3, in which Process A is used to produce 1 41/49 Bushels corn, and Process C is used to produce 4 4/49 Tons iron. When the firm operates these processes in parallel, it requires a total of 41/49 bushels corn as input. The output of the corn-producing process can replace this input, leaving a net output of one bushel corn. Notice that the total input of iron are 3 33/49 + 20/49 = 4 4/49 tons iron, which is exactly replaced by the output of Process C. So Table 4 shows a technique in which 5 45/49 person-years labor are used to produce a net output of one bushel corn. The firm, when operating this technique can produce any desired output of corn by scaling both processes equally.

Table 3: The Alpha Technique
InputsProcess AProcess C
Labora0, 1(A) qA =
1 41/49 person-yrs.
a0, 2(C) qC =
4 4/49 person-yrs.
Corna1, 1(A) qA =
36/49 bushels
a1, 2(C) qC =
5/49 bushels
Irona2, 1(A) qA =
3 33/49 tons
a2, 2(C) qC =
20/49 tons
OutputsqA = 1 41/49 bushelsqC = 4 4/49 tons

Table 5 shows the application of the same sort of arithmetic to the Beta technique. The labor-intensity of the Beta technique is 5 185/357 person-years per bushel. Neither the Gamma nor the Delta technique are profit-maximizing for the prices considered below.

Table 4: The Beta Technique
InputsProcess AProcess D
Labora0, 1(A) qA =
1 2/3 person-yrs.
a0, 2(D) qD =
3 304/357 person-yrs.
Corna1, 1(A) qA =
2/3 bushels
a1, 2(D) qD =
0 bushels
Irona2, 1(A) qA =
3 1/3 tons
a2, 2(D) qD =
3 59/357 tons
OutputsqA = 1 2/3 bushelsqD = 6 178/357 tons

4.0 Prices

Which technique will the firm adopt, if any? The answer depends, in this analysis, on which is more profitable. So one has to consider prices. I assume throughout that inputs of iron, corn, and labor are charged at the start of the year. Corn is the numeraire; its price is unity throughout. Two different levels of wages are considered.

4.1 Prices with a Low Wage

Accordingly, assume wages are initially 3/2780 bushels per person-year. Under the assumptions of perfect competition, this price of labor is a given for the firm.

If all corn-producing firms are vertically integrated, a market price for iron is not available. At the end of the year, the firm will have a stock of produced corn and iron. Even though the managers of the firm intend all of the iron to be used as an input to further production, the question arises for accountants of how to evaluate the stock of gross output. I suggest the accountants set a price of iron such that the firm is making the same rate of profits in all of the processes that it is operating. According let the price of iron, p, be 55/1112 bushels per ton.

Table 5 shows accounting with these prices. The column labeled "cost" shows the cost of the inputs needed to produce one unit output, a bushel corn or a ton iron, depending on the process. Accounting profits for a unit output are the difference between the price of a unit output and this cost. The rate of (accounting) profits, shown in the last column, is the ratio of accounting profits to the cost. The rate of profits is independent of the scale at which each process is operated.

Table 5: Costs and the Rate of Profits at a Low Wage
ProcessCostsRate of Profits
Aa1, 1(A) + a2, 1(A) p + a0, 1(A) w = 1/2100 percent
Ba1, 1(B) + a2, 1(B) p + a0, 1(B) w = 6959/1112059.8 percent
Ca1, 2(C) + a2, 2(C) p + a0, 2(C) w = 69/222459.4 percent
Da1, 2(D) + a2, 2(D) p + a0, 2(D) w = 55/2224100 percent

These prices are compatible with the use of the Beta technique to produce a net output of corn. The Beta technique specifies that process A be used to produce corn and process D be used to produce iron. Notice that process B is more expensive than process A, and that process C is more expensive than process D. These prices do not provide signals to the firm that processes outside the Beta technique should be adopted. The vertically-integrated firm is making a rate of profit of 100 percent in producing corn with the Beta technique. The same rate of profits are earned in producing corn and in reproducing the used-up iron by an iron-producing process.

4.2 One Set of Prices with a Higher Wage

Suppose this firm faces a wage more than 25 times higher, namely 109/4040 bushels per person-year. Consider what happens if the firm doesn't revalue the price of iron on its books. Table 6 shows this case. Since labor enters into each process, the rate of profits has declined for all processes. The ratio of labor to the costs of the other inputs is not invariant across processes. Thus, the rate of profits has declined more in some processes than in others. Notice especially, than the rate of profits is no longer the same in the processes, A and D, that comprise the Beta technique.

Table 6: Costs and the Rate of Profits at a Higher Wage
ProcessCostsRate of Profits
Aa1, 1(A) + a2, 1(A) p + a0, 1(A) w ≈ 0.525990.1 percent
Ba1, 1(B) + a2, 1(B) p + a0, 1(B) w ≈ 0.651753.4 percent
Ca1, 2(C) + a2, 2(C) p + a0, 2(C) w ≈ 0.05693-13.1 percent
Da1, 2(D) + a2, 2(D) p + a0, 2(D) w ≈ 0.0400823.4 percent

This accounting data does not reveal the firm's rate of return in operating the Beta technique. The firm cannot be simultaneously making both 23 percent and 90 percent in operating that technique. Furthermore, this data provides a signal to the firm to withdraw from iron production and make only corn. So this data says that something must change.

4.3 Another Set of Prices with a Higher Wage

Perhaps all that is needed is to re-evaluate iron on the firm's books. Higher wages have made iron more valuable. Table 7 shows costs and the rate of profits when iron is evaluated at an accounting price of approximately 0.10569124 bushels per ton.

Table 7: Costs and the Rate of Profits with Iron Repriced
ProcessCostsRate of Profits
Aa1, 1(A) + a2, 1(A) p + a0, 1(A) w ≈ 0.638456.7 percent
Ba1, 1(B) + a2, 1(B) p + a0, 1(B) w ≈ 0.679847.1 percent
Ca1, 2(C) + a2, 2(C) p + a0, 2(C) w ≈ 0.0625569.0 percent
Da1, 2(D) + a2, 2(D) p + a0, 2(D) w ≈ 0.0674756.7 percent

This revaluation of iron reveals that the firm makes a rate of profits of 57 percent in operating the Beta technique. The firm makes the same rate of profits in producing corn and in producing its input of iron. But the manager of the iron-producing process would soon notice that the cost of operating process C is cheaper.

4.4 A Final Set of Prices with a Higher Wage

So the firm would ultimately switch to using process C to produce iron. The price of iron the firm would enter on its books would fall somewhat, but still be higher than the original price at the low wage. Table 8 shows the accounting with a price of iron of 10/101 Bushels per Ton. The firm has adopted the cheapest process for producing iron, and the rate of profits is the same in both corn-production and iron-production. The accounting for this vertically-integrated firm is internally consistent.

Table 8: Costs and the Rate of Profits at a High Wage
ProcessCostsRate of Profits
Aa1, 1(A) + a2, 1(A) p + a0, 1(A) w = 5/860 percent
Ba1, 1(B) + a2, 1(B) p + a0, 1(B) w ≈ 0.676547.8 percent
Ca1, 2(C) + a2, 2(C) p + a0, 2(C) w = 25/40460 percent
Da1, 2(D) + a2, 2(D) p + a0, 2(D) w ≈ 0.0642254.2 percent

5.0 Conclusion

Table 9 summarizes these calculations. The ultimate result of a higher wage is the adoption of a more labor-intensive technique. If this firm continues to produce the same level of net output and maximizes profits, its managers will want to employ more workers at the higher of the two wages considered.

Table 9: A More Labor-Intensive Technique at a Higher Wage
3/2780 ≈ 0.00108 bushels per person-yearBeta5 185/357 ≈ 5.52 person-years per bushel
109/4040 ≈ 0.0270 bushels per person-yearAlpha5 45/49 ≈ 5.92 person-years per bushel

Economists, such as Edwin Burmeister, have investigated what conditions on technology might be necessary to rule out the illustrated effects. They know that no such conditions are known, and would be extremely restrictive anyways. A marginalist special case has not been specified for the case in which more than one commodity is produced.

So much for the theory that wages and employment are determined by the interaction of well-behaved supply and demand curves on the labor market.

Appendix: Production Functions

The data above allow for the specification of two well-behaved production functions, one for corn and the other for iron. For illustration, I outline how to construct the production function for corn.

Let L be the person-years of labor, Q1 be bushels corn, and Q2 be tons labor allocated as inputs for corn-production during the production period (a year). Let X1 be the bushels corn produced with Process A, and X2 be the bushels corn produced with Process B. The production function for corn is the solution of an optimization problem in which as much corn as possible is produced from the given inputs.

Choose X1, X2

To maximize X = X1 + X2

subject to

a0, 1(A) X1 + a0, 1(B) X2L
a1, 1(A) X1 + a1, 1(B) X2Q1
a2, 1(A) X1 + a2, 1(B) X2Q2

X1 ≥ 0, X2 ≥ 0,

Let f(L, Q1, Q2) be the solution of this Linear Program, that is, the production function for corn. (This production function is not Leontief.) The production functions constructed in this manner exhibit properties typically assumed in marginalist economics. In particular, they exhibit Constant Returns to Scale, and the marginal product, for each input, is a non-increasing step function. The production functions are differentiable almost everywhere.

The point of this example, that sometimes a vertically integrated firm will want to hire more labor per unit output at higher wages, is compatible with the existence of many more processes for producing each commodity. As more processes are used to construct the production functions, the closer they come to smooth, continuously-differentiable production functions. The point of this example seems to be compatible with smooth production functions. It also does not depend on the circular nature of production in the example, in which corn is used to produce more corn.

  • Pierangelo Garegnani. 1970. Heterogeneous capital, the production function and the theory of distribution. The Review of Economic Studies 37(3): 407-436.
  • Arrigo Opocher and Ian Steedman. 2015. Full Industry Equilibrium: A Theory of the Industrial Long Run. Cambridge University Press.
  • K. Sharpe. 1999. Notes and comment. On Sraffa's price system. Cambridge Journal of Economics 23(1): 93-1010.
  • Paul A. Samuelson. 1966. A summing up. Quarterly Journal of Economics 80(4): 568-583.
  • Ian Steedman. 1985. On input "demand curves". Cambridge Journal of Economics 9(2): 165-172.
  • Robert L. Vienneau. 2005. On labour demand and equilibria of the firm, Manchester School 73(5): 612-619.

Wednesday, August 24, 2022

Sraffa I/141: Correspondence Beween Marguerite Kuczynski And Piero Sraffa

A Bad Reproduction Of An Engraving Of Quesnay In Kuczynski And Meek

This folder consists of:

  • A 20 Sep. 1965 letter from Marguerite Kuczynski to Piero Sraffa. Sraffa’s handwritten annotation suggests his response is not in the archives.
  • Handwritten notes made by Sraffa.
  • An 18 Oct. 1965 letter from Marguerite Kuczynski to Piero Sraffa.
  • A 25 Nov. 1965 handwritten draft letter from Piero Sraffa to Marguerite Kuczynski.
  • An 18 Dec. 1965 letter from Marguerite Kuczynski to Piero Sraffa.
  • A typed copy of a 10 Feb. 1966 letter from Piero Sraffa to Marguerite Kuczynski.
  • A 26 Feb. 1966 letter from Marguerite Kuczynski to Piero Sraffa.
  • A 2 Dec. 1971 letter from Marguerite Kuczynski to E. A. G. Robinson.
  • A 9 Mar. 1972 letter from Marguerite Kuczynski to Piero Sraffa. Sraffa’s handwritten annotation suggests his response is not in the archives.
  • Notes by Marguerite Kuczynski. Sraffa’s handwritten note says this is a copy, and it starts with page 2. Presumably, the original was enclosed with Kucznski’s December 1965 letter.

This transcription needs checking more than usual. I dropped many accents and have not even attempted to ensure the french makes sense. I believe there are translations from some of the last document in Kucynski and Meek (1974). The letters from Kuczynski are on her personal letterhead. I find this to be part of an exciting story.

From Marguerite Kuczynski

Handwritten by Sraffa on upper left:
R. 11 Oct,
Sent copy of B, N. first edition dated 1956-58, but Pt. VI not.-p.

112 Berlin Weissensee, Sept. 20th, 1965
Parkstrasse 94

Pietro Sraffa, Esq.
Trinity College

Dear Sir,

A short while ago I published the long-lost "third edition" of Quesnay's Tableau Economique which it been my good fortune to locate. The reproduction is accompanied by a comparison with Mirabeau's more extensive explanation of the Tableau which he made on the basis of Quesnay's "third edition" and which he published in the Sixth Part of his Ami des Hommes. For that comparison, I was obliged to use one of the 1760 editions of the Sixth Part, and references to the Fifth Part of Ami des Hommes also make use of that same edition (1760). For so far, I have not been able to trace the 1759 edition of these two parts which Georges Weulersse, for one, mentions in his Mouvement physiocratique, Paris 1910, vol. I, pp. 69-70, note 7. The context is such that a printer’s error -- putting 1759 for 1760 - seems impossible, and I should consider it most unlikely that Weulersse would have mentioned this early edition had he not been certain that it existed.

In his Bibliography of Economics, 1751-1775, Cambridge 1935, p. 167, Henry Higgs also mentions the year 1759 in connection with the Fifth Part of Ami des Hommes: he lists an edition "Avignon, 1759, issued 1770, 12". Am I right in hoping that owing to your association with the work of Henry Higgs, you might be able to throw light on the sources which establish the date "1759"? And would have the kindness of enabling me to follow up these sources? (The year "1770" I have assumed to be a misprint for 1760.)

Please believe me most grateful for any help which you may be able to give me in the matter of dating Parts Five and Six of Ami des Hommes.

May I add a further query? Henry Higgs mentions (Introduction, p. XV) the work of "M. Daniel Morant who analyzed the contents of 500 private libraries belonging to ... notabilities in the time of Louis XV.". I have not been able to trace the work referred to and beg you to help me find it.

Very truly yours,

Sraffa's Notes

Marshall Library, Pryne Collection

LAmi des Hommes

Pt 1-4 "Nouvelle edition, augmentee d'une quatrienne Pourtie et de Sou.." N. P. 1759

Pt. 5-6 N. P. 1760

Pt 6 divided in two parts, the first "Response a la Voierie" the second ("Suite de la VI Partie") the "Tableau Economique avec ses explications" This latter has at the end a whole page of extracts (Fautes a corriger)

From Marguerite Kuczynski

112 Berlin Weissensee, Oct 18th, 1965
Parkstrasse 94

Piero Sraffa, Esq.
Trinity College

Dear Mr. Sraffa,

Thank you very much indeed for your very detailed answer to my query. I’ve examined the editing of L'Ami des Hommes, 1756-1758, 7 tomes en 6 parties en 2 vol., in 4, in the Munich State Library: the fifth part bears the year 1760. I shall of course follow up your suggestion and write to the Librarian of the Goldsmiths' Library. I shall be at the Bibliotheque nationale shortly, but I am not in great hopes of finding such there, in the particular respect.

As to my reproduction of the "third edition" of the Tableau economique, I am forwarding a copy to you under separate cover. I would appreciate it very such indeed if you would give me your critical remarks on the publication.

Yours sincerely.

From Piero Sraffa

25 Nov 65

Dear Mrs Kuczynski

It was most kind of you to send me a copy of your edition of the Tableau econ. It is really a most welcome discovery remarkable really a sensational feat to have found this edition, for which has eluded so many people who have been tried before looking for many years, and I should like to I congratulate on your success discovery and on the excellent presentation and annotation.

I have tried hard therefor to satisfy your request As you ask me for critical remarks and here is this here this is the best, or rather the worst, I can do. It seems a little is [unclear] unfortunate that the facsimile should be an enlargement not be in the original size: the grounds requirement of legibility which you mention could have been satisfied met by reproducing from good full size photograph instead of a microfilm. Also your printer has betrayed you on Page ij, line 9 (cp. Errata) – not 400, nor 500, but [crossed out] 100! (he has also left a humble revealing fingerprint by [crossed out] adopting the wrong font for, 1 instead of I)

I had not a little trouble understanding what it is that you meant in connection with referring to as with the "Korrektur-fragment" until I [crossed out] note 12 and saw that note 12 must be read as part of the text.

This is the best, or rather the worst I can do. If I find any other big and quite small points, when I come to read it more carefully, I shall write again let you know. (I have an idea of proposing writing preparing a notice for for the Economic Journal). By the way, it would have been interesting if you had told the full story of how you came to discover it.

Thank you again

Yours sinc

From Marguerite Kuczynski

Gorisch/Erzgebirge, December 18th, 65
as from Berlin Weissensee
Parkstrasse 94

Professor Piero Sraffa
Trinity College

Dear Professor Sraffa,

Please do excuse this very belated acknowledgement of your letter of November 25th: the last weeks in Paris and the ensueing week in Berlin have been rather hectic. But we have now come here for a few days of rest (my husband returned from a prolonged stay in Cuba just as I came back from Paris), and one of the very first things I would like to do in this very peaceful place is to thank you for the very kind letter you wrote to me about "my" Quesnay. Please let me say that I appreciated very much indeed the fact that you discovered th error on p.ij of the reproduction! I have been guilty of a twofold negligence there: 1. Thinking that I finally convinced the printers that they were in no way to touch up what seemed to them deplorable irregularities in printing, I did not do sufficient proof-reading the pages reproduced from the films and I discovered the "correction" of what the printers had taken to be an ink-spot too late to have an erratum inserted; 2. in sending you a copy from Paris, the stress of the work there made me forget to point out to you this blotch on the edition.

I have been repeatedly been asked how I came to discover the edition. For quite some time I tried the ordinary hiding places - libraries archives, monasteries etc. in Europe and in Japan; neither this, nor a notice which Jean Maitron published in his "Revue" in 1962, brought forth anything new. I finally followed up a hunch that the striking similarity in the astounding degree of reticence observed by Schelle when he wrote his life of Du Pont de Nemours (1888) and his article on the "edition definitive" (1905) augured, in spite of the many years between the two publications, one common cause: the Du Pont family itself. The enquiry about the whereabouts of the books and papers left by Du Pont de Nemours led at once to the discovery of the "3rd edition". (I have assembled a sort of tableof parallels which you may like to see. That means that I shall have to delay the sending off of this letter until I shall be back in Berlin. If you would let me have the list back after having done with it, I would appreciate it.)

May I, in concluding, thank you for your idea that you may write a notice on the republication of the "3rd edition" for the Economic Journal. I would be most happy about your doing this?

Sincerely yours,

From Piero Sraffa

Trin. Coll.
10th February, 1966

Dear Mrs Kuczynski

I must apologize for my delay in replying to your most interesting letter of last December. It reached me in Italy, where I did not have by me the relevant books, and I only returned here after a prolonged vacation.

I found the study of the steps in your argument absolutely fascinating and greatly admired the perspicacity which enabled you to achieve this remarkable success.

I do hope that you will publish the full story as well as presentations in French and English of the newly formed Tableau. It will not only make exciting reading as a piece of detection, but it should inspire others by showing what results can be obtained by bringing a fresh mind to bear on puzzles which had defeated generations of foot-sloggers!

Did you get the answer about the "1759" edition of the 5th Part of l'Ami des hommes?

With kind regards,

Yours sincerely,

P. S.

P.S. I found that the Economic Journal had already sent to a reviewer your Tableau. But I may have another chance with your next publication.

From Marguerite Kuczynski

112 Berlin Weissensee, Febr. 26th, 1966
Parkstrasse 94

Professor Piero Sraffa
Trinity College

Dear Professor Sraffa,

I do thank you for the very kind letter which accompanied the notes which I had sent you on the steps taken to find the Tableau. Indeed, your letter encouraged me to write up the material into an article (a Japanese journal had asked me for a contribution dealing with the Tableau).

As to your questions about the 1759 editions of Parts V and VI of L'Ami des Hommes, I have, for the time being, come to the reluctant conclusion that the earliest edition may well be the one published as vol. III of the 1760 4-edition. Of two contradictory statements of Mirabeau's, the one which establishes the date as 1760 was written in 1760 and eight years before the other one. I should have preferred it to be the other way around, of course.

May I say that I am sorry you will not be reviewing my Tableau-edition?

With best wishes

Sincerely yours,

From Marguerite Kuczynski to E. A. G. Robinson

112 Berlin Weissensee, December 2., '71
Parkstrasse 94

Professor E. A. G. Robinson
Secretary, The Royal Economic Society
The Marshall Library
Sidgwick Avenue

Dear Professor Robinson,

I have just received a first copy of our Tableau-edition. It is beautifully printed and beautifully set up, and the engraving, so kindly furnished by Piero Sraffa, adds such a fine touch to it. I do thank you for all the trouble you have taken with the edition!

Since we are already in the month of December I would like to add the season’s greetings and my very best wishes for the coming Year.

Sincerely yours,

From Marguerite Kuczynski

Handwritten in upper left:
R 19 going to Italy for a few weeks
Not yet rec’d book. If on my return, have anything of interest, will write.
Reviews, Economica, U. S. journal hist. of theory. In Italy, G. d. E.

112 Berlin Weissensee, March 9, 1972
Parkstrasse 94

Piero Sraffa, Esq.
Trinity College

Dear comrade Sraffa,

I have to-day posted to you the first volume of my German edition of Quesnay's main economic writings. It covers the years 1756 to 1759, trailing a bit into 1760. It should of course have gone to you already about the middle of January but I have been hard pressed for time (and by ill health) and am only now beginning to catch up.

You may be interested in some of the new materials I have used, among them perhaps No. 4, p. 813; No. 10, pp. 814-815; No. 14, p. 816); and I need, of course, not say, how very much interested I would be in any comments you may have in the edition.

A review copy of this volume has of course been sent to the Economic Journal. Perhaps Professor Robinson will have passed it on to Ronald Meek (who is, I suppose, still in England? I have not heard from him since June of last year). If you have any advice as to additional reviews in England, or, for that matter, in Italy where no copies have been sent so far, I would gladly pass on your suggestions to the publishers.

In my work on the second Quesnay-volume I find that I am using the English Tableau edition quite a bit. It is so very useful to have the three Tableaus together (I have complete the first edition" by two "Remarques" pages). And it is such a pleasure to work with such a beautifully printed book. Please, believe in my gratitude for all you have done to give this volume its shape and beauty.

With many good wishes,

Notes by Marguerite Kuczynski

I decided to start from the indications contained in Schelle's Du Pont de Nemours et l'Ecole physiocratique and to disregard, for the time being, the odd period of time which had elapsed between that publication, in 1880, the piece-meal revelations on the Tableau in 1905. I did this because

  1. the pattern of reticence was so much the case the same in the two publications that it suggested a cause common to both cases – the Du Pont family’s inordinate insistence on anonymity;
  2. the chapter on the descendants of the physiocrat Du Pont suggested that family papers etc. were more likely to be found in the USA than in France, for instance:
  3. not only the pattern of reticence was similar: the period at which the Du Ponts themselves came a bit out of their reserve coincided rather closely with the resumed publication, on the part of Schelle, of unknown matter concerning Quesnay and Turgot and, a little latter, with nisecsening anonymity of his acknowledgements to the owners of the Du Pont documents.

I have assembled the more important quotations from the 1888 study on Du Pont:

"Sans la bienveillance que nous a temoignee sa famille, nous aurions meme renomce a achiever notre tache, mais grace a elle, nous avons pu poursuivre nos recherches sans trop do difficiltes et les appuyer sur des documents dune valeur exceptionnelle" (p. 5).

"Bien que ces precieux papiere soient aujourd’hui en Ano-rique, il nous a ete donne d'en consulter les parties les plus interessantes" (p. 5).

"Nous avons ou notament, entre les mains, copie de plus de trois cente lettres que Turgot adresse a (Du Pont) ... Nous n’a-vone pas ou la permission de publier cette correspondence, ... mais nous avons pu citer quelques passages do ces lettres et nous y avons fait de nombreux emprunts" (p. 5 and 6).

"L'un des arridre-petits-fils de Du Pont de Nemours a bien voulu on outre nous fournir d'indications dd detail, ou revir, corriger et completer avec un soin extreme la bibliographie qui toraine ce livre" (p. 6, note 2).

"Nous pourrione aussi signaler in grace bienveillante des lettres de la seule fille d'Irenee (son of the phsiocrat DP de N. - M. K.) qui soit encore vivante; mais nous ne veulone parler due des morte" (p. 395).

Everything rather pointed to America and, I repeat, it is only when I started following the old spoor that I got to the lair.

I admit that I hesitated for some time to follow the spoor to the end. For one thing, I had, in the eyes of such a family, not even the virtue of being an ancestor's biographer. When I finally did take the plunge I discovered that the papers and books that had belonged to the physiocrat Du Pont had passed -- at least sufficiently for my purposes -- out of the family’s immediate control into the Eleutherian Mills Historical Library and had thus become to some extent public property

That is the story. I have in addition jotted down, on a separate page, some of the particular dates, which illustrate my point 3 above.

Juxtaposition of some dates on the Du Pont and Schelle side
Du Pont familySchelle
After a long struggle on the part of the family, Rear-Admiral Du Pont is largely exonerated from the charge of having lost an important Civil War naval battle in 1865.
Strictest anonymity is preserved regarding all living members of Du Pont family who gave documents and information toward the biography of the physiocrat Du Pont de Nemours.
Henry Algernon Du Pont, later US senator, retires from business (railways, among other things) and devotes himself to literary and historical pursuits.
Schelle retires from his work at the ministry of public works (railways) and devotes himself to economic and literary studies. Among a number of other articles he publishes in
H.-A.Du Pont publishes, for private circulation only, a small edition of L'Enfance et la Jeunesse de Du Pont de Nemours, Paris 1906.
Parts of the "3rd edition" of the Tableau economique. Strictest discretion as to the source of the discovery.
Gabrielle Josephine Du Pont de Nemours (the lady whose bienveillance Schelle mentions in his 1888 study, p. 5997 – M. K.) brings out as "publication strictement privee", and in an edition limited to 50 copies, Souvenive de Madame V. M. du Pont de Nemours, Wilmington.
La Vie de Turgot, Paris
Released (?) from preserving the anonymity of at least one member of the Du Pont family, Schelle writes in the preface to vol. 1 of his Oeuvres de Turgot: “J’avais ou le Bonheur d’entretenir depais (la preparation de Du Pont de Nemours et l’Ecole physiocratique) avec le descendant de ce dernier, le colonial Du Pont, senateur des Etats-Unis, des reations affectueusse” (p.11).
Even in the edition of Turgot’s works there is no precise indication of the whereabouts of the long series of letters from Turgot to Du Pont (1763-1781) whereas
in all other cases the location of the documents included is meticulously set down for each individual item.
H.-A. Du Pont publishes, for normal circulation, The Early Generations of the Du Pont and Allied Families, New York.
Schelle finishes publishing his Turgot edition.

Saturday, August 20, 2022


  • INET has a collection of links in memory of Lance Taylor.
  • Alex Thomas has a focused review of A Reflection on Sraffa’s Revolution in Economic Theory, which was edited by Ajit Sinha.
  • John E. King has an overview in Jacobin, of Paul Sweezy's work.
  • Ian Birchall, also in Jacobin, tells us about Daniel Guérin. I have read his Anarchism, but I am currently reading Iain McKay's Proudhon collection.
  • Monthly Review reposts Ksenia Arapko's review of Michael Heinrich's How to Read Marx's 'Capital'. I found that not knowing the first edition, which variants Marx added in the French edition, and so on, I did not really know the opening chapters.
  • I want to note the existence of symposia on intangible capital and on human capital in the summer 2022 issue of the Journal of Economic Perspectives. The first has three articles and the second has two.

Friday, August 19, 2022

Sraffa I/33: Alexander Gray to Gerald F. Shove

This is about Shove's review of The Socialist Tradition. Apparently Gray does not take those important in the development of economic thought seriously. Since Piero Sraffa is neither the recipient nor the sender, and the topic is not his work, maybe the editors of his collected works should not include this.

8, Abbotsford Park,
Edinburgh. 10.
3rd November, 1946

Dear Shove,

(If the fact that we occupied adjacent seats on the occasion of one of my rare visits to the Annual Meeting of the Economic Society justifies this assumption of familiarity) - I should like, if I may, to exchange friendly greetings on the excuse of your review of my Socialist Tradition.

First of all I should like to say as a sheep before the shearers is dumb, so in general a reviewee ought to open not his mouth. Nevertheless, I would like to thank you for your kindness: I gather the perusal of my interminable book was not an unusually burdensome task, and I am grateful to you for passing on to others an implied hint that they might do worse than read it, -- if they have time!

This should perhaps be the end of the letter; but even if the sheep should be dumb, perhaps I may classify myself as a tender lamb, and in this capacity be allowed a few bleats by way of comment on your comments.

First of all, as to your main criticism, I agree and plead guilty. I am aware that my various chapters are too independent of each other: in fact when I said something in the Preface to the effect that the chapters were reasonably self-contained, I said this partly in self-criticism. For in a book like this, the chapters should not be too much independent of each other. I can only plead that this springs partly from the way the book arose; and partly from my make-up and (may I say it?) modesty! It does not require much insight to see that the book represents more or less lectures which I given to certain students in alternate years for the last quarter of a century more or less, the dose of course varying somewhat each time. And in these circumstances one tends to skip lightly from one mountain summit to the next. Also perhaps I am more interested in people than in movements; and distrust my power to write that complete history in which all my characters would be integrated with the history of their times. I am glad that you also have a regard for Paguet. I attended his lectures in 1904; and I have always looked upon him as the supreme lecturer and expositor. But, looking back, I think that perhaps he also may have been subject to the criticism you have passed on me. Also perhaps I may say, in the light of your observations, that the title of the book is by no means what I wished to call it. Down to the Galley proof stage, I called it Towards a History of Socialism, meaning thereby that is was a mere contribution to be supplemented later by a better writer, or supplemented now by reference to other books dealing with other aspects and phases. But the Publishers -- and who can resist the publishers -- told me that the title would just not do at all. So I fished round for the second best: but I have always known it was only a second best.

So far we are in agreement! But there are two points on which I should like to utter a minor bleat -- not of protest, God forbid, -- but of comparative innocence: or at least a mild suggestion that I am not as guilty of certain shortcomings as you suggest. Even with the limitation imposed by my 'selective' method of treatment, it was obviously my duty to link up, and consider the permanent legacy of my exhibits. I certainly intended doing so; and I thought I had! But obviously I have not done it well enough. If I may illustrate what I mean: you mention Saint Simon. I certainly point out his relation to Comte and to Carlyle; I point out his relation to all the big-business stuff and the idea of technocracy; I underline his relation to what we still have, the desire to separate administration from politics; through the Saint-Simonians, I indicate that he led by a short-cut to much of Marx. And I specifically refer to him as 'one of the great influences of the 19th century'. Doubtless one could have said all these things at greater length in a book: but I am not sure that I could have done much more in a chapter of 30 pages.

Again at the top of p. 444, you say that I hardly bring out the extent to which Marx draws together the threads running through the writings of his contemporaries and immediate predecessors. I use a different metaphor; but if you look at p. 299, you will see that I am quite alive to the point. I say that he collected his bricks from many masons' yards, but used them to construct a building to his own design; and thereafter, doubtless inadequately, I indicate in the next page and a half a number of the sources from which he drew these bricks. And while on Marx, and the suggestion that my treatment of the M.C.H. is an example of failure to ask whether there may not be a 'substratum of significant truth', I would in the mildest tone point out that in summing up on Marx, I say that the most significant and enduring portion of Marx is contained in the Materialist Conception of History.

The other minor bleat I should like to utter is against myself and not you. I should be sorry if you got the impression that I was not taking my subject seriously, -- indeed almost to the point of regarding the whole socialist and anarchist tradition as a joke. God forgive me: apart from government activities which come and go, this is the only thing I have taken seriously in the last 25 years! Nor would I poke fun at any of my sitters: with very few exceptions, I love them too much. I would suggest, for instance, that I am just about the first person (in English at least) who has given Proudhon a fair run for his money (I think Brogran is rather disappointing on Proudhon). In my youth he was looked on as a dreadful person who said that God was evil; and he also said that if any one deserves to be in Hell, it is God. I have almost made it possible for a Scots Elder to shake hands with him. Nor would I admit that my book is a Fool's Gallery: in the earlier stages, a Gallery of Eccentrics, if you like: and therein lies their fascination. I may have failed ignominiously at what I tried to do; but I had hoped that I was giving every one a fair run. Though I do not say so, my Preface is chiefly directed towards Hearnshaw, for whom, if a man is called a Socialist, it is already sufficient proof that he is also a twirp and a twister and also a consummate fool. I certainly had no intention of compiling a record of folly. You will observe that in the Preface I say that the Socialists are interesting, because, among other things, they are prophets. In the concluding Chapter (p. 506) I say that 'much of what the socialists contended for forty years ago has passed into a fairly general acceptance in the minds of the population at large'. With this as my beginning and end, I do not think that I can quite fairly be regarded as in search of folly undiluted with wisdom.

You ask two specific questions.

(i) I have no doubt you are right about the date of the conversion of the Marx household. I shall look it up. I see that I speak of a 'recent conversion' which is reprehensively vague. If I am not exactly trembling on the brink of a Second Impression; I am at least on the brink of that point in the stage of exhaustion of the First Impression when the Publisher asks for a complete list of all misprints etc with a view to a second impression (And there are a Hell of a lot of French accents that have gone astray!) And if I can get it done I shall put this right.

(ii) On the St. Luke and St. Matthew point, I rely on the authentic text alone. It is obvious that Luke gives an abridged version of what is in Matthew. The fuller text is, I should think, the more correct: and the abridgement, whether intentionally or not does not greatly matter, has been made in such a way as to convert the spiritual hunger into a physical hunger etc. I do not know what the theologians would say to it. Needless to say, in this age, when we all get our ideas from others, I got this idea also from elsewhere. It was put into my head by Adler, Geschichte des Sozialismus.

I hope that you do not regard this as a querulous letter: it is not so intended. Meanwhile as a token of appeasement and an emblem of good will, I enclose a copy of a book which I see I published 14 years ago. You may understand the lengthy Introduction, if you do not understand the body of the Book. I send it to you chiefly that you may see what I look like when I am in fact not taking my subject seriously.

Yours sincerely,
Alexander Gray

I do not know who Paquet or [F. J. C.?] Hearnshaw are.

Anyways, The Socialist Tradition did undergo a second impression in 1947. Gray does not like Marx and writes in a straightforward, non-Hegelian style. Topics covered include Plato, the Old Testament, the New Testament, church fathers such as Thomas Aquinas, and Thomas More and a couple other utopians. Gray writes about Rousseau some others who I do not recognize. William Godwin, Saint-Simon, Charles Fourier, Robert Owen, Louis Blanc, and Proudhon each get a separate chapter. (I finally have Iain McKay's collection of Proudhon's writing on order.) English Ricardian socialists have most of a chapter. Marx and Engels are grouped with Lassale and Rodbertus in a chapter on "scientific socialism". Gray writes about some anarchists. Fabians and Eduard Bernstein are in a chapter on "evolutionary socialism". Syndicalism, guild socialism, and Lenin are the three final substantial chapters before a Postface. One could certainly argue about some of these selections and groupings, but the book seems quite comprehensive. With the index, it is 523 pages.

  • Alexander Gray. 1937. The Development of Economic Doctrine: An Introductory Survey.
  • Alexander Gray. 1946. The Socialist Tradition: From Moses to Lenin.

Thursday, August 11, 2022

Nonsense Taught At MIT

First Lecture For MIT Microeconomics

I associate Jonathan Gruber with Obamacare. I think the Affordable Care Act is totally insufficient and a great advance. If politicians hire you to model the effects of some policy change, might you want to use, more or less, the most widely accepted techniques? I am also appreciative that I can watch this.

When you are teaching, should you present claims in the most romantic way possible?

"That is why I can teach you the entire field of microeconomics, which is really sort of - macro is kind of a fun application - micro is really economics." (around 9:20)

Thinking of (micro)economics as a matter of constrained optimization is only one approach. I like the idea of investigating the conditions needed for a capitalist economy to reproduce itself. This is mesoeconomics, I guess, but should be mentioned in an honest class on microecnomics.

From Thomas Kuhn, I know history of a subject is often widely distorted in introductory courses. Is this justification for spouting nonsense?

Adam Smith did not have a supply and demand model, that is, of an equilibrium price formed by the intersection of a supply curve and a demand curve (balderdash after about 11:23). Mashall's scissors certainly do not appear in Adam Smith's Wealth of Nations. Maybe Gruber should note the difference between market prices and natural prices. The model Gruber's teaches is known to be incoherent nonsense, not derivable from basic first principles.

Can one coherently talk about a value-free postive economics? I guess saying that a distinction exists between positive and normative economics does not say that positive economics is value-free. But it certainly suggests that. What Gruber presents (after 34:30) for examples is enlightening, albeit not necessarily in the way that he intends. Do some teachers of introductory courses talk about Schumpeter's "vision"?

If economics is a science, why do this preaching after 26:30? By the way, do the Seninelese have a capitalist economy? Or do they practice Stalinist central planning? How about the society envisioned by the P.O.U.M. in Barcelona during the Spanish Civil War?

Update (13 August 2022): Lecture 5 is on production theory, supposedly. If economists were scientist, one would not be able to discomfort them by asking about units of measure for variables in their equations, such as K.

Sunday, August 07, 2022

Correspondence Between Rudiger Soltwedel And Piero Sraffa

This is C/294 in the Sraffa archives. Rudiger Soltwedel had his own letterhead.

D 66 Saarbrucken 3, 28. Febr. 1968
Waldhausweg 7
Evangelisches Studentenheim

Professor Piero Sraffa
Trinity College

Dear Sir,

I am student of economics at the University of Saarbrucken and I just began my finals work for my diploma.

The topic of this study that Prof. E. Schmen formulated is your essay and its title is exactly that of your book: ‘Sraffa’s production of commodities by means of commodities’.

My task is to state the intention of your book and to explain its relation to input-output analysis.

After looking around in literature I only found three reviews (AER: Reder; Ec. Journ.: Harrod; Jorn. Of Pol. Econ.: Quandt; all 1961) but nothing beyond that.

I would be very indebted to you if you could give me some hints of literature directly concerned with your book or with its subject.

At the moment, I think the aim of your study not to be a theory of distribution or a development of input-output analysis, but rather a theory of price-determination in input-output models, given the physical amount of the surplus, economy in equilibrium and infinite elasticity of factor supply. The outcome is an antithesis to what Dorfman/Samuelson/Solow said about relative prices in the Leontief-model: "... in a Leontief-technology relative prices can’t change". (Lin. Programming …, p. 224) in saying that they have to change with changes in distribution of the surplus, And, finally, the profitability of distinct methods of production is dependent on the distribution of the surplus to wages or profits respectively.

This is a bird-eye look on your essay and it is not equivalent to a complete understanding of it. In particular it is the chapter V that charges my brains with its argumentation of extreme density.

I hope that you are willing to excuse my attack on the ‘pater spiritorum’ and would be very thankful for some advice on your part.

Yours respectfully,
Rudiger Soltwedel

Underlines are presumably Sraffa's. "in equilibrium" and "elasticity of factor supply" have underlines in squiggly lines, while the others are solid lines.

Trinity College

Dear Mr. Soltwedel,

Thank you for your letter. I shall try to help you as far as I can in a short letter. As regard my aims, I have kept them in the background in the hope that the constructions offered might be of use to others, who have different standpoints. I have given hints in the Preface and in Appendix IV. The reviews you have are not very helpful. Reder, in particular, is a string of misunderstandings. A good review is that of Peter Newman, in Schweitrerische Zeitschrift fur Volkswirtschaft u. Statistik, No. 1 of 1962, p. 58-75. I disagree with many of his points & had some correspondence with him; we came only to partial agreement, but his review is a good piece of work. There were also good reviews in the Economic Record (Australia, Sept. 1964, p. 442 ff. by Harcourt and Massaro) and in the Economic Weekly (Indian, 24 Aug. 1963, by Krishna R. Bharadwaj). By the way, I replied to Harrod in the June 1962 number of the Economic Journal (p. 477-9).

As regard your own your own interpretation, I must say frankly that you have gone astray the moment you speak of "equilibrium" or of "elasticity of factor supply": all the quantities considered are what can be observed by taking a photograph. There are no rates of change, etc. This point of view was that of the classical economists (e.g. Ricardo) whereas supply & demand curves were introduced in the middle of the 19th century. Economists are now obsessed with them and cannot think without them. My chapter V, which gives you such a headache, could be understood as an attempt to solve a problem set out by Ricardo, & which I described in my Introduction (sections IV & V) of Vol. I of the Works of Ricardo, 1951.

With good wishes for your work,

Yours sincerely
Piero Sraffa

Any errors in journal names, numbers, pages are presumably from my transcription.

66 Saarbrucken 3, 12. ??. 1968
Waldhausweg 7
Evangelisches Studentenheim

Dear Sir,

I thank you very much for your kind reply to my letter.

There was good progress in my work based on your remarks and on the reviews mentioned, in particular the mathematical proof of some propositions in the work of Newman was of great help.

But there is a point in nearly all reviews I don’t agree with and that receives illumination by your book: the claim of the rates of profits being the same in all industries is interpreted as a condition of long run competitive equilibrium prices. Now the structure of your economy is far away from ??determined by competition that this approach does not fit the problem. It looks like a challenge consequent upon a distinct notion of justice in distribution (that could, however, be attained through perfect competition). Unfortunately, your book provides no explanation.

I hope it not to be too unconscionable asking for another explanation.

Yours sincerely,
Rudiger Soltwedel

Sraffa has handwritten “given up” on the top of this letter.