Some Positions Some Take On Sraffa's Book

This post lists some views on Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory.

• The quantity flows Sraffa takes as given are those observable in an actual economy at a given time, as with a snapshot (Roncaglia 1978).
• These quantity flows, on the contrary, are at the level of effectual demand (Garegnani 1990).
• These quantity flows are for an economy in a self-replacing state.
• The assumption of constant returns to scale is necessary for drawing any interesting conclusions from Sraffa's work (Samuelson 1990, Samuelson 2000).
• Market prices tend towards or orbit around Sraffa's prices of production in a process akin to gravitational attraction (Garegnani 1990).
• Sraffa's book is an investigation of logical consequences in a system of prices of production, akin to reasoning in geometry; no claims are put forth about tendencies or paths of market prices (Sinha 2012).
• Sraffa started, in the 1920s, in his research for his 1960 book from labor values and Marx's schemes of reproduction in Volume 2 of Capital (De Vivo 2003 and Gilibert 2003).
• Sraffa began, on the contrary, with a formalization of prices in terms of physical real cost; labor values are a corruption of this notion of real costs and Sraffa was not originally inspired by Marx in his economics (Gehrke and Kurz 2006).
• Sraffa showed that labor values are unnecessary and redundant for defining prices of production (Steedman 1981).
• Sraffa, on the contrary, vindicated Marx in his work (Porta 2012 and Bellofiore 2014).
• Sraffa's work cannot be set in historical time (Robinson 1985).
• Sraffa, for methodological reasons, rejected counterfactual reasoning and thus the marginal revolution (Sen 2003).

Some of the above statements are probably stated more strongly than the referenced scholars might endorse. I am also not at all sure those are the best references. They certainly are not the most up-to-date. It is clear at any rate that the Cambridge Capital Controversy was not solely about difficulties in aggregating capital and that Sraffa's approach to economics cannot be subsumed by general equilibrium theory (Hahn 1982).

References

• Bellofiore, Riccardo. 2014. The loneliness of the long distance thinker: Sraffa, Marx, and the critique of economic theory. In Bellofiore and Carter (2014).
• Bellofiore, Riccardo and Scott Carter. 2014. Towards a New Understanding of Sraffa: Insights from Archival Research. New York: Palgrave Macmillan.
• Bharadwaj, Krishna and Bertram Schefold (eds.). 1990. Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory. London: Unwin Hyman.
• de Vivo, Giancarlo. 2003. Sraffa's path to Production of Commodities by Means of Commodities. An interpretation. Contributions to Political Economy 22 (1): 1-25.
• Garegnani, Pierangelo. 1990. Classical versus Marginalist Analysis. In Bharadwaj and Schefold (1990).
• Gehrke, Christian & Heinz D. Kurz. 2006. Sraffa on von Bortkiewicz: Reconstructing the classical theory of value and distribution. History of Political Economy 38 (1): 91-149.
• Gilibert, Giorgio. 2003. The equations unveiled: Sraffa's price equations in the making. Contributions to Political Economy 22 (1): 27-40.
• Hahn, Frank H. 1982. The neo-Ricardians. Cambridge Journal of Economics 6: 352-374.
• Kurz, Heinz D. (ed.). 2000. Critical Essays on Piero Sraffa's Legacy in Economics. Cambridge: Cambridge University Press.
• Porta, Pier Luigi. 2012. Piero Sraffa's early views on classical political economy. Cambridge Journal of Economics 36: 1357-1383.
• Robinson, Joan. 1985. The theory of normal prices and the reconstruction of economic theory.
• Roncaglia, Alessandro. 1978. Sraffa and the Theory of Prices (trans. by J. A. Kregel). New York: John Wiley & Sons.
• Samuelson, Paul A. 1990. Revisionist findings on Sraffa. In Bharadwaj and Schefold (1990) and reprinted in Kurz (2000).
• Samuelson, Paul A. 2000. Sraffa's hits and misses. In Kurz 2000.
• Sen, Amartya. 2003. Sraffa, Wittgenstein, and Gramsci. Journal of Economic Literature 41: 1240-1255.
• Sinha, Ajit. 2012. Listen to Sraffa's silences: a new interpretation of Sraffa's Production of Commodities. Cambridge Journal of Economics 36 (6): 1323-1339.
• Steedman, Ian. 1981. Marx after Sraffa. London: Verso.

Contrasting Views On Sraffa's Mathematics

"...Sraffa's prices produce questions, besides whatever else, about the mathematics of his arguments." --S. N. Afriat (2008) "Sraffa's Prices", Sraffa or an Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan.

Here are two perspectives:

"I think that a very important difference exists between: (i) the process through which a mathematical result is reached, and (ii) a rigorous proof of the result. ... Regarding (i) I mean a sequence of mental objects: examples that appear to contain all of what is essential, graphical tools providing proofs that are only valid for dimensions two or three, incomplete proofs that appear as 'almost' correct, auxiliary constructions that show what is not immediately visible in the problem..."

...We know that all the results contained in Production of Commodities, Part I, can be restated in the language of standard mathematics (matrix theory, eigenvalues, eigenvectors, Perron-Frobenius Theorem, etc.) and rigorously proved. My opinion ... is that Sraffa's presentation is closer to the process that I have indicated by (i) in the Introduction, than to formal proofs. In some cases Sraffa's arguments are defective or insufficient, in others they introduce useless complications." --Marco Lippi (2008) "Some Observations on Sraffa and Mathematical Proofs with an Appendix on Sraffa's Convergence Algorithm", Sraffa or an Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan.

Lippi's position that Sraffa's mathematics contains defects is strengthed by his demonstration of a bug in Sraffa's algorithm for the construction of the standard commodity.

Is Velupilla in disagreement:

"From a purely mathematical point of view, PCC lacks nothing. The concerns in PCC are the solvability of equations systems and, whenever existence or uniqueness proofs are considered, they are either spelled out in completeness, albeit from a non-formal, non-classical point of view or detailed hints are given, usually in the form of examples, to complete the necessary proofs in required generalities. Pure laziness, inertia and ignorance of alternative traditions in mathematical philosophy have caused untold mischief and created an industry of re-casting and distorting PCC, a work of aesthetic purity and mathematical elegance, into a trivial application, to a large extent, of linear algebra." --Kumaraswamy Velupillai (2008) "Sraffa's Mathematics in Non-Classical Mathematical Modes", Sraffa or an Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan.

Velupilla is severely critical of the use of Perron-Fobenius theorems in the recasting of Sraffa's theory, when Sraffa essentially gave a constructive proof in demonstrating the existence of the standard commodity.

Robert Murphy On Sraffa: In Error

Some discussion with Peter Boettke has inspired me to point out some technical mistakes in Robert Murphy's on-line comments on Sraffa and reswitching.

I begin with Murphy's comments on reswitching. He looks at Samuelson's example in Samuelson's "Summing Up" article. Murphy implicitly suggests that reswitching is only possible in models in which a finite number of techniques are available:

"What Samuelson has done is simply invent a fictitious world in which there are only two ways of producing a particular good... Böhm-Bawerk felt that [his] story was accurate, because at any given time there are more technically efficient but very time-consuming processes 'on the shelf' that are unprofitable at the market rate of interest, but would become profitable at lower rates."

But reswitching is possible when a continuum of techniques lie along the so-called factor price frontier. That is, the possibility of reswitching is consistent with the existence of an uncountably infinite number of techiques. It is also consistent, of course, with the existence of only a countably infinite number and only a finite number of techniques.

Murphy also writes an equally informed comment on Sraffa's book, The Production of Commodities by Means of Commodities. I will adopt Austrian - in fact, Misian - terminology. Sraffa compares prices in Evenly Rotating Economies (EREs) in which the same commodities are produced with the same inputs. Under Sraffa's assumptions in the first part of his book, the construction of the so-called factor price frontier is perfectly valid mathematically. Murphy notes that Sraffa does not model utility-maximization and states that if utility maximization is introduced into the model, the location on the frontier becomes determined uniquely:

"Sraffa's techniques leave no room for the individual members of society to influence the methods of production that end up being used (whether or not there is a surplus), ultimately because there are no individuals in Sraffa's models... However, if we also require that the market rate of interest reflects the subjective premium placed by consumers on present versus future consumption—a feature lacking in Sraffa's aggregate models—then this will eliminate the multiplicity of equilibrium rates of interest."

But Murphy is, again, mathematically incorrect. Multiple equilibrium rates of interest can arise in an ERE model with utility maximization, including intertemporally.

One might look outside a model of an ERE. Murphy suggests he wants to consider models of an approach to an ERE:

"Sraffa's method of determining equilibrium prices in a surplus economy already assumes that the system has settled down at the optimum level of production in all possible lines."

The Arrow-Debreu model of intertemporal equilibrium, despite all its problems, is sufficient for my point here. In such a model of an economy not in an ERE, the equilibrium rate of interest at any point in time for loans of a given length is also not necessarily unique. Not only can multiple equilbrium rates of interest arise, so can a continuum of equilibrium interest rates, if the technology is modeled as discrete.

Why might Murphy be inclined to insist on mathematical error? Consider his statements:

"Sraffa derives results that depict a tradeoff between the real wage and rate of profits. In particular, Sraffa's analysis suggests that in a developed economy, the proportion of the 'surplus' that goes to the workers versus the capitalists is arbitrary, and not at all 'determined' by technological or economic facts... Although he was wrong to condemn interest as an unnecessary and exploitive institution, Sraffa was perfectly correct to criticize the conventional, mainstream justification of the capitalists' income."

But none of these claims, including about exploitation, are made in Sraffa's book.

On Ajit Sinha On Sraffa

Over at the Institute for New Economic Theory (INET), Ajit Sinha discusses the Sraffian revolution. Scott Carter cautions that, in interpreting Sraffa's thought, his archives have barely been touched.

Sinha's article has this blurb, with which I entirely agree:

"The prominence of the debate over 'reswitching' has obscured the importance of Piero Sraffa's profound contribution to economics. It's time to revisit and build on that body of work."

One can agree with the above without following Sinha very far. In analyzing the choice of technique, I often point out more than reswitching. I try to find effects in other markets than the capital markets and go in other directions. Since my motivation for working through these examples is frequently an internal criticism of neoclassical economics, I am frequently willing to assume Constant Returns to Scale and perfect competition, in the sense that firms take prices as given. One might argue that this misses Sraffa's point. Besides one can use 'reswitching' as a synecdoche for such analyses of the choice of technique.

How do I know that Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory was about more than Sraffa effects, as seen in the analysis of the choice of technique? Only the last chapter in the book deals with the choice of technique. (Maybe, earlier chapters on joint production, rent, and fixed capital might have been clearer if they came after this chapter.) Sraffa doesn't present this one-chapter, final part of his book as a climax that all before is leading up to. In fact, he explicitly says, in the first paragraph, that the status of that chapter is somewhat different from the rest of the book:

"Anyone accustomed to think in terms of the equilibrium of demand and supply may be inclined, on reading these pages, to suppose that the argument rests on a tacit assumption of constant returns in all industries. If such a supposition is found helpful, there is no harm in the reader's adopting it as a temporary working hypothesis. In fact, however, no such assumption is made. No changes in output and (at any rate in Parts I and II [Part III presents switches in methods of production - RLV]) no changes in the proportions in which different means of production are used by an industry are considered, so that no question arises as to the variation or constancy of returns. The investigation is concerned exclusively with such properties of an economic system as do not depend on changes in the scale of production or in the proportions of 'factors'."

The analysis of the choice of technique shows that much neoclassical teaching and "practical" applications is humbug. But that does not exhaust Sraffa's point. Turning to the first sentence of the next paragraph in the preface can help:

"This standpoint, which is that of the old classical economists from Adam Smith to Ricardo, has been submerged and forgotten since the advent of the 'marginal' method."

A second major emphasis of Sraffa's scholarship, including his 1960 book, is the rediscovery of the logic of the classical theory of value and distribution. Sraffians can claim to have a theory that can serve as an alternative to neoclassical theory and that is empirically applicable (for example, by Leontief and those aware of the National Income and Product Accounts (NIPA).) This rediscovery provides an external critique of neoclassical theory.

By the way, the development of this external critique provides, for example, Pierangelo Garegnani for a defense of the claim that the analysis of the attraction of market prices to prices of production is building on Sraffa's work. Sraffa's book does not discuss market processes or the classical theory of competition:

"A less one-sided description than cost of production seems therefore required. Such classical terms as 'necessary price', 'natural price' or 'price of production' would meet the case, but value and price have been preferred as being shorter and in the present context (which contains no reference to market prices) no more ambiguous." (PoCbMoC, p. 9)

One could read Sraffa as being able to take many aspects of classical political economy as given, including analyses of market prices. How should ideas that Sraffa explicitly choose to include in his archives, but not publish in his lifetime, influence our interpretation?

None of this gets to Sinha's point. He thinks, as I understand it, that Sraffa offers more than a rediscovery of classical political economy. Sraffa offers innovations in our understanding of prices and distribution, and these innovations can help us better understand actually existing capitalist economies. (Some of these innovations might be Wittgenstein-like in that they allow us to improve by discarding lots of rubbish.) I daresay Scott Carter agrees with that claim, even though he might disagree with details of Sinha's understanding of the Standard Commodity.

Comments on Yoshihara and Kwak on Sraffian Indeterminancy

1.0 Introduction

Yoshihara and Kwak (henceforth YK) presented a paper, on Sraffian indeterminacy, at the last annual meeting for the American Economic Society. I want to register my qualified disagreement.

2.0 Yoshihara and Kwak against Mandler

YK are arguing against Michael Mandler. In a 1999 paper, a book, and a series of papers since, Mandler has been criticizing Sraffa and his followers. In Mandler's reading, Sraffa argues that, in neoclassical theory, the distribution of income is generically indeterminate. That is, for any long-period equilibrium solution, one can find another solution as nearby as you want. Or, in still other words, equilibrium solutions are a continuum in some space. In much simpler terms, any distribution and prices along the wage-rate of profits curve is a long-period equilibrium in a circulating capital model with a single technique. Mandler says that Sraffa is more-or-less mistaken.

YK say that Mandler is correct if one confines oneself to stationary equilibria. But, if one considers steady states, with a not-necessarily zero, endogenous rate of growth, then indeterminate equilibria are generic.

3.0 Clarifications and Caveats

I should offer some clarifications and caveats. First, Mandler's claim is consistent with multiple, non-unique equilibria. Equilibria are not indeterminate, as long as the number of equilibrium is finite or, I guess, at most countable. So, if I produce a model in which several points on the wage frontier are neoclassical equilibria, I am not offering a counter-example or disproof of Mandler's claim that Sraffian equilibria are determinate.

Second, Mandler has a caveat. In particular, he argues indeterminancy arises in a short-run model with technology modeled as Leontief matrices. The capital goods that exist at the start of any period are the result of production in the previous period. If they were taken as given, some might be in excess supply with an equilibrium price of zero. And those not in excess supply would have a determinate price. But there is a boundary, just before capital goods are in excess supply price. There, equilibrium prices would range from zero to some upper bound. For strategic reasons, managers of firms have an incentive to produce just this quantity of capital goods.

Third, YK are arguing in the framework of a model of overlapping generations. The production technology is specified by a Leontief matrix. The model is extended to include utility maximization by households. Each household must decide how much and what to consume out of wages and what to consume, at the end of a second period, out of retirement savings. I think assumptions that households only live for two periods and that they must work the first period and be retired the second period are inessential. Their results are most likely consistent with labor supply being determined by including a preference for leisure in the utility function. And one can have households lasting more than two periods, with more than two generations being included in the demand for consumer goods at any period.

4.0 My Objections

4.1 Objections to Mandler's Reading of Sraffa

I have not read Sraffa for decades, if ever, in line with Mandler. Sraffa does not mention utility functions. And he does not model quantity equations, although I find it natural to add a system of steady state growth to Sraffa's model. Sraffa says he intends his book to provide a foundation for a critique of (neoclassical?) economics, but he certainly presents problems of interpretation for stating what that critique is.

I think of Sraffa as presenting an open model. I guess one can say his solutions are indeterminate, but I do not see him as saying that a neoclassical closure is necessarily indeterminate.

Rather Sraffa shows that one can still model prices and distribution without any reference to subjective, neoclassical theory. He presents a model that can be closed in various ways. Neoclassical theory is only one approach out of others. Furthermore, Neoclassical economists do not seem to have any theoretical foundation for their vision of prices as indices of relative scarcity, as reflecting the result of an overriding principle of substitution.

4.2 An Objection to Yoshihara and Kwak

As I understand it, YK define a steady-state equilibrium by a stationary vector of relative prices, wage, rate of profits, a vector of gross outputs, and a rate of growth. The gross outputs and the rate of growth specify a time path for gross outputs and employment, all components of which grow at the steady state rate.

One can vary the rate of growth continuously in a certain range. Since the parameters of the household utility functions are given, the steady state distribution of income and, consequently, prices must vary too. Voila, steady state equilibrium are indeterminate.

I guess this is consistent with an extension of Mandler's concept of indeterminancy. But it does not seem in the spirit of neoclassical economics, which is the about the allocation of given resources. In my excursions into models of overlapping generations, I have always taken the rate of growth of the population as given, that is, exogenous. I have seen, at least, that if one varies certain parameters in the utility function, the stationary state equilibrium varies continuously. By labeling this a model of endogenous time preferences, have I proven Mandler wrong, even for stationary state equilibria? Do not these disproofs, if that is what they are, even work for aggregate Cobb-Douglas production functions?

5.0 An Empirical Issue?

I am not at sure these are at all questions that can be settled by mathematical modeling. Sraffa presents an open model. Why feel obligated to close it with a formal model, much less with neoclassical assumptions of utility maximizing?

Instead, one can say that Sraffa has presented a model where one can find a place for political forces to impact the distribution of income, in all runs. One can use Sraffa as a justification for, for example, looking at the impact of the policies of the Federal Reserve on income distribution, without being required to create a formal model at the level of abstraction of Sraffa's book.

Likewise, isn't the question of whether the size of the workforce varies endogenously also an empirical question? Offhand, I think of how the labor force participation rate has varied over the last decade, with the advent of the Global Financial Crisis; how estimates of the Non-Accelerating Inflation Rate of Unemployment (NAIRU) have fallen with unemployment over decades; and the increased participation of women in the workforce during World War II as cases to pursue.

REFERENCES

• James K. Galbraith (2000). Created Unequal: The Crisis in American Pay, University of Chicago Pay
• Michael Mandler (1999). Sraffian Indeterminancy in General Equilibrium. Review of Economic Studies 66: 693-711.
• Frank Hahn (1982). The Neo-Ricardians. Cambridge Journal of Economics 6: 353-374.
• Stephen A. Marglin (1984). Growth, Distribution, and Prices. Boston: Harvard University Press.
• Naoki Yoshihara and Se Ho Kwak (2017). Sraffian Indeterminacy in General Equilibrium Revisited. Proceedings of the American Economic Society

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

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

Introduction

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
Cambridge/England

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
Cambridge/England

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
Cambridge/England

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
Cambridge/England

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
Cambridge

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
Cambridge/England

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,
Sincerely,

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 family	Schelle
1880ies 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.	1888 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.
1902 Henry Algernon Du Pont, later US senator, retires from business (railways, among other things) and devotes himself to literary and historical pursuits.	1903 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
1905 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.	1905 Parts of the "3rd edition" of the Tableau economique. Strictest discretion as to the source of the discovery.
1908 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.
	1909 La Vie de Turgot, Paris
	1913 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). But 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.
1924 H.-A. Du Pont publishes, for normal circulation, The Early Generations of the Du Pont and Allied Families, New York.	1925 Schelle finishes publishing his Turgot edition.

Backstop Technologies And Natural Resources

1.0 Inroduction
Patch writes:

"I just finished reading Pasinetti's

Lectures on the Theory of Production (New York: Colombia University Press and London: The Macmillan Press Ltd., 1977.).

It is a readable introduction of production price models and it gave me an idea of what actually is the difference between prices optimizing the use of endowments and production prices. But then again I found some problems and I thought I might ask you before I send an email to Pasinetti himself.

The most important problem is, how do the production models work if you don't have an endowment? If you need commodity A to produce commodity B AND VICE VERSA, you can't start off producing at all because you don't have the necessary A to produce B and vice versa. The second problem maybe already is solved but I don't know: Can you use these models to say anything about natural resources? These resources are 'given', but you don't have to use them up in the first period so you still need an optimization I think."

Luigi Pasinetti, I think, has an ability to distill his ideas and express them remarkably clearly. His Lectures is a great textbook, and I could easily imagine Pasinetti getting a "Nobel" prize. Perhaps Sraffa's abstractions can be combined with Joan Robinson's emphasis on historical time to provide insight into actually existing capitalist economies. If so, such an advance might be based on Pasinetti's work, especially on structural economic dynamics.

I think both of Patch's questions are good questions, and I am going to decompose each into two.

2.0 Proportions and Endowments
One can think of the first as asking one of the following:

1. What happens if the means of production are not in the proportions needed for steady growth at the start of a production period?
2. What happens if none of some input needed for a cost-minimizing technique exists at the start of the production period?

An orthodox economist might want to analyze the first question by talking about intertemporal equilibria, the turnpike theorem, or tranverses between long period equilibria. However:

"5. Thus, if Sraffa's propositions are to be contained in an 'orthodoxy', which as [Frank] Hahn states has the endowment of factors among its data, such a datum should be present also in Production of Commodities. But how can Hahn trace it since that datum is not there?

6. Hahn attempts to do so when he introduces a simplified model of 'neoclassical theory' involving two commodities - wheat and barley - each of which is both a capital good and a consumption good. He asserts that, in order to obtain Sraffa's uniform rate of return on the two capital goods, the initial endowments of wheat and barley must bear some particular proportion to each other, because 'It cannot be part of the doctrine of Sraffa that you are uninterested in whether there is enough ... wheat and barley to meet demand" (Hahn, 1982, p. 365; emphasis added). In other words, Hahn finds it inconceivable that the simple answer to the question he raises in that passage might be:

Yes, it can, and it is, part of the doctrine of Sraffa's that distribution and normal prices do not require the initial endowments of wheat and barley for their determination.

Clearly, Hahn has begged his question here. He has assumed, and not proved, that what constitutes a characteristic feature of 'neoclassical' theory by his own definition of it - the determining role of factor endowments - is present in Sraffa's analysis. To that extent he has assumed what he intended to prove, namely that Sraffa's analysis is a 'special case' of neoclassical theory.

In fact, as he tells us in his Preface, Sraffa's standpoint is that 'of the old classical economists from Adam Smith to Ricardo', and, as we shall presently see, this standpoint does not attribute a determining role to 'the endowment of agents'. Therefore, his analysis can hardly be a 'special case' of the 'neoclassical' theory, which does admittedly rest on such a role." - P. Garegnani, "Sraffa" Classical versus Marginalist Analysis", in Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory (Edited by K. Bharadwaj and B. Schefold), Unwin Hyman (1990).

The second question is addressed by postulating the existence of a backstop technology in which, say, B can be produced without the existence of any A. I think this accords well with experience. Maybe no industry in the USA today produces without inputs of computer software and hardware, at least indirectly. Yet clearly this situation has come about without computer software and hardware being produced forever in the past.

3.0 Natural Resources
I think of natural resources as falling into two kinds:

1. Resources, like land in classical economics, that are given in quantity, cannot be manufactured, and provide services over a production period without ever suffering any diminution.
2. Resources, like oil, that are used up over time and cannot be replaced.

Land is usefully thought of as a case of joint production. Many economists, including Pasinetti himself, have analyzed joint production. I think of Christian Bidard, Bertram Schefold, and Heinz Kurz & Neri Salvadori. I even have an example treating land in the theory of joint production.

Although issues exist in extending Sraffa's results for single production to the theory of joint production, I think how to treat exhaustible resources in the long-period method is more problematic. As I understand it, Kurz and Salvadori have treated exhaustible resourses in what they call the guano model.

Nick Rowe Knavery

So much nonsense packed into so few words:

"But the lefty Sraffian model has only labour and time as inputs." -- Nick Rowe

I do not know what politics has to do with it. I'd like to see some evidence of the political beliefs of, say, Neri Salvadori. When Sraffa states, in the preface of Production of Commodities By Means of Commodities, that "Others have ... independently taken up [similar] points of view," I think he includes John Von Neumann. Von Neumann wanted to wage an atomic war against the Soviet Union. I guess Rowe must think Von Neumann was a Trotskyite.

The Sraffa model, of course, includes non-produced inputs other than labor. "Land" is the title of Chapter 11 of Sraffa's book. I have attempted to explain some of the points in this chapter here and here. Heinz Kurz, Neri Salvadori, and Bertram Schefold are just some of the economists who have contributed to the literature building on Sraffa's analysis of land.

To address another Rowe misconception, Sraffians have also analyzed heterogeneous labor. In fact, "Heterogeneous Labor" is the title of Chapter 7 of Ian Steedman's book, Marx After Sraffa. I have an example with heterogeneous labor here.

The bit about time being an input in Sraffa's model is apparently some convex combination of a lie and begging the question. Sraffa explicitly states, in the title of his book, that he is considering production processes with inputs of commodities. These commodities include seed corn, iron, pigs, and so on. Although Sraffa assumes a yearly cycle of production for convenience, time is explicitly not an input in Sraffa's model. In fact, Sraffa can be said to have proven that "capital" cannot be reduced to time. In the case of joint production without land, the technique cannot even be reduced to labor inputs applied over time. (By the way, in the first chapter in her Essays in the Theory of Economic Growth, Joan Robinson explicitly analyzes an economy in which robots are produced by robots.)

Does anybody expect Rowe to acknowledge that he has no concern whatsoever over whether what he says is true or even makes sense?

Minsky Versus Sraffa

Kevin "Angus" Grier reminisces about Hyman Minsky's dislike for Piero Sraffa. But he doesn't recall points at issue. Minsky expressed his views in print:

"Given my interpretation of Keynes (Minsky, 1975, 1986) and my views of the problems that economists need to address as the twentieth century draws to a close, the substance of the papers in Eatwell and Milgate (1983) and the neoclassical synthesis are (1) equally irrelevant to the understanding of modern capitalist economies and (2) equally foreign to essential facets of Keynes's thought. It is more important for an economic theory to be relevant for an understanding of economies than for it to be true to the thought of Keynes, Sraffa, Ricardo, or Marx. The only significance Keynes's thought has in this context is that it contains the beginning of an economic theory that is especially relevant to understanding capitalist economies. This relevance is due to the monetary nature of Keynes's theory.

Modern capitalist economies are intensely financial. Money in these economies is endogenously determined as activity and asset holdings are financed and commitments of prior contracts are fulfilled. In truth, every economic unit can create money - this property is not restricted to banks. The main problem a 'money creator' faces is getting his money accepted...

...The title of this session, 'Sraffa and Keynes: Effective Demand in the Long Run', puzzles me. Sraffa says little or nothing about effective demand and Keynes's General Theory can be viewed as holding that the long run is not a fit subject for study. At the arid level of Sraffa, the Keynesian view that effective demand reflects financial and monetary variables has no meaning, for there is no monetary or financial system in Sraffa. At the concrete level of Keynes, the technical conditions of production, which are the essential constructs of Sraffa, are dominated by profit expectations and financing conditions." -- Hyman Minsky "Sraffa and Keynes: Effective Demand in the Long Run", in Essays of Piero Sraffa: Critical Perspectives on the Revival of Classical Theory (edited by Krishna Bharadwaj and Bertram Schefold), Unwin-Hyman (1990)

I gather, from second or third-hand accounts, that debates along these lines became quite acrimonious at the annual summer school in Trieste during the 1980s. I've always imagined Paul Davidson and Pierangelo Garegnani would be the most vocal advocates of the extremes in these debates. And I think of Jan Kregel, Edward Nell, and Luigi Pasinetti as being somewhere in the middle, going off in different directions. I don't know much about monetary circuit theory, but such theory may provide an approach to integrating money into Sraffianism.

Of course, Minsky's theories and Davidson's proposals for national and international reforms are of great contemporary relevance.

Impact Of Piero Sraffa On Industrial Organization

1.0 Introduction

Piero Sraffa, with his 1926 Economic Journal article on the laws of returns, had a great impact on the emerging field of Industrial Organization (I/O). For the purposes of this post, Sraffa's paper can be said to have made two major contributions:

1. An internal critique of Marshall's theory of partial equilibrium, showing it holds only under the most specious conditions.
2. Suggestions for how to analyze the wide range of markets between perfect competition and monopoly.

The first contribution is still relevant today, given how the theory of the perfectly competitive firm is still presented in introductory textbooks. One might also argue that how the theories of imperfect and monopolistic competition were developed, they still are vulnerable to Sraffa's critique. In this post, however, I concentrate on a broad historical overview focused on the second contribution above. But Cameron Murray shows that some still find Sraffa's 1920s work of importance for contemporary theorizing about the theory of the firm.

I apologize for lacking references to recent secondary literature. I do not think that the thesis of this post is not well known among historians of economics or the authors of secondary literature.

2.0 Selected Quotes

Sraffa articulated the need for and possibility of theories of market forms between monopoly and perfect competition:

"...when we are supplied with theories in respect to the two extreme cases of monopoly and competition as part of the equipment required in order to undertake the study of the actual conditions in the different industries, we are warned that these generally do not fit exactly one or other of the categories, but will be found scattered along the intermediate zone, and that the nature of an industry will approximate more closely to the monopolist or the competitive system according to its particular circumstances, such as whether the number of autonomous undertakings in it is larger or smaller, or whether or not they are bound together by partial agreements, etc. We are thus led to believe that when production is in the hands of a large number of concerns entirely independent of one another as regards control, the conclusions proper to competition may be applied even if the market in which the goods are exchanged is not absolutely perfect, for its imperfections are in general constituted by frictions which may simply retard or slightly modify the effects of the active forces of competition, but which the latter ultimately succeed in substantially overcoming. This view appears to be fundamentally inadmissible. Many of the obstacles which break up that unity of the market which is the essential condition of competition are not of the nature of 'frictions,' but are themselves active forces which produce permanent and even cumulative effects. They are frequently, moreover, endowed with sufficient stability to enable them to be made the subject of analysis based on statical assumptions." -- p. 542

He stated some basic ideas developed in the theory of monopolistic competition:

"The causes of the preference shown by any group of buyers for a particular firm are of the most diverse nature, and may range from long custom, personal acquaintance, confidence in the quality of the product, proximity, knowledge of particular requirements and the possibility of obtaining credit, to the reputation of a trade-mark, or sign, or a name with high traditions, or to such special features of modelling or design in the product as-without constituting it a distinct commodity intended for the satisfaction of particular needs-have for their principal purpose that of distinguishing it from the products of other firms.

What these and the many other possible reasons for preference have in common is that they are expressed in a willingness (which may frequently be dictated by necessity) on the part of the group of buyers who constitute a firm's clientele to pay, if necessary, something extra in order to obtain the goods from a particular firm rather than from any other." -- p. 544

He described what could be seen as a forerunner of the theroy of kinked demand curves:

"...the forces which impel producers to raise prices are much more effective than those which impel them to reduce them; and this not merely owing to the fear which every seller has of spoiling his market, but mainly because an increase of profit secured by means of a cut in price is obtained at the cost of the competing firms, and consequently it impels them to take such defensive action as may jeopardise the greater profits secured; whereas an increase of profit obtained by means of a rise in prices not only does not injure competitors but brings them a positive gain, and it may therefore be regarded as having been more durably acquired. An undertaking, therefore, when confronted with the dual possibility of increasing its profits by raising its selling prices, or by reducing them, will generally adopt the first alternative unless the additional profits expected from the second are considerably greater." -- p. 548

Sraffa is also a forerunner of the theory of contestable markets, in which one analyzes the effects on existing firms of potential entrants into their markets.

"It should be noted that in the foregoing the disturbing influence exercised by the competition of new firms attracted to an industry the conditions of which permit of high monopolist profits has been neglected. This appeared justified, in the first place because the entrance of new-comers is frequently hindered by the heavy expenses necessary for setting up a connection in a trade in which the existing firms have an established goodwill - expenses which may often exceed the capital value of the profits obtainable; in the second place, this element can acquire importance only when the monopoly profits in a trade are considerably above the normal level of profits in the trade in general, which, however, does not prevent the prices from being determined up to that point in the manner which has been indicated."-- p. 549

I suppose I could also quote Sraffa's suggestion that developments along some of these lines would lead to models with determinate solutions. To summarize, you can see in this paper an outline of a program for the I/O field.

3.0 Impact on Economists Developing I/O

Sraffa was not a voice crying in the wilderness, ignored by economists of his day and thereafter. His paper was one contribution, among many in the 1920s, attempting to articulate the logical requirements for a theory of perfect competition. Sraffa was not even alone in expressing skepticism that one could confidently connect Marshall's theory to the empirical facts. I think of, for example, what has come to be known as the "empty economic boxes" debate.

Edward Chamberlin and Joan Robinson, with their 1933 books on, respectively, monopolistic and imperfect competition, is an example of simultaneous discovery in I/O. Richard Kahn provided Robinson quite a bit of help with her book and was also working on the theory of imperfect competition, if I recall correctly, in his thesis. Kahn and Robinson were directly inspired by Sraffa and interacted with him in Cambridge.

Joe S. Bain and Paolo Sylos Labini provide a later example of simultaneous discovery in I/O. They develop what has become known as "old" I/O, as opposed to more game-theoretic approaches. Sylos Labini, at least, thought of himself as following a Sraffian tradition inasmuch as he was attempting to develop I/O in keeping with a revival of classical political economy. But this observation takes me into Sraffa's later work and beyond the scope of this post.

Reference

• Franco Modigliani (1958). New Developments on the Oligopoly Front, Journal of Political Economy, V. 66, no. 3 (Jun.): pp. 215-232.
• Piero Sraffa (1926). The Laws of Returns under Competitive Conditions, Economic Journal, V. 36, no. 144 (Dec.): pp. 535-550.
• Paolo Sylos Labini (1995). Why the interpretation of the Cobb-Douglas production function must be radically changed, Structural Change and Economic Dynamics, V. 6, no. 4 (Dec.): pp. 485-504.

A Derivation Of Sraffa's First Equations

1.0 Introduction

Piero Sraffa wrote down his 'first equations' in 1927, for an economy without a surplus. D3/12/5 starts with these equations for an economy with three produced commodities. I always thought that they did not make dimensional sense, but Garegnani (2005) argues otherwise. This post details Garegnani's argument, albeit with my own notation.

There are arguments about how and why Sraffa started on his research project I do not address here. The question is how did he relate what he was doing at this early date to Marx. In addition to Garegnani, DeVivo, Gehrke, Gilibert, Kurz, and Salvadori are worth reading here.

2.0 Givens

I assume an economy in a self-replacing state in which n + 1 commodities are produced.

• c_0,0 is the input of the first commodity used in producing the output of the first industry.
• (c_{., 0})^T = [c_1,0, c_2,0, ..., c_n,0] are the inputs of the remaining n commodities used in producing the output of first industry.
• c₀ = [c_0,1, c_0,2, ..., c_0,n] are the inputs of the first commodity used in producing the output of the remaining industries
• The element c_i,j, i, j = 1, 2, ..., n, of the matrix C is the input of the ith commodity used in producing the output of the jth industry.
• q₀ = is the quantity produced of the first commodity.
• (q)^T = [q₁, q₂, ..., c_n] are the outputs of the remaining n commodities used in producing the output of first industry.

All quantities are given in physical units. I abstract from fixed capital; all inputs are used up in the production of the outputs. Table 1 presents these parameters for the first example in the first chapter in Sraffa 1960.

Table 1: The Example from Sraffa (1960), Chapter 1

Input	Industry
	Iron	Wheat
Iron	c0, 0 = 8 tons iron	c0 = [12 tons iron]
Wheat	c., 0 = [120 quarters wheat]	C = [280 quarters wheat]
Output	q0 = 20 tons iron	q = [400 quarters wheat]

The following must hold for economy to be in a self-replacing state:

q_i = c_i,0 + c_i,1 + ... + c_i,n, i = 0, 2, ..., n

All quantities are non-negative. The economy must hang together in some sense. In Sraffa's terminology, all commodities are basic.

3.0 Coefficients of Production

I like to think of the coefficients scaled for unit output in each industry. Accordingly, define:

a_{0, 0} = c_{0, 0}/q₀

(a_{., 0})_i = (c_{., 0})_i/q_j, i = 1, 2, ..., n

(a₀)_j = (c₀)_j/q_j, j = 1, 2, ..., n

(A)_i,j = (C)_i,j/q_j, i, j = 1, 2, ..., n

4.0 All Quantities Measured in Unit Outputs of the First Industry

The given inputs can be thought of as produced in the previous year. The amount of, say, iron directly used as input in producing other commodities is (a₀ q). Table 2 indicates how much iron is needed as input in all previous years.

Table 2: Iron Inputs for Other Commodities

Year	Iron
0	a0 q
1	a0 A q
2	a0 (A)2q
...	...
n	a0 (A)nq
...	...

Even though my notation picks out the first commodity, there is nothing special about it. Suppose some commodity is selected. Let v₀ be the quantity of this commodity needed directly and indirectly to produce a unit of the first commodity. Let v be the quantities of this commodity needed directly and indirectly to produce each of the remaining commodities. v₀ and v must satisfy the following system of n + 1 linear equations:

v₀ a_{0, 0} + v a_{., 0} = v₀

v₀ a₀ + v A = v

For a non-trivial solution to exist, the determinant of the matrix in Table 3 must be zero, which it is in the case pf the Sraffa example.

Table 3: A Matrix

1 - a0, 0 = (3/5) tons	-a0 = [(-3/100) tons]
-a., 0 = [-6 quarters]	I - A = [(3/10) quarters]

I set v₀ to unity. The amount of this commodity used directly and indirectly in the production of all other commodities is easily found:

v = a₀(I - A)^-1

5.0 Rescaling the Givens

I then rescale the givens.

b_{0, 0} = v₀ c_{0, 0}

b_{i, 0} = v_i (c_{., 0})_i, i = 1, 2, ..., n

b_{0, j} = v₀ (c₀)_j, j = 1, 2, ..., n

b_{i, j} = v_i c_{i, j}, i, j = 1, 2, ..., n

s₀ = v₀ q₀

s_i = v_i q_i, i = 1, 2, ..., n

Table 4 presents Sraffa's example with these calculations. Here, a unit of wheat is 10 quarters. That is, one ton iron is used directly and indirectly in producing 10 quarters of wheat.

Table 4: Sraffa's Example Again

Input	Industry
	Iron	Wheat
Iron	b0, 0 = 8 tons iron	b0 = [12 tons iron]
Wheat	b., 0 = [12 tons wheat]	B = [28 tons wheat]
Output	s0 = 20 tons iron	s = [40 tons wheat]

I then have Sraffa's 'first equations':

b_{0, j} + b_{1, j} + ... + b_{n, j} = s_j, j = 0, 1, ..., n

For the economy to be in a self-replacing state, the following must hold:

b_{i, 0} + b_{i, 1} + ... + b_{i, n} = s_i, i = 0, 1, ..., n

Even though I am adding together, say, quantities of iron and wheat, the dimensions are consistent.

6.0 A Re-interpretation

Suppose the first produced commodity is labor, not iron. c_{0, 0} becomes the amount of labor performed in households (outside the market) to reproduce the labor force. c_{., 0} is the commodity basket paid out in wages when the workers obtain all of the surplus product. a₀ are the direct labor coefficients for each industry, and A is the Leontief input-output matrix. v is the vector of labor valus (also known as employment multipliers). Under the assumptions, prices of production are identical to labor values.

This model is descriptive. The givens do not show how required inputs might decrease with innovation or the formal and real subsumption of labor.

References

• Garegnani, Pierangelo (2005) On a turning point in Sraffa's theoretic and interpretative position in the late 1920s. European Journal of the History of Economic Thouht 12 (3): 453-492.
• Gehrke, Christian, Heinz D. Kurz, and Neri Salvadori (2019) On the 'origins' of Sraffa's production equations: A reply to de Vivo. Review of Ploitical Economy 31 (1): 100-114.

Some More On Hayek And Sraffa

1.0 Introduction
I have previously discussed Sraffa's review of Prices and Production, Hayek's reply, and Sraffa's rejoinder. I thought I would bring up today a couple of other aspects of that debate.

2.0 Hayek Changes His Notion Of Equilibrium
The traditional neoclassical equilibrium concept, in the period roughly from 1870 to 1930, is roughly of a stationary state. Neoclassical economists in this period erroneously thought that one could define such an equilibrium, given tastes, technology, and endowments, including the endowment of capital, by some or another definition of capital. As Walras recognized, such an equilibrium can never be expected to be established. At most, actual capitalist economies can be expected to be tending towards this kind of equilibrium at any point in time.

This was Hayek's equilibrium concept in Prices and Production. He put forth another equilibrium concept in The Theory of Capital, a concept he had been developing for some time. (Hayek is very clear on this in Chapter 2.) This equilibrium concept is of plan compatibility, a concept formally equivalent in some sense to the Arrow-Debreu model of intertemporal equilibrium.

Given spot prices, a monetary interest rate, and the past history of an economy, entrepreneurs, based on their economic theories, form expectations about future prices and the expectations and plans of others. They form their plans based on these expectations. Equilibrium exists if all these plans are mutually compatible. Under this equilibrium concept, no need exists for entrepreneurs to plan to produce the same quantities period after period. Likewise, consumers might plan to consume different quantities in different periods. Furthermore, entrepreneurs and consumers will generally expect spot prices to vary over time.


Hayek's equilibrium concept of plan compatibility, as I understand it, cannot be used to ground Austrian Business Cycle Theory.

3.0 Austrian Business Cycle Theory Outside Of Historical Time
Sraffa destroyed Hayek's version of Austrian Business Cycle Theory, as Robert Skidelsky notes.

I am amused in noting part of Sraffa's critique. Keynes sets his General Theory in historical time, not logical time. I read Sraffa as pointing out that Hayek's theory, like neoclassical theory on Keynes's reading, is set in logical time:

"That the position reached as the result of 'voluntary saving' will be one of equilibrium... is clear enough; though the conclusion is not strengthened by the curious reason he gives for it.¹³

But equally stable would be that position if brought about by inflation; and Dr. Hayek fails to prove the contrary. In the case of inflation, just as in that of saving, the accumulation of capital takes place through a reduction in consumption. 'But now this sacrifice is not voluntary, and is not made by those who will reap the benefit from the new investments... There can be no doubt that, if their money receipts should rise again [and this rise is bound to happen as Dr. Hayek promises to prove] they would immediately attempt to expand consumption to the usual proportion', that is to say, capital will be reduced to its former amount; 'such a transition to less capitalistic method of production necessarily takes the form of an economic crisis'...

As a moment's reflection will show, 'there can be no doubt' that nothing of the sort will happen. One class has, for a time, robbed another class of a part of their incomes; and has saved the plunder. When the robbery comes to an end, it is clear that the victims cannot possibly consume the capital which is now well out of their reach. If they are wage-earners, who have all the time consumed every penny of their income, they have no wherewithal to expand consumption. And if they are capitalists, who have not shared in the plunder, they may indeed be induced to consume now a part of their capital by the fall in the rate of interest; but not more so than if the rate had been lowered by the 'voluntary savings' of other people.

¹³The reason given is that 'since, after the change had been completed, these persons [i.e., the savers] would get a greater proportion of the total real income, they would have no reason' to consume the newly acquired capital... But it is not necessarily true that these persons will get a greater proportion of the total real income, and if the fall in the rate of interest is large enough they will get a smaller proportion; and anyhow it is difficult to see how the proportion of total income which falls to them can be relevant to the 'decisions of individuals'. Dr. Hayek, who extols the imaginary achievements of the 'subjective method' in economics, often succeeds in making patent nonsense of it." -- Piero Sraffa (March 1932)

And again:

"The first question is whether, as Dr. Hayek asserts, the capital accumulated by 'forced saving' will be, 'at least party' dissipated as soon as inflation comes to an end: 'It is upon the truth of this point that my [Dr. H's] theory stands or falls'. My simple-minded objection was that forced saving being a misnomer for spoliation, if those who had gained by the inflation chose to save the spoils, they had no reason at a later stage to revise the decision; and at any rate those on whom forced saving had been inflicted would have no say in the matter. This appeal to common sense has not shaken Dr. Hayek: he describes it as 'surprisingly superficial', though unfortunately he forgets to tell me where it is wrong." -- Piero Sraffa (June 1932)

The distribution of endowments - who owns what - is a datum for traditional neoclassical theory. Disequilibria employment, production, and purchases will change this data. So one cannot expect, contrary to Hayek, the previous equilibra corresponding to previous data to be restored after the economy is on some disequilibrium path for some extended time.

Sraffa, like later Post Keynesians, suggested a coherent economic theory must be set in historic time.

References

• P. Garegnani (1976) "On a Change in the Notion of Equilibrium in Recent Work on Value and Distribution", reprinted in Keynes's Economics and Theory of Value and Distribution (edited by J. L. Eatwell and M. Milgate, 1983), Oxford University Press.
• F. A. Hayek (1935) Prices and Production, 2nd. Edition, Routledge and Sons.
• F. A. Hayek (June 1932) "Money and Capital: A Reply", Economic Journal, V. 42: 237-249.
• F. A. Hayek (1941) The Pure Theory of Capital, University of Chicago Press.
• M. Milgate (1979) "On the Origin of the Notion of 'Intertemporal Equilibrium'", Economica, V. 46, N. 1: 1-10.
• P. Sraffa (March 1932) "Dr. Hayek on Money and Capital" Economic Journal, V. 42: 42-53.
• P. Sraffa (June 1932). "A Rejoinder", Economic Journal, V. 42: 249-251.

What Is Mathematics - And Sraffa

An Unsurveyable Rule For Generating A Real Number In Binary Format

Noah Smith offers a definition: "Mathematics is the manipulation of the symbols of a language according to explicit, syntactical rules." ("Unlearning Economics" has also recently written on mathematics in economics). To me, the manipulation of meaningless symbols is a powerful form of reasoning. Taking this definition as is, I think two questions can be raised here:

• What is the interest that mathematicians find in these rules and these symbols in the historical circumstances current at the time?
• What does it mean to follow a rule?

Ludwig Wittgenstein is the philosopher most known, I think, for raising the question of what it means to follow a rule. Any summary of his views will be controversial, but I suppose one can fairly say that he adopted an anthropological point of view, at least for some purposes. Describing how to follow a rule by another rule raises the prospect of an infinite regression. Rather, one might show how people do actually follow a rule, how these uses and practices work pragmatically in some form of life. I find it difficult to see how such description conveys the logical must, so to speak, of many rules. But Wittgenstein was alive to this difficulty. He notes that a judge does not seem to treat a statute book as a manual of anthropology.

Furthermore, Wittgenstein spent quite some time in elaborating how these ideas relate to the philosophy of mathematics. His views on the foundations of mathematics seems to have been constructivist and included questioning whether mathematics needs a foundation. Wittgenstein has frequently been labeled an anti-foundationalist. From this viewpoint, one might question whether existence proofs that do not specify how to construct the relevant object can be reformulated. And one even ends up doubting the meaningfulness of defining the real numbers as, say, any set isomorphic to a set of certain equivalence classes of Cauchy-convergent sequences of rational numbers. The use of the notion of infinity remains, I guess, as a standard topic in the philosophy of mathematics.

It seems one of my favorite economists, Piero Sraffa, was an important stimulus in Wittgenstein's development of these views. Sraffa has been said to have led Wittgenstein to see the importance of an anthropological point of view. Sraffa's masterpiece, The Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory, is written in a unique style, not less in the presentation of the mathematics underlying the economics in the book. Sraffa frequently provides outlines of algorithms for constructive existence proofs, maybe most famously for the Standard Commodity. So Sraffa and Wittgenstein might be said to have shared a certain attitude to the philosophy of mathematics, although I do not expect to ever see oral discussions on this topic to be well documented. Sraffa's book can also be said to address only a limited range of topics in economics. An earlier statement of his seems to suggest that he thought room should exist in economics for non-formal treatment of some topics:

"The causes of the preference shown by any group of buyers for a particular firm are of the most diverse nature, and may range from long custom, personal acquaintance, confidence in the quality of the product, proximity, knowledge of particular requirements and the possibility of obtaining credit, to the reputation of a trademark, or sign, or a name with high traditions, or to such special features of modelling or design in the product as - without constituting it a distinct commodity intended for the satisfaction of particular needs - have for their principal purpose that of distinguishing it from the products of other firms. What these and the many other possible reasons for preference have in common is that they are expressed in a willingness (which may frequently be dictated by necessity) on the part of the group of buyers who constitute a firm's clientele to pay, if necessary, something extra in order to obtain the goods from a particular firm rather than from any other." -- Piero Sraffa (1926). "The Laws of Returns Under Competitive Conditions", Economic Journal (Dec.): pp. 544-545.

Whatever you think of the speculations in this post, I think some conclusions are nearly inarguable. Advocates and opponents of the use of mathematics in economics do not neatly divide between mainstream and non-mainstream economists. In particular, one important non-mainstream economist, Piero Sraffa, demonstrated one approach to mathematical economics, while still being aware of the limits to formalism in economics. Furthermore, any comprehensive scholarly study of the philosophy of mathematics will necessarily look at his work as long as Wittgenstein's later views are considered germane to such scholarship.

Hayek Versus Sraffa

I think Piero Sraffa talks his friend Friedrich Hayek into an absurd position here:

"Mr. Sraffa denies that the possibility of a divergence between the equilibrium rate of interest and the actual rate is a peculiar characteristic of a money economy. And he thinks that 'if money did not exist, and loans were made in terms of all sorts of commodities, there would be a single rate which satisfies the conditions of equilibrium, but there might, at any moment, be as many "natural" rates of interest as there are commodities, though they would not be equilibrium rates.' I think it would be truer to say that, in this situation, there would be no single rate which, applied to all commodities, would satisfy the conditions of equilibrium rates, but there might, at any moment, be as many 'natural' rates of interest as there are commodities, all of which would be equilibrium rates; and which would all be the combined result of the factors affecting the present and future supply of the individual commodities, and of the factors usually regarded as determining the rate of interest. There can, for example, be very little doubt that the 'natural' rate of interest on a loan of strawberries from July to January will even be negative, while for loans of most other commodities over the same period it will be positive." -- F. A. Hayek (1932)

"I have only a few words to add on the second cardinal question, that of the 'money' and the 'natural' rates of interest. Dr. Hayek's ideal maxim for monetary policy, like that of Wicksell, was that banks should adopt the 'natural' rate as their 'money' rate for loans... I pointed out ... that when saving was in progress there would at any one moment be many 'natural' rates, possibly as many as there are commodities; so that it would be not merely difficult in practice, but altogether inconceivable, that the money rate should be equal to 'the' natural rate... Dr. Hayek now acknowledges the multiplicity of the 'natural' rates, but he has nothing more to say on this specific point than that they 'all would be equilibrium rates'. The only meaning (if it be a meaning) I can attach to this is that his maxim of policy now requires that the money rate should be equal to all these divergent natural rates."-- Piero Sraffa (1932b)

So what does this victory of Sraffa over Hayek amount to? It's very puzzling, and you won't find any help here. This defeat for Austrian business cycle theory puzzled contemporaries too:

"I wish [Hayek] or someone would try to tell me in a plain grammatical sentence what the controversy between Sraffa and Hayek is about. I haven't been able to find anyone on this side who has the least idea." - Frank Knight to Oscar Morgenstern (as quoted by Caldwell)

Update: Some additional quotations for commentators' amusement:

"The starting-point and the object of Dr. Hayek's inquiry is what he calls 'neutral money'; that is to say, a kind of money which leaves production and the relative price of goods, including the rate of interest, 'undisturbed', exactly as they would be if there were no money at all...

...But the reader soon realizes that Dr. Hayek completely forgets to deal with the task which he has set himself... Being entirely unaware that it may be doubted whether under a system of barter the decisions of individuals would have their full effects, once he has satisfied himself that a policy of constant money would achieve this result, he identifies it with 'neutral money'; and finally, feeling entitled to describe that policy as 'natural', he takes it for granted that it will be found desirable by every right-thinking person. So that 'neutral' money ... in the end becomes 'our maxim of policy'.

If Dr. Hayek had adhered to his original intention, he would have seen at once that the differences between a monetary and a non-monetary economy can only be found in those characteristics which are set forth at the beginning of every textbook on money. That is to say, that money is not only the medium of exchange, but also a store of value, and the standard in terms of which debts, and other legal obligations, habits, opinions, conventions, in short all kinds of relations between men, are more or less rigidly fixed. As a result, when the price of one or more of these commodities changes, these relations change in terms of such commodities; while if they had been fixed in commodities, in some specified way, they would have changed differently, or not at all..

It would be idle to rehearse these platitudes had not Dr. Hayek completely ignored them... The money which he contemplates is ... used purely and simply as a medium of exchange. There are no debts, no money-contracts, no wage-agreements, no sticky prices in his suppositions..." -- Piero Sraffa (1932a)

References

• Hayek, F. A. (1932). "Money and Capital: A Reply", Economic Journal (reprinted in Hayek 1995), V. 42 (June): 237-249
• Hayek, F. A. (1995). The Collected Works of F. A. Hayek: Volume 9: Contra Keynes and Cambridge: Essays, Correspondence (edited by Bruce Caldwell), University of Chicago Press
• Sraffa, Piero (1932a). "Dr. Hayek on Money and Capital", Economic Journal (reprinted in Hayek 1995), V. 42 (March): 42-53.
• Sraffa, Piero (1932b). "A Rejoinder", Economic Journal (reprinted in Hayek 1995), V. 42 (June): 249-251

Reflections On "Sraffian Economics (New Developments)"

Michael Mandler has an article, "Sraffian Economics (New Developments)" in the latest edition of The New Palgrave Dictionary of Economics. I have been trying to read this. (Paul Samuelson's article, "Sraffian Economics", in the original New Palgrave is also heavy going.)

I have previously read Mandler as an anti-Sraffian willing to take the views he opposes seriously. I wonder if he is more positive now. Perhaps he feels that, although Sraffians are mistaken in theory, their mistakes are worthwhile to explore.

That is all subjective on my part, of course. Mandler is explicit on the issues of the indeterminateness of equilibrium and of tâtonnement stability. An indeterminate equilibrium is not merely a case of multiple equilibria. Rather, a continuum of equilibria arise. Perturbations of an equilibrium along this continuum would not set up stable or unstable forces driving the economy back towards or away from the original equilibrium. Rather the economy would just be in another equilibrium. The tâtonnement is a particular kind of exchange process that arises before the beginning of time in the Arrow-Debreu model of intertemporal equilibrium. Mandler argues that Sraffa has failed to demonstrate indeterminateness, and that issues of tâtonnement instability are not essentially connected to Sraffa's model of production; they arise from elements of utility-maximization.

Mandler has certainly been engaged by Sraffians (or vice versa) on exactly these issues. But I'm not sure that I agree that Mandler has picked out the essential points of Sraffa's book. The distribution of income is indeterminate in Sraffa's open model. I do not read Sraffa as claiming this property would still obtain if he closed his model by appending a specification of utility-maximizing consumers, including intertemporally. Rather, I take Sraffa as offering an open model demonstrating non-neoclassical theories of value and distribution can be constructed. If one insists on a closed mathematical model (for example), an empirical issue arises. I think Sraffa did not insist that his model be closed, at least, with elements of a model at the same level of abstractness and generality.

While tâtonnement (in)stability is interesting, I take Sraffian analysis to point towards stability isses elsewhere in, say, the Arrow-Debreu model. One can construct models of spot prices corresponding to the forward prices in the Arrow-Debreu model. These spot prices have their own dynamics that would arise even if spot markets always cleared instantaneously over time. Sraffa's model of production supports an exploration of limit points of this dynamics.

I have constructed examples with bifurcations, pointing to possibilities of complex dynamics in models of temporary or momentary equilibrium. (I don't claim to have a good grasp of the distinction, if any.) One can also show, through an analysis of structural stability, that many of the stories applied economists like to tell are without logical foundation.

Variations in the supply of labor can be modeled by perturbing a parameter in utility functions. An increased supply of labor is modeled by an increased desire for consumption, as opposed to leisure. Nevertheless, the corresponding equilibrium associated with an increased supply of labor, all other parameters held constant, might have a higher wage. The increased supply of labor need not drive the equilibrium wage down.

Likewise, variations in the supply of savings can be modeled by perturbations in a parameter describing intertemporal utility-maximizing. And greater savings can be associated, all other parameters held constant, with a higher equilibrium interest rate.

Relating the structural (in)stability of equilibrium limit points to the dynamics of temporary or momentary equilibria is a challenge to me. I am not sure whether interesting bifurcations are tied to capital-theoretic "paradoxes" such as reswitching and capital-reversing. I think it may depend on details of the model. In one reswitching example, I have found that whether the normal or "perverse" switch is associated with bifurcations depends on whether intertemporal maximizing representative agents are also modeled as choosing between leisure and consumption. Whether the latter choice is included or not seems to flip the result. But perhaps in some model where one has fixed the modeling choice, the existence of interesting dynamic behavior, in some sense, may be tied to the existence of perverse switches.

I may never resolve these theoretical issues to my own satisfaction.