Ricardo On Profits

Sraffa started a controversy on the interpretation of Ricardo's theory of value and distribution. Or perhaps Hollander did in his reaction against Sraffa.

In Sraffa's view, important developments in Ricardo's understanding happened the year before Ricardo's 1815 publication of "An Essay on the Influence of a low Price of Corn on the Profits of Stock". A fortiori, these developments precede the 1817 first edition of On the Principles of Political Economy and Taxation.

Hutches Trower, in his 2 March 1814 letter to Ricardo, states he is returning Ricardo's now lost "papers on the profits of Capital". Ricardo's response is important evidence for Sraffa's interpretation. Here is Ricardo's letter in full:

Upper Brook Street
8^th March 1814

Dear Trower

I called at your house yesterday; I wished to tell you that though well disposed to enter into the defence of my opinions, I was now so much occupied by business, that I could not devote the necessary time to it. Not having found you at home I must tell you so by “these present”. At the same time I must observe that what I feared, I believe, has happened. To one not aware of the whole difference between Mr. Malthus and me, the papers you read were not clear, and I think you have not entirely made out the subject in dispute.

Without entering further into the question I will endeavor to state the question itself. When Capital increases in a country, and the means of employing Capital already exists, or increases, in the same proportion, the rate of interest and of profits will not fall.

Interest rises only when the means of employment for Capital bears a greater proportion than before to the Capital itself, and falls when the Capital bears a greater proportion to the arena, as Mr. Malthus has called it, for its employment. On these points I believe we are all agreed, but I contend that the arena for the employment of new Capital cannot increase in any country in the same or greater proportion than the Capital itself, [footnote:] the following to be inserted: unless Capital be withdrawn from the land [end footnote] unless there be improvements in husbandry, - or new facilities be offered for the introduction of food from foreign countries; - that in short it is the profits of the farmer which regulate the profits of all other trades, - and as the profits of the farmer must necessarily decrease with every augmentation of Capital employed on the land, provided no improvements be at the same time made in husbandry, all other profits must diminish and therefore the rate of interest must fall. To this proposition Mr. Malthus does not agree. He thinks that the arena for the employment of Capital may increase, and consequently profits and interest may rise, altho' there should be no new facilities, either by importation, or improved tillage, for the production of food; - that the profits of the farmer no more regulate the profits of other trades, than the profits of other trades regulate the profits of the farmer, and consequently if new markets are discovered, in which we can obtain a greater quantity of foreign commodities in exchange for our commodities, than before the discovery of such markets, profits will increase and interest will rise.

In such a state of things the rate of interest would rise as well as the profits of the farmer, he thinks even if more Capital were employed on the land. Do you understand?

Nothing, I say, can increase the profits permanently on trade, with the same or an increased Capital, but a really cheaper mode of obtaining food. A cheaper mode of obtaining food will undoubtedly increase profits says Mr. Malthus but there are many other circumstances which may also increase profits with an increase of Capital. The discovery of a new market where there will be a great demand for our manufactures is one.

Believe me
Y^rs very faithfully
David Ricardo

I have written this in great haste after devoting the necessary time to my accounts. You must excuse the scrawl, and corrections.

For Sraffa, Ricardo can be understood as claiming that wages are spent entirely on corn and that corn is the only basic commodity in the system. Sraffa defines "basic commodities" in his book. According to this interpretation, the rate of profits is a physical ratio in agriculture. The prices of manufactured commodities adjust, under the Classical understanding of supply and demand, until this same rate of profit prevails, both in agriculture and in manufacturing.

Blaug Versus Sraffians

Apparently, Gavin Kennedy delivered a paper, "Adam Smith's Invisible Hand: From Metaphor to Myth", at the 40th Anniversary Conference of the History of Economic Thought (HET). Kennedy reports the conference was held in Edinburgh on 3-5 September. And he uses a report on Marg Blaug's keynote address to express irritation at Sraffians:

"Professor Tony Brewer, University of Bristol, took over the chair, for Professor Mark Blaug's keynote address, which did not stir up the opposition I had expected, but then I did not know the economics of most of the participants, and I was relieved to find out that there were no vocal 'Sraffians' among the audience (the obscurity of the Sraffian economics monologue defies summary and any explanation for why it excites, or once excited, the in-group enthusiasm of a small cell in Cambridge).

Mark Blaug's paper was on 'The Trade-off Between Rigor and Relevance: Straffian economics as a case in point', and what a demolition job it was too, summed up neatly in the title." -- Gavin Kennedy

I was unable to find any other references to Blaug's address on the web. I am aware, however, that Blaug has been, for a number of years, griping about the formalist revolution that occurred in economics after World War II (e.g., Blaug 2003). And that he groups Sraffa's Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory with Debreu's Theory of Value: An Axiomatic Analysis of Economic Equilibrium as exemplars of formalism in economics.

Blaug has had something to say about Sraffians in the past. For example, he has written at least two pamphlets for the Institute of Economic Affairs. As I understand it, IEA is a right-wing think tank in Britain. Blaug (1975) is an attack on the Cambridge school, as it stood after the successes of the Cambridge Capital Controversies. In this attack, Blaug misunderstands Sraffa's mathematics in ways that he carries forward into his textbook. He also adopts the curious position that a demonstration, based on reswitching and capital-reversing, of the logical invalidity of neoclassical economics does not hold without the identification of empirical occurrences of the phenomena. Blaug (1988) is a review of The New Palgrave. Blaug claims that John Eatwell, Murray Milgate, and Peter Newman ("A Sraffian Trio") edited a "tendentious work":

"To have invited three Sraffians to edit a new Palgrave dictionary of economics is roughly equivalent to asking three atheists to edit an encyclopedia of Christianity" -- Mark Blaug (1988)

Since the incorrectness of most doctrines of orthodox economics are not recognized by many practitioners, editors of reference works have a problem. I welcome the recognition that belief in these doctrines are a matter of faith, although I am not sure Blaug is being fair to Christianity.

Sraffa had a revolutionary impact on how historians read Ricardo, in particular, and the Classical economists more generally. Recently, Blaug (1999) disputed the Sraffian interpretation of Classical economics. Kurz and Salvadori (2002), Blaug (2002), and Garegnani (2002) is a selection from the literature of responses and counter-responses to Blaug's article. The Sraffians seem to agree that Blaug disputes a straw person. In the Sraffian interpretation, the theory of value can be set out with rigorous mathematics. But the givens of the Classical theory of value are themselves explained within economics (in contrast to neoclassical General Equilibrium theory). Thus, the theory of value is only an element in an approach to a larger economics which investigates such issues as growth, development, population demographics, etc. Blaug failed to understand the instrumental role of the theory of value in the Sraffian interpretation. His criticism of the Sraffians for setting out the theory of value, in their understanding, without encompassing, for example, growth is simply misdirected.

Some Sraffians are competing with Blaug's Economic Theory in Retrospect (nth edition) in the market for textbooks on the history of economic thought. I gather that this market is shrinking, as mainstream economists purge the history of their field from the curriculum. Alessandro Roncaglia (2005) and Ernesto Screpanti & Stefano Zamagni (2005) are two textbooks from Sraffians.

• Mark Blaug (1975) The Cambridge Revolution: Success or Failure?, Institute of Economic Affairs
• Mark Blaug (1988) Economics Through the Looking Glass: The Distorted Perspective of The New Palgrave Dictionary of Economics, Institute of Economic Affairs
• Mark Blaug (1999) "Misunderstanding Classical Economics: The Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 31, N. 2: 213-236
• Mark Blaug (2002) "Kurz and Salvadori on the Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 34, N. 1: 237-240
• Mark Blaug (2003) "The Formalist Revolution of the 1950s", Journal of the History of Economic Thought, V. 25, N. 2: 145-156
• Pierangelo Garegnani (2002) "Misunderstanding Classical Economics? A Reply to Blaug", History of Political Economy, V. 34, N. 1: 241-254
• Heinz D. Kurz and Neri Salvadori (2002) "Mark Blaug on the 'Sraffian Interpretation of the Surplus Approach'", History of Political Economy, V. 34, N. 1: 225-236
• Alessandro Roncaglia (2005) The Wealth of Ideas: A History of Economic Thought, Cambridge University Press
• Ernesto Screpanti and Stefano Zamagni (2005) An Outline of the History of Economic Thought (Second edition)

Scholarly Fantasies

Maybe many that read old books might find interest the rediscovery of works whose existence was previously unknown or thought to be gone forever. Some examples:

• The Gospel According to Thomas and other gnostic manuscripts: Two Egyptian farmers discovered the Nag Hammadi library in 1945. This story is fairly incredible. While these Egyptian brothers pursued a feud with one of their neighbors, they left them in the keeping of their mother. She, in turn, I guess, started a fire with them every morning, until a coptic priest recognized their importance. And then they were smuggled out of Egypt.
• Thomas Malory's Le Morte d'Arthur: While cataloging the Winchester College library, in 1934, Sir Walter Fraser Oakshott discovered a manuscript of this book. This manuscript suggests that Malory conceived his work as a collection of tales. Caxton, the printer, edited it into an unified tragedy.
• Third edition of François Quesnay's Tableau Économique: Marguerite Kuczynski, in the late 1960s, asked the heirs of Pierre Samuel Du Pont de Nemours if they had any printed works by Quesnay in their possession. And the Eleutherian Mills Historical Library told her "Yes".
• David Ricardo's unknown correspondence and manuscripts: Piero Sraffa's discovered, in 1934, a bundle in F. E. Cairnes castle at Raheny. Raheny is near Dublin, and F. E. Cairnes, son of a 19th-century economist, had recently died. The bundle contained 57 letters from Ricardo to James Mill and various manuscripts written by Ricardo
• Ludwig Von Mises' papers from his apartment in Vienna: Unbeknownst to Mises, the Nazis preserved these after Mises fled. The Soviets captured them from Germany at the end of WW II, catalogued them, and preserved them in the KGB archives. Richard Ebeling brought them back from Russia in 1996 after their discovery by western scholars after the collapse of the Soviet Union.

Eatwell Exposition of a Sraffian Research Program

"The revival of the analytical principles of classical political economy that has gathered pace since the mid-1960s has been based on the firm foundation of a logically coherent theory of value and distribution. It was the failure to provide this foundation which for many years confined the classical approach to being, at best, a repository of useful ideas on growth and technological progress (Smith's discussion of the division of labour and Marx's dissection of the labour process being good examples), or, at worst, identified with simple-minded devotion of the labour theory of value as the 'qualitative' expression of capitalist exploitation - the position to which Hilferding retreated in the face of Bohm-Bawerk's critique of Marx, so depriving the surplus approach of any quantitative significance as a theory of value and distribution. The publication of Piero Sraffa's Production of Commodities by Means of Commodities changed all that. Sraffa not only generalized the mathematical solutions to the surplus approach which had been advanced by Dmitriev and Bortkeiwicz, but also presented the analytical structure of the surplus approach with stark clarity. Moreover, Sraffa produced a critique of the neo-classical theory of the rate of profit and so of the entire neo-classical explanation of value, distribution, and output - hence clearing the ground for the redevelopment of classical theory.

With the analytical core now secure, attention can be turned to the development of other facets of classical and Marxian theory and to the empirical insights which this theory provides. In stark contrast to the neo-classical approach, which reduces all economic activity to a single principle - the competitive resolution of individual attempts to maximize utility subject to the constraints of technology and endowment - classical theory is constructed from a number of analytically separable components. The core of the theory, the surplus approach to value and distribution, takes as data the size and composition of output, the technology in use (the conditions of reproduction) and the real wage (or, in some cases, the rate of profit). These data do not, however, lie outside the realm of economics (as,for example, the neo-classical economists' utility functions do). We need to provide theoretical explanations of their determination. Hence Smith, Ricardo and Marx advanced theories of the real wage and of the level of output (Say's law in the case of Ricardo), and Smith and Marx presented detailed analyses of technological change. Assembled around the core, these theories are the building-blocks of a general theory of the operations of the capitalist economy. There is in all this a clear danger of constructing a disjointed ad hoc collage of theories and empirical generalisations. This is avoided by enveloping the entire edifice in a general characterisation of the economic system, the clear specification, that is, of the capitalist mode of production. This serves both to cement the elements of the theory together and to eliminate propositions that do not fit.

Broadly, there are two jobs to be done in developing and extending the classical framework.

First, the classical theory itself must be developed and generalised. All the elements surrounding the core analysis of value and distribution - theories of output and employment, of accumulation, of technology, of the wage, of competition and so on - require restatement and 'modernisation' in the light both of Sraffa's results and of the many changing facets of the modern capitalist system. This will involve both theoretical development and empirical analysis, for one of the important characteristics of classical theorising is the manner in which theory is grounded in the socio-economic data of the system under consideration - the institutional environment is an essential part of the theory.

Second, the rejection of the now discredited neoclassical theory throws open a wide range of problems in international trade, development economics, fiscal and monetary policy and so forth, into which the classical approach can provide new insights. In part these will lead to the refreshing task of debunking the policy prescriptions of orthodox theory which revolve primarily around the fundamental theorem of welfare economics and the supposed 'efficiency' of competitive markets. But there is also a positive job to be done. The reconstruction of economic theory will inevitably precipitate a reinterpretation of economic policy and problems." -- John Eatwell (1987). "Foreword", in The Economics of François Quesnay, by Gianni Vaggi, Duke University Press

Ricardo And The Iron Law Of Wages

1.0 Introduction
The interpretation of classical economists by historians of economic thought is an area of intense debate that Sraffians have contributed to. Sraffians claim that Classical economics has a distinct and coherent approach to economics. And that the theory of value and distribution within this theory has a different structure and role than within so-called neoclassical theory. I want to focus here particularly on the interaction of the Classical theory of wages and the theory of value. I think Ricardo's treatment of wages is a particularly controversial topic in this interpretation. This post notes a couple of difficulties for understanding Ricardo on wages. I developed it in response to an essay on the iron law of wages that the author e-mailed me.

2.0 Contending Interpretations of Classical Political Economy
As usual, I deny much, if any, originality. But I am going to be vague on references. As I understand it, Sraffa and Dobb's introduction in Sraffa (1951) was not initially perceived as offering a novel interpretation of Ricardo. Bharadway (1989) and Garegnani (1984) offer other statements of the Sraffian interpretation. Stirati (1994) focuses specifically on the theory of wages.

Samuel Hollander, I think, has the highest stature of those today arguing, pace Sraffa, for the continuous evolution of Classical economics into Neoclassical economics. I take Hollander to be continuing the line of argument to be found in Appendix I of Alfred Marshall's Principles of Economics. Despite my respect for Hollander, I have yet to thoroughly read any of his massive tomes of scholarship (e.g., Hollander 1979). My acquaintance with Hollander's primary work is mainly in the journal literature, such as his tournament with Giancarlo de Vivo in the mid 1980s and later Cambridge Journal of Economics over de Vivo's discovery in Robert Torrens of something much like Sraffa's standard commodity.

Others have entered into this controversy, while taking positions that I think differ from both Sraffian positions and Hollander's. I mention Carvale and Tosato (1980), which, as I recall, contains dynamic models which formalize an interpretation of Ricardo's views on wages. I also like Peach (1993), which surveys other interpretations and offers Peach's own reading of Ricardo.

2.0 Sraffian Interpretation
The givens in Ricardo's theory of value include, the level of effective demand for the output of each industry and the technique in use. From these givens, the capital equipment that must be advanced in each industry is also known. The level of wages is also among the givens of the theory of value. The rate of profit then is roughly the ratio of the surplus to the advances, including wages.

A problem arises here. The surplus output of the economy, the commodities on which wages are spent, and the capital equipment are each heterogeneous collections. How can these quantities be treated as commensurate? Ricardo's corn-ratio model, the labor theory of value, and Sraffa's standard commodity are all approaches to address this issue.

So the Sraffians claim that the Classical theory of value makes sense, at least formally if the natural rate of wages is exogenous to the theory of value, albeit still to be explained within Political Economy. This is not a novel position:

"Therefore the foundation of modern political economy, whose business is the analysis of capitalist production, is the conception of the value of labour-power as something fixed, as a given magnitude-as indeed it is practice in each particular case. The minimum of wages therefore correctly forms the pivotal point of Physiocratic theory. They were able to establish this although they had not yet recognised the nature of value itself, because this value of labour-power is manifested in the price of the necessary means of subsistence, hence in a sum of definite use-values. Consequently, without being in any way clear as to the nature of value, they could conceive the value of labour-power, so far as it was necessary to their inquiry, as a definite magnitude. If moreover they made the mistake of conceiving this minimum as an unchangeable magnitude-which in their view is determined entirely by nature, and not by the stage of historical development, which is itself a magnitude subject to fluctuations-this in no way affects the abstract correctness of their conclusions, since the difference between the value of labour-power and the value it creates does not at all depend on whether the value is assumed to be great or small." -- Karl Marx (1963) p. 45

4.0 The Natural Wage Outside The Stationary State
I have pointed to a theory of the natural level of prices above, where the natural level of prices is to be contrasted with market prices. Adam Smith uses the metaphor of centers of gravitation for the natural levels. They attract market prices. Ricardo focuses his analysis on natural levels. One might think the given wage in Ricardo's theory of value and distribution must be the natural rate of wages.

This quote seems to say that the natural rate of wages is defined to be the wage that prevails in the stationary state:

"Notwithstanding the tendency of wages to conform to their natural rate, their market rate may, in an improving society, for an indefinite period, be constantly above it; for no sooner may the impulse, which an increased capital gives to a new demand for labour be obeyed, than another increase of capital may produce the same effect; and thus, if the increase of capital be gradual and constant, the demand for labour may give a continued stimulus to an increase of people." -- David Ricardo (p. 94-95 in Sraffa 1951)

And Ricardo says that the stationary state is far distant:

"But if our progress should become more slow; if we should attain the stationary state, from which I which I trust we are far distant, then will the pernicious nature of these [Poor] laws become more manifest and alarming; and then, too, will their removal be obstructed by many additional difficulties." -- David Ricardo (p. 109 in Sraffa 1951)

So Ricardo seems to be inconsistent. He thinks that the system of natural prices and wages is explanatory for empirical tendencies at any moment, that the stationary state is far distant, and the natural rate of wages is defined only for the stationary state. Maybe he has different theories for the long run and the intermediate run, so to speak.

5.0 The Iron Law of Wages and Ricardo
As I understand it, the iron law of wages is that wages tend towards the natural rate of wages, defined as physiological subsistence. Outdated teaching in the history of economic thought is that Ricardo held to this iron law.

Ricardo clearly states that natural rate of wages is not defined solely by physiological requirements. It includes habits and social norms:

"It is not to be understood that the natural price of labour, estimated even in food and necessaries, is absolutely fixed and constant. It varies at different times in the same country, and very materially differs in different countries. It essentially depends on the habits and customs of the people. An English labourer would consider his wages under their natural rate, and too scanty to support a family, if they enabled him to purchase no other food than potatoes, and to live in no better habitation than a mud cabin; yet these moderate demands of nature are often deemed sufficient in countries where 'man's life is cheap', and his wants are easily satisfied. Many of the conveniences now enjoyed in an English cottage, would have been thought luxuries in an earlier period of our history." -- David Ricardo (p. 96-67 in Sraffa 1951)

Hystersis arises in this approach. If the market rate is above the natural wage for a long time, the norms and habits embodied in workers' consumption can change. In a sense, the natural level of wages moves towards the market wage, as well as vice-versa. Ricardo draws on this idea for some policy ideas:

"The friends of humanity cannot but wish that in all countries the labouring classes should have a taste for comforts and enjoyments, and that they should be stimulated by all legal means in their exertions to procure them. There cannot be a better security against a superabundant population. In those countries, where the labouring classes have the fewest wants, and are contented with the cheapest food, the people are exposed to the greatest vicissutudes and miseries. They have no place of refuge from calamity; they cannot seek safety in a lower station; they are already so low, that they can fall no lower..." -- David Ricardo (p. 100-101 in Sraffa 1951)

You can see the same idea later in John Stuart Mill:

"It would, however, be of little avail that either or both these measures of relief [emigration for colonization and something like homesteading] should be adopted, unless on such a scale as would enable the whole body of hired labourers remaining on the soil to obtain not merely employment, but a large addition to the present wages - such an addition as would enable them to live and bring up their children in a degree of comfort and independence to which they have hitherto been strangers. When the object is to raise the permanent condition of a people, small means do not merely produce small effects, they produce no effect at all. Unless comfort can be made as habitual to a whole generation as indigence is now, nothing is accomplished..." J. S. Mill (1848, Book II, Chapter XIII)

How can Ricardo's words be reconciled with the claim that Ricardo held the iron law? My preferred approach is to reject the claim. Ricardo did not endorse the iron law of wages.

This raises the question of who came up with the iron law of wages, if it was not Ricardo. Apparently the "Iron Law" was named by Ferdinand Lassalle. Stirati (1994) reads Marx as here saying that Malthus was the law's creator:

"It is well known that nothing of the 'iron law of wages' is Lassalle's except the word 'iron' borrowed from Goethe's 'great, eternal iron laws'. The word 'iron' is a label by which the true believers recognize one another. But if I take the law with Lassalle's stamp on it, and consequently in his sense, then I must also take it with his substantiation for it. And what is that? As Lange already showed, shortly after Lassalle's death, it is the Malthusian theory of population (preached by Lange himself). But if this theory is correct, then again I cannot abolish the law even if I abolish wage labor a hundred times over, because the law then governs not only the system of wage labor but every social system. Basing themselves directly on this, the economists have been proving for 50 years and more that socialism cannot abolish poverty, which has its basis in nature, but can only make it general, distribute it simultaneously over the whole surface of society!" - Karl Marx (1875)

As I understand it, the formal mathematics of the theory of value merely requires the wage to be given. But, as my email correspondent points out, if the wage is above subsistence, workers can save and class structure of capitalism will not be reproduced.

As I understand it, in the formal mathematics of the theory of value, the wage, for example, is taken as given. The formalism does not require the wage to be any particular value between zero and some maximum. But, as my email correspondent points out, if the wage is appreciably is above subsistence, workers can accumulate capital before retirement age and the class structure of capitalism will not be reproduced.

Updated 19 July 2008

References

• Krishna Bharadwaj (1989) Themes in Value and Distribution: Classical Theory Reappraised, Unwin Hyman
• Giovanni A. Caravale and Domenico A. Tosato (1980) Ricardo and the Theory of Value, Distribution and Growth, Routledge & Kegan Paul
• P. Garegnani (1984) "Value and Distribution in the Classical Economists and Marx", Oxford Economic Papers, V. LXXIII: 291-325
• Samuel Hollander (1979) The Economics of David Ricardo, Toronto: University Press
• Karl Marx (1875) Critique of the Gotha Program
• Karl Marx (1963) Theories of Surplus Value, Part I (Trans. by E. Burns), Progress Publishers
• John Stuart Mill (1848) Principles of Political Economy
• Terry Peach (1993) Interpreting Ricardo, Cambridge University Press
• Piero Sraffa (editor) (1951) The Works and Correspondence of David Ricardo: Volume I: On the Principles of Political Economy and Taxation, Cambridge University Press
• Antonella Stirati (1994). The Theory of Wages in Classical Economics: A Study of Adam Smith, David Ricardo and Their Contemporaries (trans. by Joan Hall), Edward Elgar

Kurz And Salvadori Peeved With Mark Blaug?

Usually when Heinz Kurz and Neri Salvadori want to explain some economist is mistaken, they confine themselves to saying something along the lines of certain propositions "cannot be sustained". Recently, I stumbled upon a 2010 paper in which they answer Mark Blaug. I find their tone sometimes striking:

"A careful scrutiny of [Blaug (2009)] shows that Blaug reiterates once again his previous criticisms, adds a few new ones, but does not enter into a serious discussion of the replies to his earlier efforts... Answering him in detail would necessitate repeating again our counter-arguments. We spare the readers this and ask them to consult our earlier replies to Blaug."

"Blaug has already been given the opportunity in this journal to answer his critics; see Blaug (2002). Apparently, he feels that his rejoinder was not effective. This is hardly surprising because Blaug did not attempt to counter the objections of his critics.

Scrutiny of his new effort reveals that the situation has not changed. Once again Blaug merely reiterates his previous criticisms, adds a few new ones, but neglects to answer his critics. He seems to feel that repeating his story often will render it credible."

"If Blaug was concerned with an historical reconstruction of the case under consideration, he needs to spend some time in Trinity College Library, Cambridge (UK), as we did, in order to study Sraffa's papers and library and find out when Sraffa had arrived at which results, and why. He would then see that his above speculation as well as many other statements he put forward concerning Sraffa's contributions are without foundation; they are pure fiction. Historians of economic thought ought to be aware of the usefulness of archival work."

"In order to give credibility to his (in itself rather strange) complaint that 'Sraffians' have not contributed to certain themes or fields in economics, Blaug re-labels some authors: in case X has/has not contributed to field Y, he or she is not/is a 'Sraffian'."

"In the context of a discussion of the problem of the gravitation of market prices to their 'natural' or normal levels, he contends that while Kurz and Salvadori point out 'that little is known about the dynamic behaviour of even simple linear production models; nevertheless, they express the hope that the problem will be "settled in the foreseeable future" (Kurz and Salvadori 1998[a], 20)' (229 n.20). The reader who checks the source mentioned will not find this statement. Has Blaug got the page wrong? No, in the entire book the reader won't find the statement quoted. Has Blaug perhaps confounded some of our books? Yes, he has, but things are worse still. The only passage we are aware of having written that can be related to Blaug's criticism is contained in a book published in 1995. After having pointed out the extreme complexity of the issue at hand ('gravitation') and the dependence of the results obtained on the specific conditions assumed, we conclude: 'It should then be clear that there is no fear that the issue of gravitation will be settled in the foreseeable future' (Kurz and Salvadori 1995, 20; emphasis added). Hence we say exactly the opposite of what Blaug contends we are saying. This is not only annoying but also raises doubts about the seriousness of the entire enterprise. What is the relevance of a critique that lacks the elementary rigor of not misrepresenting (let alone reversing) the view of the people criticised? Misconstruction is an error surely worse even than historically unfaithful reconstruction?"

"None of Blaug's criticisms stands up to close examination. He attributes views to us (and to other authors) we (they) never advocated. He contends that 'Sraffian' authors have not written about certain problems, while referring to writings which show precisely the opposite. He commits a number of elementary blunders and mistakes the mathematical form of an argument for its content. He variously contradicts himself in the paper. He puts forward bold statements that are contradicted by the facts."

I have commented before on the specific Mark Blaug paper Kurz and Salvadori are rejecting; on the history of Blaug's incomprehension of Sraffianism; and even on the Institute of Economic Affairs, a right-wing think tank sponsoring some of Blaug's work.

References

• Mark Blaug (1975) The Cambridge Revolution: Sccess or Failure? A Critical Analysis of Cambridge Theories of Value and Distribution, Institute of Economic Affairs
• Mark Blaug (1985) Economic Theory in Retrospect, Fourth Edition, Cambridge University Press
• Mark Blaug (1988) Economics Through the Looking Glass: The Distorted Perspective of the New Palgrave Dictionary of Economics, Institute of Economic Affairs
• Mark Blaug (1999) "Misunderstanding Classical Economics: The Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 31, N. 2: pp. 213-236.
• Mark Blaug (2002a) "Kurz and Salvadori on the Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 34, N. 1: pp. 237-240.
• Mark Blaug (2002b) "Misunderstanding Classical Economics: The Sraffian Interpretation of the Surplus Approach", in Competing Economic Theories: Essays in Memory of Giovanni Caravale (Edited by S. Nisticò and D. Tosato), Routledge
• Mark Blaug (2009) "The Trade-Off Between Rigor and Relevance: Sraffian Economics as a Case in Point", History of Political Economy, V. 41, N. 2: pp. 219-247.
• Pierangelo Garegnani (1987) "Misunderstanding Classical Economics? A Reply to Mark Blaug", History of Political Economy, V. 34, N. 1: pp. 241-254.
• Heinz D. Kurz and Neri Salvadori (2002) "Mark Blaug on the 'Sraffian Interpretation of the Surplus Approach'", History of Political Economy, V. 34, N. 1: pp. 225-236.
• Heinz D. Kurz and Neri Salvadori (2010) "In Favor of Rigor and Relevance. A Reply to Mark Blaug" (4 Feb).
• Carlo Panico (2002) "Misunderstanding the Sraffian Reading of the Classical Theory of Value and Distribution: A Note", in Competing Economic Theories: Essays in Memory of Giovanni Caravale (Edited by S. Nisticò and D. Tosato), Routledge

Prices Of Production And A Wheat Theory Of Value

1.0 Introduction
In this post, I describe a theory of prices that is an alternative to the neoclassical supply-and-demand theory of prices as scarcity indices. In this exposition, I consider the simple case in which the modeled economy does not produce a surplus. In this simple case, prices of production are in the ratios of labor values and of commodity values, for any specified commodity. This post illustrates this claim too.

I do not draw the conclusion from the equivalence illustrated here that labor values have no priority over commodity values. After all, the formal model illustrated here does not include a principal agent problem arising with labor.

2.0 Technology and Advanced Wages
Consider a simple economy in which only three commodities are produced, namely, wheat, iron, and pigs. Each commodity is produced by a specified process requiring (possibly zero) inputs of labor, wheat, iron, and pigs. Suppose these processes are observed to produce the quantities of outputs shown in Table 1 from the inputs shown there. In other words, these processes are observed to operate at the scale shown. No assumption about returns to scale is made here. In particular, it is not necessary for Constant Returns to Scale to prevail.

TABLE 1: Technique in Use

INPUTS	Wheat Industry	Iron Industry	Pig Industry
Labor	1 Person-Year	2 Person-Years	3 Person-Years
Wheat	230 Quarters	70 Quarters	90 Quarters
Iron	12 Tons	6 Tons	3 Tons
Pigs	12 Pigs		12 Pigs
OUTPUTS	450 Quarters	21 Tons	60 Pigs

Suppose wages are advanced at the start of the production period, and that these advanced wages consist of 10 quarters wheat and 6 pigs per person-year. Then one could specify the inputs to the production processes as consisting exclusively of wheat, iron, and pigs, with no labor input (as shown in Table 2). This is now the example from paragraph 2 of Sraffa's Production of Commodities by Means of Commodities. Notice that the outputs can just replace the inputs, including the advanced wages, with no commodity surplus being left over. Capitalists do not make an accounting profit in this economy.

TABLE 2: Production of Commodities by Means of Commodities

INPUTS	Wheat Industry	Iron Industry	Pig Industry
Wheat	240 Quarters	90 Quarters	120 Quarters
Iron	12 Tons	6 Tons	3 Tons
Pigs	18 Pigs	12 Pigs	30 Pigs
OUTPUTS	450 Quarters	21 Tons	60 Pigs

3.0 Prices of Production
With the social division of labor in this economy, firms in each industry at the end of the production period have an inventory of a single commodity. To continue production, they must trade some of that commodity for the other commodities they need as inputs. Prices of (re)production are time-invariant prices that allow these trades to occur and the economy to be smoothly reproduced through the actions of the agents in the economy. For this simple example, prices of production must satisfy three equations:

240 p_w + 12 p_i + 18 p_p = 450 p_w

90 p_w + 6 p_i + 12 p_p = 21 p_i

120 p_w + 3 p_i + 30 p_p = 60 p_p

where:

• p_w is the price of a quarter of wheat,
• p_i is the price of a ton of iron, and
• p_p is the price of a pig.

These equations are linearly dependent. Any multiple of a solution set of prices is also a solution. I arbitrarily pick a quarter of wheat as the numeraire. The solution set of prices is then $1 per quarter wheat, $10 per ton iron, and $5 per pig.

4.0 Labor Values
One can work out a consistent accounting in which the amount of labor time embodied in each commodity is measured. Labor values are found as the solution to the following system of three linear inhomogeneous equations in three unknowns:

1 + 230 v_w + 12 v_i + 12 v_p = 450 v_w

2 + 70 v_w + 6 v_i = 21 v_i

3 + 90 v_w + 3 v_i + 12 v_p = 60 v_p

where:

• v_w is the person-years labor embodied in a quarter of wheat,
• v_i is the person-years labor embodied in a ton of iron, and
• v_p is the person-years labor embodied in a pig.

This system of equations has a unique solution. The labor values for the commodities are 1/40 person-years per quarter wheat, 1/4 person-years per ton iron, and 1/8 person-years per pig.

5.0 Wheat Values
One can also work out a consistent accounting system in which the amount of wheat embodied in each commodity is measured. Wheat values for iron and pigs are found as the solution to the following system of two linear inhomogeneous equations in two unknowns:

90 + 6 w_i + 12 w_p = 21 w_i

120 + 3 w_i + 30 w_p = 60 w_p

where:

• w_i is the quarters wheat embodied in a ton of iron and
• w_p is the quarters wheat embodied in a pig.

The wheat values of commodities are w_i = 10 quarters per ton and w_p = 5 quarters per pig.

Calculating iron values for wheat and pigs and calculating pig values for wheat and iron are left as an exercise to the reader.

6.0 Contrast and Comparison
For any set of values (prices of production, labor values, or commodity values), one can find quantities of each commodities that are valued as equal for that set. Table 3 illustrates by showing the values of specified quantities of each commodity. In this example, the following equation holds:

10 quarters wheat = 1 ton iron = 2 pigs,

whether commodities are valued in terms of dollars, embodied labor, or any commodity value (such as wheat). The equivalence of all these values is a special case. This equivalence works out from considering a pure circulating capital case in which an economic surplus not paid out in wages is not produced.

TABLE 3: Value of Specified Quantities of Commodities

Quantities	Value in
	Prices of Production	Person-Years of Embodied Labor	Quarters of Embodied Wheat
10 Quarters Wheat	$10	1/4 Person-Years	10 Quarters
1 Ton Iron	$10	1/4 Person-Years	10 Quarters
2 Pigs	$10	1/4 Person-Years	10 Quarters

J. S. Mill on Method

1.0 Introduction
John Stuart Mill wrote an essay on the methodology of economics or rather, in the language of his day, Political Economy. I look at it in a Whiggish fashion to show some of his ideas are still around today, namely:

• The distinction between positive and normative propositions
• The notion of economic man as being motivated solely by monetary considerations (Homo Economicus)
• The argument that economics should be a deductive, not an inductive, science
• The complexity of society and the nature of humankind precludes controlled experimentation

(I do not claim that Mill was original with any particular concept here.) Some of these distinctions you will find critics of mainstream economics imposing on the mainstream, while mainstream economists say that they have been long rejected. I am thinking especially of Mill's claim that economics examines the logical implications of a separate economic motive. Humankind has other motives that are altruistic or not directed towards money. Lionel Robbins, for example, rejected this distinction. (Whether economists' pronouncements about what they do matches what they do is a question not examined here.)

2.0 Positive Versus Normative Propositions
J. S. Mill introduces a distinction between positive and normative propositions. He uses the terms "science" and "art". Mill thinks political economy is and should be a science.

"... the essentially distinct, though closely connected, ideas of science and art. These two ideas differ from one another as the understanding differs from the will, or as the indicative mood in grammar differs from the imperative. The one deals in facts, the other in precepts. Science is a collection of truths; art, a body of rules, or directions for conduct. The language of science is, This is, or, This is not; This does, or does not, happen. The language of art is, Do this; Avoid that. Science takes cognizance of a phenomenon, and endeavours to discover its law; art proposes to itself an end, and looks out for means to effect it.

If, therefore, Political Economy be a science, it cannot be a collection of practical rules; though, unless it be altogether a useless science, practical rules must be capable of being founded upon it." -- J. S. Mill, "On the Definition of Political Economy; and on the Method of Investigation Proper to It", in Essays on Some Unsettled Questions of Political Economy (1844: 312).

This particular essay was originally published in the October 1836 issue of the London and Westminster Review. The page numbers refer to the fourth volume of The Collected Works of John Stuart Mill, from 1967.

In discussing the relationship of art to science, Mill echoes a distinction between "empirics" and "technique" (if I guess correctly from my knowledge of the greek alphabet) to be found in the "Gorgias" of Plato. Technique, in this sense, is art founded on science.

Mill, in discussing an analogy accompanying a definition of economics that he ultimately rejects, writes:

"domestic economy, so far as it is capable of being reduced to principles, is an art. It consists of rules, or maxims of prudence, for keeping the family regularly supplied with what its wants require, and securing, with any given amount of means, the greatest possible quantity of physical comfort and enjoyment." -- J. S. Mill (1844: 313)

And Mill proposes a definition for criticism:

"Political Economy [is] the science which treats of the production and distribution of wealth, so far as they depend upon the laws of human nature." -- J. S. Mill (1844: 318)

3.0 Homo Economicus
Mill says economics is a type of moral or psychological science, as opposed to a physical science (p. 316 for the distinction). Mill decomposes the subject matters of the moral sciences:

"We may inquire what belongs to man considered individually, and as if no human being existed besides himself; we may next consider him as coming into contact with other individuals; and finally, as living in a state of society, that is, forming part of a body or aggregation of human beings, systematically co-operating for common purposes." -- J. S. Mill (1844: 319)

Mill, insofar as he is interested in the social sciences, is concerned with the "laws of human nature in the social state" (p. 320). Here is an important grouping of the moral sciences:

"The science of social economy embraces every part of man's nature, in so far as influencing the conduct or condition of man in society; and therefore may it be termed speculative politics ..." -- J. S. Mill (1844: 320)

Mill then defines a part:

"'Political Economy' is not the science of speculative politics, but a branch of that science. It does not treat of the whole of man's nature as modified by the social state, nor of the whole conduct of man in society. It is concerned with him solely as a being who desires to possess wealth, and who is capable of judging of the comparative efficacy of means for obtaining that end. It predicts only such of the phenomena of the social state as take place in consequence of the pursuit of wealth. It makes entire abstraction of every other human passion or motive; except those which may be regarded as perpetually antagonizing principles to the desire of wealth, namely, aversion to labour, and desire of the present enjoyment of cosily indulgences." -- J. S. Mill (1844: 321)

"Political Economy considers mankind as occupied solely in acquiring and consuming wealth; and aims at showing what is the course of action into which mankind, living in a state of society, would be impelled, if that motive, except in the degree in which it is checked by the two perpetual counter-motives above adverted to, were absolute ruler of all their actions." -- J. S. Mill (1844: 322)

I think Mill's language here is echoed by some "libertarians":

"[Political economy] shows mankind ... establishing laws to prevent individuals from encroaching upon the property of others by force or fraud" -- J. S. Mill (1844: 322)

Mill draws an analogy between the effects of the motives treated by political economy and all other motives with the superposition of forces in Newtonian astronomy (p. 322). And he states that the motives not treated in Political Economy are "disturbing causes" resembling "frictions in mechanics" (p. 330).

Here is Mill's approved definition of Political Economy:

"The science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object." -- J. S. Mill (1844: 323)

Mill has much else to say of interest, e.g.:

"... those who are accused of despising facts and disregarding experience build and profess to build wholly upon facts and experience; while those who disavow theory cannot make one step without theorizing." -- J. S. Mill (1844: 324)

4.0 Economics as a Deductive Science
Mill characterizes Political Economy:

"as essentially an abstract science, and its method as the method a priori." -- J. S. Mill (1844: 325)

5.0 Economics as Not Supporting Controlled Experimentation

"There is a property common to almost all the moral sciences, and by which they are distinguished from many of the physical; this is, that it is seldom in our power to make experiments in them. -- J. S. Mill (1844: 327)

Mill talks about the "circumstances, moreover, of great complexity" (p. 327) in which observations for Political economy are generated. And he refers to the inability of "rarely obtain[ing] an experimentum crucis." -- J. S. Mill (1844: 328).

Economists have recently been performing controlled experiments. I refer not only to behaviorial economics, but also to field experiments.

Against Supply And Demand

1.0 Introduction

(I will not be blogging for maybe a week after maybe tomorrow.)

The dominant economic theories during the classical period did not explain prices by the interaction of supply and demand. In particular, the leading economic theorists of the time rejected the following ideas:

• Supply and demand explain not only market prices, that is, temporary deviations from natural prices, but natural prices themselves.
• Supply and demand are schedules relating the quantity demanded or supplied as a function of price.

I point out some texts relevant to this thesis below.

I am not denying that precursors to marginalist economics can be found during the classical period. I conclude by pointing out some backsliding from the classical school.

1.0 Classical Economics

1.1 Adam Smith

The distinction between market and natural prices apparently goes back to William Petty. Adam Smith defines 'market price':

"The actual price at which any commodity is commonly sold is called its market price. It may either be above, or below, or exactly the same with its natural price.

The market price of every particular commodity is regulated by the proportion between the quantity which is actually brought to market, and the demand of those who are willing to pay the natural price of the commodity, or the whole value of the rent, labour, and profit, which must be paid in order to bring it thither. Such people may be called the effectual demanders, and their demand the effectual demand..." -- Adam Smith, An Inquiry into the nature and Causes of the Wealth of Nations, Book I, Chap. VII: "Of the Natural and Market Price of Commodities"

Notice "proportion". I think it unnatural to read this passage as presuming supply and demand are described by schedules. It seems to me Smith is talking about the ratio between two quantities, the quantity available on the market and the level of effectual demand.

1.2 David Ricardo

I want to make use below of a distinction clearly stated by Ricardo:

"There are some commodities, the value of which is determined by their scarcity alone. No labour can increase the quantity of such goods, and therefore their value cannot be lowered by an increased supply. Some rare statues and pictures, scarce books and coins, wines of a peculiar quality, which can be made only from grapes grown on a particular soil, of which there is a very limited quantity, are all of this description. Their value is wholly independent of the quantity of labour originally necessary to produce them, and varies with the varying wealth and inclinations of those who are desirous to possess them.

These commodities, however, form a very small part of the mass of commodities daily exchanged in the market. By far the greatest part of those goods which are the objects of desire, are procured by labour; and they may be multiplied, not in one country alone, but in many, almost without any assignable limit, if we are disposed to bestow the labour necessary to obtain them.

In speaking then of commodities, of their exchangeable value, and of the laws which regulate their relative prices, we mean always such commodities only as can be increased in quantity by the exertion of human industry, and on the production of which competition operates without restraint." -- David Ricardo, On the Principles of Political Economy and Taxation (3rd edition), Chapter I: "On Value", Section 1

I think Ricardo is clear here that he does not think natural prices are determined or explained by supply and demand:

"It is the cost of production which must ultimately regulate the price of commodities, and not, as has been often said, the proportion between the supply and demand: the proportion between supply and demand may, indeed, for a time, affect the market value of a commodity, until it is supplied in greater or less abundance, according as the demand may have increased or diminished; but this effect will be only of temporary duration." -- David Ricardo, Principles (3rd edition), Chapter XXX: "On the Influence of Demand and Supply on Prices"

(Ricardo, in Chapter XXXI, "On Machinery", says that he thinks that persistent unemployment is consistent with his theory where some of "the population will become redundant, compared with the funds which are to employ it." This view is inconsistent with explaining wages and employment by supply and demand. By the way, Ricardo is not denying Say's law here. He doesn't expect unused capacity for production to be created or to persist.)

1.3 Karl Marx

Karl Marx makes many of the same points as Ricardo. Here he points out that supply and demand do not determine natural prices for commodities:

"Nothing is easier to understand than the disproportion between demand and supply, and the consequent divergences of market prices from market values... If demand and supply coincide, they cease to have any effect, and it is for this very reason that commodities are sold at their market value... If demand and supply cancel one another out, they cease to explain anything, have no effect on market value..." -- Karl Marx, Capital: A Critique of Political Economy (Trans. by David Fernbach), V. 3, Chapter 10: "The Equalization of the General Rate of Profit through Competition. Market Prices and Market Values. Surplus Profit."

1.4 Piero Sraffa

I thought about going into the diverse theories the classical economists and Marx had for natural prices. But this post is already too long. Instead, I will point out a modern economist taking over the distinction between market and natural prices:

"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." - Piero Sraffa, Production of Commodities by Means of Commodities p. 9

2.0 Vulgar Economics

2.1 Thomas Malthus

Thomas Malthus rejected the classical theory of value and distribution:

"The principle of demand and supply is the paramount regulator of the prices of labour as well as of commodities, not only temporarily but permanently; and the costs of production affect these prices only as they are the necessary condition of the permanent supply of labour, or of commodities." -- Thomas Malthus, Principles of Political Economy, Chapter IV: "Of the Wages of Labour", Section 1

I don't know whether Malthus regarded supply and demand as schedules.

2.2 John Stuart Mill

I think Schumpeter described Mill as being a half-way house between classical and marginalist economics. Mill noted his predecessors did not regard supply and demand as schedules, and he thinks they should be so regarded:

"Meaning, by the word demand, the quantity demanded, and remembering that this is not a fixed quantity, but in general varies according to the value... The demand, therefore, partly depends on the value...

Thus we see that the idea of a ratio, as between demand and supply, is out of place, and has no concern in the matter: the proper mathematical analogy is that of an equation. Demand and supply, the quantity demanded and the quantity supplied will be made equal. If unequal at any moment, competition equalizes them, and the manner in which this is done is by an adjustment of the value. If the demand increases, the value rises; if the demand diminishes, the value falls: again, if the supply falls off , the value rises; and falls if the supply is increased. The rise or the fall continues until the demand and supply are again equal to one another: and the value which a commodity will bring in any market is no other than the value which, in that market, gives a demand just sufficient to carry off the existing or expected supply.

This, then, is the Law of Value, with respect to all commodities not susceptible of being multiplied at pleasure. Such commodities, no doubt, are exceptions. There is another law for that much larger class of things, which admit of indefinite multiplication. But it is not the less necessary to conceive distinctly and grasp firmly the theory of this exceptional case. In the first place, it will be found to be of great assistance in rendering the more common case intelligible. And in the next place, the principle of the exception stretches wider, and embraces more cases, than might at first be supposed." - John Stuart Mill, Principles of Political Economy with Some of their Applications to Social Philosophy, Book III, Chapter II: "On Demand and Supply in their Relation to Value", Section 4.

Notice that Mill uses supply and demand to explain the prices of only those commodities that cannot be (re)produced - here is where that distinction stated by Ricardo comes in. But Mill stretches this exceptional case further than others had.

Marginalism As A Reaction To Marxism

I should be able to find older citations and by non-Sraffians for this thesis. Nikolai Bukharin would be good to reread, or at least rebrowse. Neoclassical economics seems to be a type of vulgar political economy, as Marx labelled it. Are these ideas complementary with Mirowski’s account of neoclassical economics as an imitation of nineteenth century physics?

"What turned out to be so devastating was the social impact of [Marx's] writings. The immediate practical effect of Marx's call for a social revolution was to elicit a strong social reaction. The establishment of the Western nations, at the end of the nineteenth century, became scared by Marx's revolutionary call. This by itself explains a lot of the fortune that in academic circles blessed marginalism in the 1870s, whose success was essentially analytical. By simply going back to the pre-industrial age concept of wealth considered as a set of given endowments of scarce natural resources (a stock concept), the marginalists succeeded in reaching an analytical breakthrough, against which Classical economic theory had nothing to compare. They elaborated a formally sophisticated and elegant scheme capable of dealing with the problems of a simpler society - a society in which the more traditional concept of wealth, as consisting of a stock endowment of resources provided by nature in given and, for most components, scarce quantities, could be placed at the very centre of the whole investigation. Hence, not the dynamism of a changing society as, paradoxically, could be observed all around, but the problems of managing efficiently the wealth that existed already became the crucial subject of economic investigation, through the assumption of a perfectly rational behaviour of the single individuals, in a perfectly competitive, strictly atomistic stationary society.

In academic circles, this no doubt represented a radical change, but not in the strict sense of a scientific 'revolution', though some historians of economic thought later hastened to call it so (the 'Marginal Revolution'). Conceptually, it was a 'counter-revolution', an anachronistic achievement, yet a beautiful one, reached with the most sophisticated tools of economic analysis (precisely what the Classical economists had lacked).

At the end of the nineteenth and the beginning of the twentieth century, marginal economic theory, marginal economic theory led to conclusions which were pleasing to the establishment, especially in terms of a splendid detachment from the hot social issues that were boiling up in the real world, and in terms of arguments that could easily be used for the advocacy of unrestricted laissez-faire policies, supposedly leading, in ideal conditions, to optimal positions..." -- Luigi L. Pasinetti (2007).

"The labour theory of value was devised by Ricardo as a stick to beat landlords (rent does not enter into cost of production.) But later, having been advocated by Marx to beat the capitalists, it was necessary for the defenders of the present system to devise a new theory, the utility theory of value. As for Ricardo, it should not be thought that he was consciously biased in his theory, that he was the champion of the rising capitalist against the landlord. ... As for Marx, the fact that the utility theory of value had been found several times before (by Dupuit, Gossen) and had fallen flat while when it was again almost simultaneously published by Jevons, Menger, and Walras in the years immediately following the publication of vol. I of Capital, found suddenly a large body of opinion prepared to accept it and support it is significant enough." -- Piero Sraffa (1927, quoted in Bellofiore 2008)

Sraffa references Ashley:

"The marginal conception of value which this generation owes to Jevons and Menger was clearly enough expounded by Longfield in 1833, but it passed unregarded... It is evident that their inattention was due, not to dissatisfaction with what men like Longfield offered them, but to satisfaction with the apparently sufficient formulae they had already mastered...

...Meanwhile ... the dissemination of the teachings of the so-called 'scientific' socialists - of Lassalle's 'Iron Law of Wages,' and Marx's 'Surplus Value' - disposed conservatively minded thinkers to re-examine that Ricardian teaching to which the Socialists, with so much show of reason, were in the habit of appealing." -- W. J. Ashley (1907).

Update (17 Feb.): Added Ashley quotation.

References

• W. J. Ashley (1907). "The Present Position of Political Economy", Economic Journal, V. 17, N. 68 (Dec.): 467-489.
• Ricardo Bellofiore (2008). "Sraffa After Marx: An Open Issue", Sraffa or an Alternative Economics (Ed. by Gugielmo Chiodi and Leonardo Ditta), Palgrave Macmillan.
• Nikolai Bukharin (1972). Economic Theory of the Leisure Class, Monthly Review Press
• Luigi L. Pasinetti (2007). Keynes and the Cambridge Keynesians: A 'Revolution in Economics' to be Accomplished, Cambridge University Press.

Therefore I Ain't Got No Money To Pay The Rent

1.0 Introduction
A vulgar belief is that competitive factor prices reward factor owners for the physical contributions of their services to output, in some sense. Although David Ricardo was not a vulgar economist - he is one of the paradigms for defining Classical economics - he made a similar mistake. In particular, Ricardo treated land as capable of being ordered from high rent to low rent based on physical data (fertility) alone. He only considered a special case where the order of rentability can be read off of physical data alone, rather than the more general case where the order of rentability can be altered by differences in distribution between wages and profits. Understanding the more general case seems appropriate for one who considers economics a social science.

This post demonstrates the limitations of the Ricardian doctrine. These limitations are shown by means of an example. Since so-called Neoclassical economics is often claimed to have been developed by extending the Ricardian theory of rent, the analysis presented here may be of slightly more contemporary interest as well.

2.0 The Technology
Consider a very simple economy that produces a single consumption good, corn, from inputs of labor and (seed) corn. Corn is grown on two grades of land. All production processes in this example require a year to complete. Only one production process is known for producing corn on each grade of land. These processes require the inputs shown in Table 1 to be available at the beginning of the year for each bushel corn produced and available at the end of the year.

Table 1: Inputs Required Per Bushel Corn Produced

Grade I Land	Grade II Land
1 Acre	1 Acre
1/4 Person-Years	2/3 Person-Years
1/2 Bushels Corn	1/3 Bushels Corn

Notice that the proportions of labor and seed corn differ on the two grades of land. This idea can be generalized to a model of the choice of technique in long period positions, where this model includes both extensive and intensive rent:

"...it is very well possible that a larger output per hectare is obtained by using less (or even nothing) of some input(s) and more of some other input(s) or some positive amount of some input(s) not used at all at the smaller level of production." -- Heinz D. Kurz and Neri Salvadori

Assume that the total corn output required in this economy can be grown on some combination of both grades of land, but exceeds the amount that can be grown on either grade alone. In other words, when enough corn is produced to satisfy this economy's requirement for use, some, but not all, of one grade of land will lie fallow. Thus, rent will almost always be paid on one grade of land, and the other is free (non-scarce).

Here's how Ricardo explains the emergence of rent:

"On the first settling of a country, in which there is an abundance of rich and fertile land, a very small proportion of which is required to be cultivated for the support of the actual population, or indeed can be cultivated with the capital which the population can command, there will be no rent; for no one would pay for the use of land, when there was an abundant quantity not yet appropriated, and, therefore, at the disposal of whosoever might choose to cultivate it...

If all land had the same properties, if it were unlimited in quantity, and uniform in quality, no charge could be made for its use, unless where it possessed peculiar advantages of situation. It is only, then, because land is not unlimited in quantity and uniform in quality, and because in the progress of population, land of an inferior quality, or less advantageously situated, is called into cultivation, that rent is ever paid for the use of it. When in the progress of society, land of the second degree of fertility is taken into cultivation, rent immediately commences on that of the first quality, and the amount of that rent will depend on the difference in the quality of these two portions of land...

Thus suppose land - No. 1, 2, 3, - to yield, with an equal employment of capital and labor, a net produce of 100, 90, and 80 quarters of corn. In a new country, where there is an abundance of fertile land compared with the population, and where therefore it is only necessary to cultivate No. 1, the whole net produce will belong to the cultivator, and will be the profits of the stock which he advances. As soon as population had so far increased as to make it necessary to cultivate No. 2, from which ninety quarters only can be obtained after supporting the labourers, rent would commence on No. 1; for either there must be two rates of profit on agricultural capital, or ten quarters, or the value of ten quarters must be withdrawn from the produce of No. 1, for some other purpose. Whether the proprietor of the land, or any other person, cultivated No. 1, those ten quarters would equally constitute rent; for the cultivator of No. 2 would get the same result with his capital, whether he cultivated No. 1, paying 10 quarters for rent, or continued to cultivate No. 2, paying no rent. In the same manner it might be shown that when No. 3 is brought into cultivation, the rent of No. 2 must be ten quarters, or the value of ten quarters, whilst the rent of No. 1 would rise to twenty quarters; for the cultivator of No. 3 would have have the same profits whether he paid twenty quarters for the rent of No. 1, ten quarters for the rent of No. 2, or cultivated No. 3 free of all rent." -- David Ricardo (1821)

3.0 Prices
Consider stationary prices where seed corn is paid for at the beginning of the year, and wages and rent are paid at the end of the year. Then prices must satisfy the following pair of equations:

( 1/2 )( 1 + r ) + ( 1/4 ) w + ρ(I) = 1

( 1/3 )( 1 + r ) + ( 2/3 ) w + ρ(II) = 1

where

• Corn is the numeraire
• w is the wage
• r is the (common) rate of profits
• ρ(I) and ρ(II) are the rents on the respective grades of land.

The condition that at least one grade of land be free is expressed by a third equation:

ρ(I) ρ(II) = 0

The last condition is that all rents must be nonnegative.

3.1 Case 1
Consider the case when wages are 1/2 bushel per person-year. The rate of profits is then 75%. The rent on grade II land is 1/12 bushel per acre, and grade I land is free.

3.2 Case 2
Consider the case when wages are 5/6 bushel per person-year. The rate of profits is 33.3%. The rent on grade I land is 1/8 bushel per acre, and grade II land is free.

4.0 Conclusions
A figure is useful for visualizing the analysis of rent. Figure 1 shows the wage-rate of profits curves for this example. One commodity is produced in the above example, and that commodity functions both as a capital good and as a consumption good. This leads to the wage-rate of profits curves being straight lines. In models with more goods, these curves, while still decreasing, can be of varying convexity. In models with more than two grades of land, more than two curves exist. The figure can be used to locate the grade of land at the extensive margin in working inward from the outer frontier. With a given real wage, one works from right to left. Can the grade of land associated with the rightmost curve satisfy the requirements for use? If so, all land is free, and that grade is used. Otherwise, look at the grade associated with the next curve inward. If both grades can satisfy the requirements for use, then the first grade pays rent, and the second grade is free. In the general case, the frontier associated with the extensive margin may be neither the outer nor the inner frontier formed by the curves on the graph. Furthermore, the order in which grades of land are introduced to satisfy higher requirements for use need not be the order from high-rent land to lower-rent land. If I fully understood my references, I probably could note other counterintuitive results.

Figure 1: Wage-Rate of Profits Frontier for Rent Analysis

Table 2: Summary

Wage Per Person-Year	Location of Extensive Margin
Between 0 and 2/3 Bushels	Land I Non-Scarce, Land II Scarce
Between 2/3 and 1 Bushels	Land I Scarce, Land II Non-Scarce

Table II summarizes the results from the example. The scarcity of land of the best grade is reflected in the use of both grades of land. But which land is best, and therefore scarce, varies with the distribution of income and the price system. Scarcity, then, generally cannot be simply read off of the technological data. It is determined with the price system.

Ricardo was wrong; the order of rentability may be altered by differences in distribution between wages and profits.

References

• Christian Bidard, Prices, Reproduction, Scarcity, Cambridge University Press (2004).
• Heinz D. Kurz and Neri Salvadori, "A Single Theory or Two? Walras's Critique of Ricardo".
• Alberto Quadri-Curzio, "Rent, Income Distribution, and Orders of Efficiency and Rentability", in Essays on the Theory of Joint Production (ed. by Luigi L. Pasinetti), Columbia University Press (1980).
• David Ricardo, On the Principles of Political Economy and Taxation, 3rd edition (1821).
• Bertram Schefold, Mr. Sraffa on Joint Production and Other Essays, Unwin Hyman (1989).