Some History of the Label 'Neoclassical"

I suppose if I want to note the origin of the term "neoclassical" in relation to economics, I should quote Aspromourgos. But I happen to have a Colander essay nearer at hand. The term grew to have a extremely general connotation:

"The term, neoClassical, was initially coined by Thorstein Veblen (1900) in his 'Preconceptions of Economic Science.'...

Hicks (1932, 1934) and Stigler (1941) extended the meaning of neoClassical to encompass all marginalist writers, including Menger, Jevons, and J.B. Clark. Most writers after Hicks and Stigler used the term inclusively. Thus it lost most of its initial meaning. Instead of describing Marshallian economics, it became associated with the use of calculus, the use of marginal productivity theory, and a focus on relative prices. As has been noted by a number of authors, while the neoClassical terminology makes some sense for Marshall, who emphasized the connection of his approach with the Classical approach, it makes far less sense for the others, such as Jevons, who emphasized the difference between his views and those of the Classicals. Some have suggested that anti-Classical would have been preferable.

...In the third edition of his principles textbook Samuelson (1955) built on Keynes' classification and turned it around on Keynes by developing the neoClassical synthesis. In the neoClassical synthesis, Keynes' dispute with Classical economists was resolved. This use of the term 'neoClassical' as an alternative to Keynesian models provides another confusion because it adds another reference point that brings to mind different elements of thought than would other comparisons." -- David Colander

By the way, shortly before World War II, Austrian economists did not see themselves as lying outside neoclassical economics or putting forth a separate doctrine:

"Referring to the usual separation of economic theorists into three schools of thought, 'the Austrian and the Anglo-American schools and the School of Lausanne', Mises (citing Morgernstern) emphasizes that these groups 'differ only in their mode of expressing the same fundamental idea and that they are divided more by their terminology and by peculiarities of presentation than by substance of their teachings' (Mises 1960 [1933])." - Israel Kirzner

For completeness, I expand the references in the above quotations.

References

• Tony Aspromourgos, "On the Origins of the Term 'Neoclassical'", Cambridge Journal of Economics, V. 10, N. 3: 265-270
• David Colander, "The Death of Neoclassical Economics"
• J. R. Hicks (1932) "Marginal Productivity and the Principle of Variation", Economica (February)
• J. R. Hicks (1934) "Leon Walras", Econometrica (October)
• Israel Kirzner (1987) "The Austrian School of Economics", The New Palgrave Dictionary of Economics
• L. von Mises (1960) Epistemological Problems of Economics, Van Nostrand (translation of Grundprobleme der Nationalökonomie, 1933)
• G. J. Sigler (1941) Production and Distribution Theories, Macmillan

Marx Was Skint - But He Had Sense / Engels Lent Him The Necessary Pence

Marx may or may not be correct in these passages. But these, and expansions of these passages, certainly contain claims worth thinking about:

"Let us take England. Its political economy belongs to the period in which the class-struggle was as yet undeveloped. Its last great representative, Ricardo, in the end, consciously makes the antagonism of class-interests, of wages and profits, of profits and rent, the starting point for his investigations, naively taking this antagonism for a social law of nature. But by this start the science of bourgeois economy had reached the limits beyond which it could not pass. Already in the lifetime of Ricardo, and in opposition to him, it was met by the criticism, in the person of Sismondi.

The succeeding period, from 1820 to 1830, was notable in England for scientific activity in the domain of Political Economy. It was the time as well of the vulgarizing and extending of Ricardo's theory, as of the contest of that theory with the old school. Splendid tournaments were held... The literature of Political Economy in England at this time calls to mind the stormy forward movement in France after Dr. Quesnay's death, but only as a Saint Martin's summer reminds us of spring. With the year 1830 came the decisive crisis.

In France and in England the bourgeoise had conquered political power. Thenceforth, the class-struggle, practically as well as theoretically, took on more and more outspoken and threatening forms. It sounded the death knell of scientific bourgeois economy. It was no longer a question, whether this theorem or that was true, but whether it was useful to capital or harmful, expedient or inexpedient, politically dangerous or not. In place of disinterested enquirers, there were hired prize-fighters; in place of genuine scientific research, the bad consequence and the evil intent of apologetic..." -- K. Marx, Capital, Volume 1, Author's Preface to the Second Edition

"A commodity is therefore a mysterious thing, simply because in it the social character of men's labour appears to them as an objective character stamped upon the product of that labour; because the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour. This is the reason why the products of labour become commodities, social things whose qualities are at the same time perceptible and imperceptible by the senses... With commodities... the existence of the things qua commodities, and the value relation between products of labour which stamps them as commodities, have absolutely no connection with their physical properties and with the material relations arising therefrom. There it is a definite social relation between men, that assumes, in their eyes, the fantastic form of a relation between things. In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with products of men's hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseperable from the production of commodities." -- K. Marx, Capital, Volume 1, Chapter 1, Section 4: The Fetishism of Commodities and the Secret Thereof

"Capital - profit (profit of enterprise plus interest), land - ground-rent, labour - wages, this is the trinity formula which comprises all the secrets of the social production process.

Furthermore, since as previously demonstrated interest appears as the specific characteristic product of capital and profit of enterprise on the contrary appears as wages independent of capital, the above trinity formula reduces itself more specifically to the following: Capital - interest, land - ground-rent, labour - wages, where profit, the specific characteristic form of surplus-value belonging to the capitalist mode of production, is fortunately eliminated.

On closer examination of this economic trinity, we find the following: First, the alleged sources of the annually available wealth belong to widely dissimilar spheres and are not at all analogous with one another. They have about the same relation to each other as lawyer's fees, red beets and music.

Capital, land, labour! However, capital is not a thing, but rather a definite social production relation, belonging to a definite historical formation of society, which is manifested in a thing and lends this thing a specific social character. Capital is not the sum of the material and produced means of production. Capital is rather the means of production transformed into capital, which in themselves are no more capital than gold or silver in itself is money. It is the means of production monopolised by a certain section of society, confronting living labour-power as products and working conditions rendered independent of this very labour-power, which are personified through this antithesis in capital. It is not merely the products of labourers turned into independent powers, products as rulers and buyers of their producers, but rather also the social forces and the future [? illegible] [A later collation with the manuscript showed that the text reads as follows: "die Gesellschaftlichen Kräfte und Zusammenhängende Form dieser Arbeit" (the social forces of their labour and socialised form of this labour). - Ed.] form of this labour, which confront the labourers as properties of their products. Here, then, we have a definite and, at first glance, very mystical, social form, of one of the factors in a historically produced social production process.

And now alongside of this we have the land, inorganic nature as such, rudis indigestaque moles, [Ovid, Metamorphoses, Book I, 7. - Ed] in all its primeval wildness. Value is labour. Therefore surplus-value cannot be earth. Absolute fertility of the soil effects nothing more than the following: a certain quantity of labour produces a certain product - in accordance with the natural fertility of the soil. The difference in soil fertility causes the same quantities of labour and capital, hence the same value, to be manifested in different quantities of agricultural products; that is, causes these products to have different individual values. The equalisation of these individual values into market-values is responsible for the fact that the 'advantages of fertile over inferior soil ... are transferred from the cultivator or consumer to the landlord'. (Ricardo, Principles, London, 1821, p.62.)

And finally, as third party in this union, a mere ghost - 'the' Labour, which is no more than an abstraction and taken by itself does not exist at all, or, if we take... [illegible], the productive activity of human beings in general, by which they promote the interchange with Nature, divested not only of every social form and well-defined character, but even in its bare natural existence, independent of society, removed from all societies, and as an expression and confirmation of life which the still non-social man in general has in common with the one who is in any way social." -- K. Marx, Capital, Volume 3, Part Seven, "Revenue and Theirs Sources", Chapter 48: The Trinity Formula

"The form of revenue and the sources of revenue are the most fetishistic expression of the relations of capitalist production. It is their form of existence as it appears on the surface, divorced from the hidden connections and the intermediate connecting links. Thus the land becomes the source of rent, capital is the source of profit, and labour the source of wages. The distorted form in which the real inversion is expressed is naturally reproduced in the views of the agents of this mode of production. It is a kind of fiction without fantasy, a religion of the vulgar. In fact, the vulgar economists - by no means to be confused with the economic investigators we have been criticizing - translate the concepts, motives, etc., of the representatives of the capitalist mode of production who are held in thrall to this mode of production and in whose consciousness only its superficial appearance is reflected. They translate them into a doctrinaire language, but they do so from the standpoint of the ruling section, i.e., the capitalists, and their treatment is therefore not naive and objective, but apologetic. The narrow and pedantic expression of vulgar conceptions which are bound to arise among those who are the representatives of this mode of production is very different from the urge of political economists like the Physiocrats, Adam Smith and Ricardo to grasp the inner connection of the phenomena." -- K. Marx, Theories of Surplus Value, Part III, Addenda, "Revenue and Its Sources. Vulgar Political Economy", 1.

It's Herd Behavior, Uh Huh, It's Evolution, Baby

Anybody interested in institutional economics should be interested in evolutionary theory, a theory that I can stand to learn more about. The interest in evolution among institutionalists goes back to Veblen. A more-or-less mid twentieth expression of interest can be seen in Ayres's biography of Thomas Huxley, also known as "Charles Darwin's bulldog". Geoffrey Hodgson is a current institutialist interested in evolution. What evolves in economies? I suggest organizational forms, business processes, and technology, at least.

I never saw anything interesting when operating Tierra on my old computer. Perhaps I understand neither the assembly language nor the visualization well-enough. Or perhaps I should have designed experiments and let it operate for more generations. I was never into Core Wars either. John Conway's Game of Life was more my speed. I don't seem to have executables for any of these for my OS X Macintosh.

But I think Thearling and Ray (1994) describe a neat idea. In Tierra, programs composed of machine instructions reproduce, perhaps with mutations. Memory is not protected, and programs can overwrite one another's code. An ability to more successfully protect one's own code and data and overwrite others is selected for.

One can do repeatable experiments with a computer program. Each generation can be saved, and the simulation can be rerun from any point in time, with random number generators restarted with new seeds. Lenski et al (2003) report such experiments with Avida, a computer simulation much like Tierra. In Avida, evolving computer programs collect energy to run their code. Programs that can do advanced logical operators are more fit. Lenski et al show that the evolution of a complex feature may depend on the prior evolutionary history of an organism providing the potential of the last few steps, even if previous mutations do not increase fitness.

I was surprised to find last week not only that repeatable experiments with evolution have been performed on simulations, but that Richard Lenski has been performing such a repeatable experiment on real-world organisms - namely, E. Coli - since 1988. (I must have missed Carl Zimmer's article, of 26 June 2008 in The New York Times, on the Long Term Evolution Experiment (LTEE).) Anyway, Blount, Borland, and Lenski's 2008 article reports on recent results.

In the LTEE, populations of each generation are isolated in a solution containing glucose for the E. Coli to eat. The isolated solution, I guess, acts like the simulated core memory in Tierra. And the E. Coli of any generation and evolutionary history can be frozen and restarted, just as an image of the computer core memory in a simulation run can be saved and reloaded. One run yielded a mutation that seems to have surprised Linski. This mutation allows the E. Coli to thrive on citrate, whatever that is, in the solution even "under oxic conditions". The ability to sample previous generations and look at other isolated population histories starting from the same initial conditions allows Linski and his colleagues to understand something about this mutation even before genetic sequencing. It is not the result of a single gene mutating, but is dependent on prior mutations in the history. These prior mutations may not have increased fitness themselves, but prepared the E. Coli to become dramatically more well-adapted for their specific environment after a couple more mutations. History matters.

References

• Ayres, Clarence (1932) Huxley, W. W. Norton
• Blount, Zachary D., Christina Z. Borland, and Richard E. Lenski (2008) "Historical Contingency and the Evolution of a Key Innovation in an Experimental Population of Escherichia Coli", Proceedings of the National Academy of Sciences V. 105, N. 23 (June 10): 7899-7906
• Hodgson, Geoffrey (2008), "Interview" Revue de la Régulation (January)
• Lenski, Richard E., Charles Ofria, Robert T. Pennock and Christoph Adaml (2003) "The Evolutionary Origin of Complex Features", Nature, V. 423 (8 May): 139-144
• Thearling, Kurt and Thomas S. Ray (1994) "Evolving Multi-celluar Artificial Life, Artificial Life IV, MIT Press

Conversations Elsewhere

Over at the Austrian Economists' blog, the comments on one post are mostly about Sraffa versus Hayek. The defenders of Hayek want to redefine the "natural rate" of interest to be the rate that would prevail in a monetary economy if the financial system did not "distort" prices somehow. This definition is opposed to the definition as the interest rate that would prevail in a barter economy. The defenders don't seem to realize that this redefinition addresses neither Sraffa's 1930s point that there are as many natural rates as there are commodities in an intertemporal equilibrium nor the 1960s reswitching results.

A Yahoo group is about Sraffa. Spanish-language discussions do me little good since I am limited to English.

Update: Gabriel Mihalache has a discussion about General Equilibrium theory that ends up overlapping with a discussion of Sraffa.

Brouhaha Over Marglin

I have been thinking about whether I want to read Stephen Marglin's new book, The Dismal Science: How Thinking Like an Economist Undermines Community. It sounds to me too much like Duncan Foley's recent book, Adam's Fallacy. A couple of reviews of Marglin's book are now available. Deirdre McCloskey has a generally positive review in the 27 March issue of the Times Higher Education. E. Roy Weintraub has a negative review in Science.

A couple of bloggers have posted on Weintraub's review. I find these posts fairly useless for clarifying either Marglin or Weintraub's perspective.

Brad DeLong comments on Weintraub's review, too. DeLong uses a German term that is not in my vocabulary:

"The gemeinschaft that is the professional community of Ivy League economists in which Marglin has been embedded for the past forty years has not treated him with 'reciprocity, altruism, and mutual obligation' but has--rather--in a very gemeinschaftlich way done what gemeinschaften traditionally do to corral their deviant members and to discourage others from imitating them. It has not been pretty.

But it seems to have had no effect on Marglin's thinking, none at all, for reasons I do not understand." -- Brad DeLong

I've had something to say about the ugliness in Harvard's economics department. Some highlights: Harvard denied tenure to those among Marglin's colleagues who could provide useful feedback on his ideas. I doubt very few in the Harvard department have anything useful to say about Marglin's ideas on unemployment and inflation, some of which he developed in collaboration with Amit Bhaduri. More recently, Harvard has refused to let Marglin to teach a section of the intro course for credit as a prerequisite and as a counter to Mankiw's lies.

Weintraub is part of a trend in the history of ideas that tends to see more discontinuities and at a lower level than previously:

"in the disciplines that we call the history of ideas, the history of science, the history of philosophy the history of thought, and the history of literature (we can ignore their specificity for the moment), in those disciplines which, despite their names, evade very largely the work and methods of the historian, attention has been turned, on the contrary, away from vast unities like 'periods' or 'centuries' to the phenomena of rupture, of discontinuity. Beneath the great continuities of thought, beneath the solid, homogeneous manifestations of a single mind or of a collective mentality, beneath the stubborn development of a science striving to exist and to reach completion at the very outset, beneath the persistence of a particular genre, form, discipline, or theoretical activity, one is now trying to detect the incidence of interruptions. Interruptions whose status and nature vary considerably. There are the epistemological acts and thresholds described by Bachelard: they suspend the continuous accumulation of knowledge, interrupt its slow development, cut it off from its empirical origin and its original motivations, cleanse it of its imaginary complicities; they direct historical analysis away from the search for silent beginnings, and the never-ending tracing-back to the original precursors, towards the search for a new type of rationality and its various effects. There are the displacements and transformations of concepts: the analyses of G. Canguilhem may serve as models; they show that the history of a concept is not wholly and entirely that of its progressive refinement, its continuously increasing rationality, its abstraction gradient, but that of its various fields of constitution and validity, that of its successive rules of use, that of the many theoretical contexts in which it developed and matured..." -- Michel Foucault (1972) The Archaeology of Knowledge, Pantheon Books.

I do not know the historians of ideas Foucault references, but his descriptions could perhaps characterize aspects of "thick histories".

Along with embracing these standards, Weintraub thinks they should be professionalized. Historians of economics should be writing for and to the standards of historians of science. The history of economics should not to be done by dilettantes in history taking a break from their professional work as modern economists. History is not to be done by hopping from one great book to another, ignoring all the minor thinkers of the time that contextualizes the contents of each book. And the story should be told forward, without imposing on the actors in the story a desire to get to where they ended up after much stumbling. One should look for what standards evolved in the protangonists' milieus. Historians of economics should not be in the business of rating past economists by current ideas and current standards of argument.

Weintraub also doesn't like the classification of the history of economic thought as heterodox economics. For him, history is not supposed to be a morality tale. Weintraub non-judgemental approach to history raises some questions. What is the usefulness of history? Why should economists, as part of their professional training, receive any information about the history of their discipline? Should university economics departments devote any resources to studying that history? I am not providing answers to these questions here. Obviously I find Weintraub's writings of enough interest to think I can assign views to him without giving any specific citations.

Without having read Marglin's book, let me finally turn to a substantial point in Weintraub's review. I can see how one might doubt that the ideas Weintraub says are engaged by Marglin were all grown up in the nineteenth century. But I have noted how some are in embryo in J. S. Mill.

I am disappointed that Weintraub cites Coleman's book positively.

For reference, here is Weintraub's review:

"ECONOMICS: First, Kill the Economists",

"The prophet Jeremiah is alive and well and teaching economics at Harvard. It is not often that a scholar with no particular historical or philosophical expertise trashes the Western enlightenment in order to stomp on the discipline of economics as a manifestation of all that was lost in creating the modern world. Stephen A. Marglin's argument in The Dismal Science is that economics--with its focus on an individual's preferences, the freedom to engage in activities to promote his or her well-being, and the pursuit of self-interest variously construed--perverts a natural moral order: 'the foundational assumptions of economics are in my view simply the tacit assumptions of modernity. The centerpiece in both is the rational, calculating, self-interested individual with unlimited wants for whom society is the nation-state.' And what modernity shunned was 'community.'

His main line is that 'The market undermines community because it replaces personal ties of economic necessity by impersonal market transactions.... The ambivalent relationship between noneconomists and economics reflects the ambivalence with which modernity is regarded.' To be sure, sociologists deal with community, as do anthropologists, as do political scientists, and so on. But economics, for Marglin, is different: 'Economics is not only descriptive; it is not only evaluative; it is at the same time constructive--economists seek to fashion a world in the image of economic theory.' Economics and thinking like an economist are bad for the health of the world. Indeed, he closes his volume stating that 'There are many ways of resolving the tensions between individualism and holism, between self-interest and obligation to others, between algorithm and experience, between the claims of various communities on our allegiance, between material prosperity and spiritual health. Economics offers one way, but as presently constituted, economics is hobbled by an ideology in which these tensions are replaced by a set of pseudo-universals about human nature. A dismal science indeed.' The argument about the proper way to do economics is an old one. An 1832 complaint in The Eclectic Review charged the work of Thomas Malthus and David Ricardo with leading the public far from 'the true path of inquiry' and making political economy 'a hideous chain of paradoxes at apparent war with religion and humanity.' In the past century or two, we have heard this lamentation from time to time from both secular and religious figures.

In much of Europe, what we now call economics developed in order to understand various matters of business law, contracts, taxation, international trade, and project management. Issues like tariff policy and currency management were discussed by individuals who were variously lawyers, engineers, politicians, managers, and business people, and training in such expertise developed pari passu.

The professionalization of economics was a late 19th century phenomenon. Cambridge's Alfred Marshall, in attempting to construct a scientific economics, was not able to establish economics as a separate discipline until the death of Henry Sidgwick, the university's professor of moral philosophy, under whose direction lectures in political economy had been organized. In the United States at that time, economics was growing from different sources. One stream followed from individuals who had obtained Ph.D.'s in Germany, where social policy issues--labor unions, socialism, the nascent welfare state, etc.--were galvanizing the universities. But a second stream nurturing the American progressive economists grew from the social gospel movement, which sought to promote the kingdom of God on Earth through enlightened social policy and the kind of market interventions that Adam Smith in fact quite welcomed.

The kind of economics from which Marglin recoils is, however, not of the sort that was present in writings of individuals (e.g., Smith, Ricardo, John Stuart Mill, Marshall, and John Commons) who have been claimed as ancestors by modern economists. It is instead what developed in the post-World War II stabilization of economic discourse and the final professionalization of the discipline. It was during that postwar period, not in the Enlightenment, that economic science became normal in Thomas Kuhn's sense.

Marglin's account appears confused by this history. Moreover, he appears to believe that the ideas he engages and then casts aside (ideas about the economic agent, preferences, equilibrium, models, and markets) all grew up not in the 20th century but hundreds of years earlier--and that those ideas have had stable meanings ever since: 'For four hundred years, economists have been active in the enterprise of constructing the modern economy and society, both by legitimizing the market and by promoting the values, attitudes, and behaviors that make for economic success. No apology is due for this--except for the pretense of scientific detachment and neutrality and the unwillingness to confront the ideological beam in our collective eye.' The ahistoricity of such a statement is startling; for instance, it assumes wrongly that there were individuals called economists 400 years ago and that science in 1600 meant the same thing as it does in 2008.

In his critique, Marglin moves back and forth between moralizing about the loss of community and contempt for the economists' tools and models. He claims, 'By promoting market relationships, economics undermines reciprocity, altruism, and mutual obligation, and therewith the necessity of community. The very foundations of economics, by justifying the expansion of markets, lead inexorably to the weakening of community.' He complains that 'it is difficult to tell a plausible story of how individuals acquire meaningful preferences between consumption today and consumption a decade or two hence, in the way one can imagine learning about peaches today and pears today.' But is not Marglin's Harvard College teaching an instruction of the young designed to shape their preferences, especially preferences about long-term versus short-term goals?

From the first times economic arguments were parsed and markets described, there were those who found both contemptible, and this was well before the Enlightenment. Attacks on money lending at interest go back even earlier than Jesus on the temple steps. Recall Aquinas's ideas about the 'just price.' One mustn't forget Shakespeare's Shylock, either. Tax collecting for kings and emperors requires economic management skills, but no one likes to pay taxes. In a prize-winning book (1), William Coleman showed how over the centuries the very idea of economics has been loathed by left, right, and center; Christian, Jew, and anti-Semite; pope and communist dictator; lawyer and business mogul; and scientist and humanist.

In this same tradition of anti-economics, Marglin sees the future of the field as bleak, with the current generation of economics students avoiding large questions in their search for career advancement. And the problems that economics creates will only get worse, he claims, because globalization will make the national community as obsolete as the market has made the local community.

I note in closing that the lead dust-jacket blurb for this volume was provided by the noted economist and social theorist Bianca Jagger (sic). Whatever was Harvard University Press thinking?" -- E. Roy Weintraub,

Real Utopias

I haven't begun to explore this "Real Utopias" project. It seems to me to have a flavor of Analytical Marxism.

Hat tip to taavi

The Moving Finger Writes...

...and, having writ,
Moves on: nor all your piety nor wit
Shall lure it back to cancel half a line,
nor all your tears wash out a word of it.

1.0 Introduction
Neoclassical economics emphasizes equilibria, for example in General Equilibrium models. In equilibria, all agents are optimizing and their plans are all pre-coordinated. But no reason exists for economists to expect actually existing more-or-less capitalist economies to ever be in such equilibria.

This post demonstrates that economies need not be near equilibria by means of an example. This example has been available for almost a half century (Scarf 1960) and is often referenced (e.g., Ackerman 1999, Hahn 1961 and 1970, McCauley 2004, Saari 1995, Sonnenschein 1972). The example is of a pure exchange economy. Since no production occurs in the example, it cannot be considered an example of a Sraffian model. Furthermore, the example is of brain-dead tâtonnement dynamics. No trading occurs at any prices other than equilibrium prices. Since the example has one locally unstable equilibrium, equilibrium prices are never achieved.

Neoclassical economic theory imposes almost no restriction on excess demand functions. The most substantial restriction is the unfounded conservation law expressed by the symmetry of the Slutsky matrix. This lack of any empirical implications of neoclassical theory for market behavior is an implication of the Sonnenschein-Mantel-Debreu results. Another implication is that any price dynamics are possible in a tâtonnement process, including chaos. So this example does not even represent the most general or complex dynamics possible in neoclassical models.

2.0 Data
This example economy consists of three individuals, each endowed with one unit of a different commodity (Table 1). The individuals also differ in tastes, as expressed by the utility functions in Table 2. Our problem is to determine equibrium prices for this simple economy and the price dynamics.

Table 1: Agents' Endowments

Agent	Endowment
	Apples	Bananas	Cantalopes
Mary	1	0	0
Nancy	0	1	0
Olivia	0	0	1

Table 2: Agents' Preferences

Agent	Utility Function
Mary	UM = min( xA, xB )
Nancy	UN = min( xB, xC )
Olivia	UO = min( xA, xC )

3.0 Demand Functions
Each agent maximizes their utility, subject to their budget constraint. Consider a single agent, for example, Mary. Mary chooses non-negative x_A, x_B, x_C to maximize

U_M = min( x_A, x_B )          (1)

such that

p_A x_A + p_B x_B + p_C x_C ≤ p_A          (2)

Since Mary derives no utility from cantalopes, she will not consume any of them. Thus, Mary's problem can be graphed in a two-dimensional space (Figure 1). The graph also shows the quantities Mary demands of apples and bananas. These quantities are on the intersection of the budget constraint with a particular isoquant of the utility function. Symbolically:

x_A^* = x_B^* = p_A/(p_A + p_B)          (3)

x_C^* = 0          (4)

Figure 1: Mary's Utility Maximizing Problem

One can find Nancy and Olivia's demand functions by symmetrical arguments. Aggregate excess demand functions are the difference between aggregate demands and aggregate supplies. Aggregate demands are individual demand functions summed across the individuals. Aggregate supplies, in this pure exchange economy, are endowments summed across individuals. In fact, the aggregate supply of each commodity is one unit here. A bit of algebra yields:

z_A = p_C/(p_A + p_C) - p_B/(p_A + p_B)          (5)

z_B = p_A/(p_A + p_B) - p_C/(p_B + p_C)          (6)

z_C = p_B/(p_B + p_C) - p_A/(p_A + p_C)          (7)

where z_B, z_B, and z_C are the aggregate excess demand functions for apples, bananas, and cantelopes, respectively.

The numeraire is arbitrary. One can confine prices to lie on the unit sphere:

p_A² + p_B² + p_C² = 1          (8)

4.0 Equilibrium

In equilibrium, aggregate excess demand functions are zero. The only equilibrium is one in which all prices are equal:

p_A^* = p_B^* = p_C^* = (1/3)^1/2          (9)

5.0 Tâtonnement Dynamics
I postulate that when the aggregate excess demand for a particular commodity is positive, the price of that commodity rises. Likewise, when aggregate excess demand is negative, the price falls. The simplest dynamical system with these properties is one in which the rate of change of prices with respect to time is equal to the aggregate excess demands:

dp_A/dt = p_C/(p_A + p_C) - p_B/(p_A + p_B)          (10)

dp_B/dt = p_A/(p_A + p_B) - p_C/(p_B + p_C)          (11)

dp_C/dt = p_B/(p_B + p_C) - p_A/(p_A + p_C)          (12)

Under these dynamics, the equilibrium is unstable. Solutions around the equilibrium spiral out on the unit sphere to a limit cycle. Figure 2 shows a two-dimensional projection of that limit cycle.

Figure 2: Two-Dimensional Projection of Dynamics

6.0 Conclusion
The failure of General Equilibrium Theory to limit dynamics, I gather, is intrinsic to methodological individualism, in which independent agents can have arbitrary preferences and endowments. Attempts to explain economies seem to need to postulate influences on tastes and income above the level of the individual, for example, by others in one's social class or through some sort of structuralist theory. In other words, there is too such a thing as society. I take Kirman (1989) to point in this direction.

I might as well mention that the arbitrary dynamics implied by orthodox economic theory undermines a certain political outlook. I refer to the idea that we ought to loosen restrictions on trade, but ensure some sort of redistribution so as to ensure that everybody participates in the supposedly enlarged pie. I take the second welfare theorem to be the basis for this view. But that redistribution doesn't necessarily lead to the economy converging to the original equilibrium, as altered by free trade.

References

• Frank Ackerman (1999) "Still Dead After All These Years: Interpreting the Failure of General Equilibrium Theory", Global Development and Environment Institute, Working Paper No. 00-01
• Frank H. Hahn (1961) "A Stable Adjustment Process for a Competitive Economy", The Review of Economic Studies, V. 29, N. 1 (October): pp 62-65.
• Frank H. Hahn (1970) "Some Adjustment Problems", Econometrica, V. 38, N. 1 (January): 1-17
• Alan Kirman (1989) "The Intrinsic Limits of Modern Economic Theory: The Emperor Has No Clothes", Economic Journal, V. 99, N. 395: 126-139
• Joseph L. McCauley (2004) Dynamics of Markets: Econophysics and Finance, Cambridge University Press
• Donald Saari (1995) "Mathematical Complexity of Simple Economics", Notices of the AMS, V. 42, N. 2 (February): 222-230
• Herbert Scarf (1960) "Some Examples of Global Instability of the Competitive Equilibrium", International Economic Review, V. 1, N. 3 (September): 157-172
• Hugo Sonnenschein (1972) "Market Excess Demand Functions", Econometrica, V. 40, N. 3 (May): 549-563

George Rickey

What Is Apathy? I Don't Care.

As far as I can see, Varian implies in the following combination of quotations that the student need not care about vast chunks of his textbook:

"...we show that the theory of utility-maximization implies certain testable restrictions on the observed choices of consumers. Such restrictions have several sorts of uses. For example, one can use these observed restrictions to test the model against actual behavior of economic units. Given some data, one can ask if it could have been generated by a maximizing unit..." -- Hal R. Varian (1978) Microeconomic Analysis, Second Edition, W. W. Norton & Company, p. 2

"...the utility maximization hypothesis imposes certain observable restrictions on consumer behavior. In particular, we know that the matrix of substitution terms... must be a symmetric, negative semidefinite matrix." -- Hal R. Varian (1978) Microeconomic Analysis, Second Edition, W. W. Norton & Company, p. 135-136

"It can be shown that any continuous function that satisfies Walras' law is an excess demand function for some economy; i.e., the utility maximization hypothesis places no restrictions on aggregate demand behavior... Thus, any dynamical system on the price sphere can arise from our model of economic behavior." -- Hal R. Varian (1978) Microeconomic Analysis, Second Edition, W. W. Norton & Company, p. 246

In other words, the empirical content of the "utility maximization hypothesis" on the level of the theory of markets is close to empty.

The Influence of Chris Hayes?

A couple of weeks back, The Nation notes Hillary Clinton's statement: "I'm not going to put my lot in with economists." I gather that Clinton's gas tax holiday is not a good idea. But, "Clinton had a point, though, not about the gas tax but about the undue influence of a certain brand of mainstream economists who dominate prestigious universities." The Nation editorialist further says:

"Hillary Clinton ... also apparently thinks the economists she knows--the ones who had her husband's ear--represent the totality of solid and relevant economic thought. In fact, many good economists have different views on trade and fiscal policies and cannot get a hearing."

Susan Jacoby, in an editorial for the New York Times has a different take:

"Senator Hillary Clinton's use of the phrase 'elite opinion' to dismiss the near unanimous opposition of economists to her proposal for a gas tax holiday was a landmark in the use of elite to attack expertise supposedly beyond the comprehension of average Americans. One might as well say that there is no point in consulting musicians about music or ichthyologists about fish."

Jacoby doesn't approve of elite-bashing. I think this point would work better if we were not talking about economists.

Steven Horwitz and Post Keynesians

Steven Horwitz has kindly made his papers available online. I find that Horwitz has engaged in a couple of controversies with Post Keynesians, broadly defined. I refer to these interchanges:

• Hill (1996a), Horwitz (1996c), Hill (1996b), and Horwitz (1998)
• Horwitz (1996a), Cottrell (1996?), and Horwitz (1996b)

What worries me about these is whether I need to add to my already-too-long critique of Austrian Business Cycle Theory (ABCT) in yet another revision. (The latest publicly available version of my critique of ABCT is here. I have submitted an even more recent version to some journal.) Luckily, nobody in these interchanges seems to bring up my points from capital theory. I already reference his later book, Horwitz (2000). I hadn't known that he developed these ideas partly by arguing with Post Keynesians. In the remainder of this post, I illustrate some deficiencies of Horwitz's arguments.

Horwitz clearly states the mistaken Austrian view that, in a coordinated state, the length of production processes is inversely related to the interest rate:

"The capital structure ... reflects ... 'roundaboutness,' of production... Recent developments of Austrian capital theory have abandoned Böhm-Bawerk's emphasis on the 'average' period of production, the idea of the capital structure as reflecting roundaboutness remains. ... At higher rates of interest we would expect shorter processes of production ... Conversely, lower rates of interest should lengthen the capital structure, as the lower cost of time will make more roundabout, and hence more productive, processes more feasible... The capital structure needs to embody some notion of intertemporal coordination, i.e., the lengths of current processes of production should correspond to the willingness of consumers to wait for the availability of consumer goods. If the capital structure is not intertemporally coordinated, ...then there is avoidable economic waste." -- Horwitz (1996a)

Allin Cottrell takes Horwitz to task for ignoring established criticisms of ABCT and for simplifying Hayek to the point of misrepresentation. One of these criticisms is a Cottrell paper, which I do cover in my critique. Cottrell's comments are focused on monetary theory, not on the capital-theoretic analysis I write about.

Consider an imaginary coordinated state of the economy in which the expectations and plans of all agents are largely consistent and in which those expectations are being fulfilled. In such a coordinated state, must all markets clear? Must the labor market clear? Keynes answers these questions in the negative. He argues that if agents' plans and expectations were being more-or-less achieved, the level of unemployment would not need to be zero or whatever level is consistent with frictional unemployment. By the way, it is along these lines that I think a synthesis of Keynes and Sraffa can be achieved. Jan Kregel probably puts this better. Horwitz, in his responses to Hill, begs these questions. I refer to Horwitz discussion of savings, investment, interest rates, and banking. To me, Keynes and the Post Keynesians are more perceptive than Austrians both about what is seen and what is not seen in a capitalist economy. Since Horwitz does not understand the argument, he cannot credibly dispute me.

Here's another example of Horwitz's lack of understanding of Keynes: he attacks Keynes with a strawperson:

"Cash is not fundamentally different than other goods or services; if the public wishes to hold more of it, there is no reason that the laws of supply and demand should take a holiday. Keynes assumed that cash is 'barren' because it provides no yield to the holder, such that holding cash was socially wasteful. If one defines 'yield' to be some sort of financial return, then Keynes was right, but the same is true of any other good or service. Compact disc players do not yield a pecuniary return, yet people choose to hold 'stocks' of them because they provide a service - the playing of music. Cash is no different, in that it provides the service of being available to buy things. By Keynes's logic, fire trucks standing in fire stations are 'doing nothing' and yield no benefits. But they provide the benefit of being available for use when needed." -- Horwitz (1996c)

This is wrong for at least two reasons. First, for Keynes, money does not necessarily have no financial yield. In chapter 13 of the General Theory, Keynes states that one can

"draw the line between "'money' and 'debts' at whatever point is most convenient for handling a particular problem... It is often convenient to include in money time-deposits with banks and, occasionally, even such instruments as (e.g.) treasury bills." -- John Maynard Keynes (1936)

Second, and more seriously, Keynes is quite aware that money is liquid, that is, available to buy things. In chapter 17 of the General Theory, Keynes states that the expected return from the ownership of an asset is "equal to its yield minus its carrying cost plus its liquidity premium".

Horwitz seems to miss the point here too:

"Hill notes that 'to hold cash is to take refuge from uncertainty.' He then quotes G. L. S. Shackle, who argues that taking refuge from uncertainty (presumably by holding cash) means that we also take refuge 'from enterprise, from the giving of employment.' In the short run, my decision to hold more money in the form of bank deposits redistributes employment among different people, but does not reduce 'the giving of employment.' And in the long run, my uncertainty-induced decision to hold more bank deposits will generate increased employment.

In really existing capitalism with central banks, an increased relative demand for currency due to uncertainty can indeed touch off a decline in aggregate demand (assuming anything less than perfectly flexible prices) if the central bank does not react properly. However, in a banking system where individual banks were allowed to create their own currencies in the same manner as their deposits, this would not be the case. Where currency is a liability of the banking system, taking refuge from uncertainty in currency is no different from taking refuge in bank deposits and the effects are the same: an increase in wealth over time, due to the increase in saving... By making currency a bank liability rather than a reserve medium, a 'free banking' system would allow one less way for the public to withdraw bank reserves and cause a major contraction in credit and aggregate demand. The problem with contemporary central-bank-controlled capitalism is the very fact that when the public wants more of certain kinds of money, private enterprise cannot legally 'produce more of it.' Such a prohibition is not an irremediable fact of the world, but a particular institutional condition of modern capitalism that could be changed by ending government control over money." -- Horwitz (1998)

Whether or not the supply of money is endogenous, the demand for money does not directly give employment (excluding data entry for those changing some bits on a computer in some bank). This contrasts for the demand for an illiquid asset which must be manufactured to be supplied. As for the indirect effects, I find nothing but argued assertion in Horwitz.

I'm not even sure that Horwitz understands his own theory. Consider this assertion of the consistency of time preference and liquidity preference theories:

"Hill is implying that ... that cash trades off against such securities, ... that the demand for money is caused by interest rates and that, therefore, the interest rate is ... overwhelmingly a function of the supply and demand for money. However, the fact that I prefer the present to the future is intimately linked with the fact that the future is uncertain. ... I never denied that people hold money due to uncertainty. In fact, that is precisely why they hold it, as I have argued elsewhere ... The desire for liquidity or availability services is a manifestation of the more fundamental concept of time-preference. If I choose to sell bonds and acquire cash, this suggests that I am worried about the future and want cash so as to leave my options open. My time preferences have shifted toward the present. When I sell my bonds, bond prices fall and interest rates rise, as they should to reflect my concerns about the future. There is no contradiction between recognizing money's liquidity or availability services and a time preference theory of the interest rate." -- Horwitz (1998)

Time preference relates to time profile of ones desired consumption stream, to whether one wants to consume goods now or later. A change in what assets one holds for transferring purchasing power in the future is not a manifestation of a change in time preference. When the financial value of my savings and income stay unchanged, but I change the assets in which my savings are held to be more liquid, my time preferences have not not shifted, toward the present or otherwise.

By the way, Horwitz points out in his second reply to Hill that he is not arguing about theories that describe actually existing economies. He is explaining how the world would work if his utopian blueprint, especially for the banking system was adopted. I like how supposed fans of Hayek exhibit no appreciation for Popper.

References

• Allin Cottrell (1996?) "Comment on Horwitz's Article", Journal of the History of Economic Thought, V. 18, N. 2 (Fall): 308-313
• Greg Hill (1996a) "The Moral Economy: Keynes's Critique of Capitalist Justice", Critical Review, V. 3: 411-434 [I need to read this]
• Greg Hill (1996b) "Capitalism, Coordination, and Keynes: Rejoinder to Horwitz" Critical Review, V. 10, N. 3: 373-387 [I need to read this]
• Steven Horwitz (1996a) "Capital Theory, Inflation, and Deflation: The Austrians and Monetary Disequilibrium Theory Compared", Journal of the History of Economic Thought, V. 18, N. 2 (Fall): 278-307
• Steven Horwitz (1996b?) "Reply to Cottrell", Journal of the History of Economic Thought, V. 18, N. 2 (Fall): 314-318
• Steven Horwitz (1996c) "Keynes on Capitalism: Reply to Hill", Critical Review, V. 10, N. 3 (Summer): 353-372
• Steven Horwitz (1998) "Keynes and Capitalism One More Time: A Further Reply to Hill", Critical Review, V 12, N. 1/2 (Winter-Spring): 95-111
• Steven Horwitz (2000) Microfoundations and Macroeconomics: An Austrian Perspective, Routledge

Krishna Bharadwaj, A Sraffian Economist

A web site devoted to freeing Binayak Sen reprints an article from The Telegraph-Calcutta. This article draws a parallel between Sudha Bharadwaj and Binayek Sen.

I don't know anything about B. Sen or S. Bharadwaj. But if Arundathi Roy and Amartya Sen are protesting your arrest, I assume you should be freed. The People's Union for Civil Liberties, at first glance, sounds like a fine organization.

Apparently Sudha Bharadwaj is the daughter of Krishna Bharadwaj. I happen to have read her review of Sraffa's book - or at least the extracts that Harcourt and Laing (1971) reprint. As I recall from somewhere, she took a couple of years to write this review. When given Sraffa's book to review, she felt obligated to reread Adam Smith and David Ricardo. This was a perceptive understanding.

I first became aware of Krishna Bharadwaj's work, though, by stumbling upon her 1989 collection of essays. These are reprinted from such journals as Australian Economic Papers, the Cambridge Journal of Economics, and others. I found these essays quite good. I later read her 1978 lecture and the 1990 conference volume she co-edited with Bertram Schefold. Until the last few years, that conference seems to have been the most thorough assessment of Sraffa's contributions - not that economists such as Pierangelo Garegnani and Paul Samuelson could agree. She also has some applied work which I haven't read.

References

• Krishna Bharadwaj (1963) "Value Through Exogenous Distribution", Economic Weekly (Bombay), 24 August: 1450-1454
• Krishna Bharadwaj (1978) Classical Political Economy and the Rise to Dominance of Supply and Demand Theories, Orient Longman
• Krishna Bharadwaj (1989) Themes in Value and Distribution: Classical Theory Reappraised, Unwin Hyman
• Krishna Bharadwaj and Bertram Schefold (editors) (1990) Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory, Unwin Hyman
• G. C. Harcourt and N. F. Laing (editors) (1971) Capital and Growth, Penguin

Reswitching With Smooth Production Functions

I cite authority:

"Something precious I gained from Robinson's work and that of her colleagues working in the Sraffian tradition. As I have described elsewhere, prior to 1952 when Joan began her last phase of capital research, I operated under an important misapprehension concerning the curvature properties of a general Fisher-von Neumann technology.

What I learned from Joan Robinson was more than she taught. I learned, not that the general differentiable neoclassical model was special and wrong but that a general neoclassical technology does not necessarily involve a higher steady-state output when the interest rate is lower. I had thought that such a property generalized from the simplest one-sector Ramsey-Solow parable to the most general Fisher case. That was a subtle error and, even before the 1960 Sraffa book on input-output, Joan Robinson's 1956 explorations in Accumulation of Capital alerted me to the subtle complexities of general neoclassicism.

These complexities have naught to do with finiteness of the number of alternative activities, and naught to do with the phenomenon in which, to produce a good like steel you need directly or indirectly to use steel itself as an input. In other words, what is wrong and special in the simplest neoclassical or Austrian parables can be completely divorced from the basic critique of marginalism that Sraffa was ultimately aiming at when he began in the 1920s to compose his classic: Sraffa (1960). To drive home this fundamental truth, I shall illustrate with the most general Wicksell-Austrian case that involves time-phasing of labor with no production of any good by means of itself as a raw material.

As in the 1893-1906 works of Knut Wicksell, translated in Wicksell (1934, Volume I), let corn now be producible by combining labor yesterday, labor day-before-yesterday, etc):

Q_t = f(L_t-1, L_t-2, ..., L_t-T) = f(L)                                                     (1)

Q = f(L₁, L₂, ..., L_T) in steady states                                              (2)

    = L₁ f(1, L₂/L₁, ..., L_T/L₁) 1st^o-homogeneous and concave      (3)

    = L₁ (df(L)/dL₁) + ... + L_T (df(L)/dL_T), Euler's theorem            (4)

df/dL_j = f_j(L), d²f/(dL_i dL_j) = f_ij(L) exist for L ≥0                         (5)

f_j > 0, (z₁, ..., z_T)[f_ij(L)](z₁, ..., z_T)' < 0 for z_j ≠ b L_j > 0                (6)

Nothing could be more neoclassical than (1)-(6). If it obtained in the real world, a Sraffian critique could not get off the ground.

Yet it can involve (a) the qualitative phenomena much like 'reswitching', (b) so-called perverse 'Wicksell effects', (c) a locus between steady-state per capita consumption and the interest rate, a(i, c) locus, which is not necessarily monotonically negative once we get away from very low i rates. This cannot happen for the 2-period case where T = 2. But for T ≥ 3, all these 'pathologies' can occur, and there is really nothing pathological about them. No matter how much they occur, the marginal productivity doctrine does directly apply here to the general equilibrium solution of the problem of the distribution of income.

Remarks. What eternal verities do always obtain, even when corners in the technology make derivatives [dQ_j/dL_j, dQ_j/dQ_ij] be somewhat undefined? Always, it remains true:

(a) To go from an initial sub-golden-rule steady state to a maintainable golden-rule steady state of maximal per capita consumption, must involve for society a transient sacrifice of current consumptions ('waiting' or 'abstinence' a la Senior, Böhm, and Fisher!).

(b) For non-joint-product systems, there is a steady-state trade-off frontier between the interest rate and the real-wage (expressed in terms of any good).

This monotone relation between (W/P_j, i) was obscurely glimpsed by Thunen and other classicists and by Wicksell and other neoclassicists. But the factor-price trade-off frontier did not explicitly surface in the modern literature until 1953, as in R. Sheppard (1953), P. Samuelson (1953), and D. Champernowne (1954). One can prove it to be well-behaved for (1)-(3), or any convex-technology case, by modern duality theory. Before Robinson (1956), I wrongly took for granted that a similar monotone-decreasing relation between ( i, Q/(L₁ + ... + L_T) ) must also follow from mere concavity - just as does the relation -d²C_t+1/(dC_t)² = di/dC_t) > 0. But this blythe expectation is simply wrong! I refer readers to my summing up on reswitching: Samuelson (1966).

I realize that there are many economists who tired of Robinson's repeated critiques of capital theory as tedious and sterile naggings. I cannot agree. Beyond the effect of rallying the spirits of economists disliking the market order, these Robinson-Sraffa-Pasinetti-Garegnani contributions deepen our understanding of how a time-phased competitive microsystem works." -- Paul A. Samuelson (1989) "Remembering Joan" in Joan Robinson and Modern Economic Theory (ed. by George R. Feiwel), New York University Press.

(I have changed some of the symbols above.) I've noted before comments from Samuelson in papers that have made claims much the same as above.

Students at Schools With Interesting Economists

E. Roy Weintraub and Edwin Burmeister are two Duke economists I find worth reading. Here are some Duke students:

Duke, Quaterfinals at Ithaca, 18 May 2008

Below are some Notre Dame students, except for the upper left. Thos are Syracuse University students. I did not ask any Notre Dame fans what they thought of their administration's shameful treatment of some of their economists or talk about an on-line petition.

Notre Dame, Quaterfinals at Ithaca, 18 May 2008

I do not have any photos of U-Mass, Amherst, students, although I did go to Syracuse's last home game of the regular season.

Days Late And A Penny Short

I find from Crooked Timber another interesting blog - Nancy Folbre's Care Talk. I don't know how much, if any, of Folbre's work I've read. She is quite prominent, if I understand correctly, as a developer of feminist economics.

Elsewhere

Some feminists have started blogging on economics: Kathy G. and Allison. Kathy G. doesn't seem to draw on Feminist Economics. I don't know about Allison.

I recently stumbled on the blog of an economist at Cambridge, UK.

As I understand it, this blog is from Edward Nell's son. I might as well give a quote from Edward Nell:

"Joan Robinson started the capital theory/production function controversies in the 1950s. After Sraffa's book in 1960 the next decades saw major battles in the journals, battles which resulted in conclusions widely held today: to wit, the technical errors are conceded, but their significance is contested. This has a practical meaning: open any major journal at random today, and there will be marginal products, aggregate production functions, et hoc genus omnia - with no hint that any technical error is involved. The critique is simply ignored. It can't be answered, but it is held to be unimportant.

The neo-Ricardian project initially aimed at reviving the Classical approach. The idea, it seemed was to develop an alternative economics, a science of economic phenomena grounded on different principles...

...The original idea was to move toward a complete reconstruction of economics, on a revived and revised form of the Classical approach, not merely critism of neo-Classical arguments, nor clarification of Classical arguments. The approach would be different: it would be sound theory, but theory based on a realistic account of institutions and history. Furthermore, such analyses could be expected to lead to new, useful, and progressive formulations of policy. That was also the hope of the summer school in Trieste.

What has emerged must be considered disappointing. A Classical 'general equilibrium' theory has been worked out, together with a critique of neo-Classical [economics] - but there has been no development of a new economics. To be sure, there are a few scattered articles on a number of ... topics. But besides the critical work and the development of price theory, the important and widely recognized work has centered on the History of Economic Thought." -- E. J. Nell (1998), The General Theory of Transformational Growth: Keynes After Sraffa, Cambridge University Press

I am aware that I have only here on this blog touched on the potential of Sraffa's work.

One of the seven bloggers here is Tiago Mata.

Tim Lee has a review of Math You Can't Use, a book by Ben Klemen objecting to software patents. Matthew Yglesias's reacts. Some of Matt's commenter's bring up another book, Patent Failure, by Bessen and Meuer. I've found a post from another blog on Matt's post and another reaction from Matt. By the way, when considering the desirability of software patents, one might distinguish between bad patents in an area of technology and the (un)desirability in principle of having patents in an area. As I understand, software patents differ from copyrights in that they impose a burden on developers of doing searches of already established intellectual property, while copyrights don't.

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.

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.

Firms Run By The Power-Mad

"In a recent biography Eleanor Dulles reports on her experience in a New York hairnet factory circa 1920. 'The owner of the factory never came out there, he just sat in New York and took the money ... The manager was a very sharp type. I told him I could increase production, so I worked out an incentive scheme whereby for a 50 percent increase in production they could make 30 to 40 percent more in wages ... The girls really began to put out. They got very much interested in their work, and the good ones were soon earning 16 dollars and more a week.'

To her astonishment, the manager didn't like it.

'"I'm not going to have those girls thinking they are good," he said. "I'm going to get rid of the good girls. I didn't pay them to get above themselves."'

'He deliberately slowed down supplies and made things awkward for the smarter girls, so they just lost spirit and left.'" -- Harvey Leibenstein (1981) "Microeconomics and X-Efficiency Theory: If There Is No Crisis, There Ought to Be", in The Crisis in Economic Theory (ed. by D. Bell and I. Kristol), Basic Books

Two Problems, One Mathematics (2 of 2)

4.0 Mathematical Notes
4.1 Questions of Existence and Uniqueness
Sections 2 and 3 of the first part present two problems in which the following system of linear equations is derived:

p^T A = p^T

The elements of A are all non-negative, and each row sums to unity. For a non-trivial solution to exist, unity must be an eigenvalue of A. In a physically-meaningful solution, a corresponding left-hand eigenvector must have non-negative entries, with at least some being strictly positive. Furthermore, we would like the solution to be unique, up to a multiple. (In the economics case, multiplying prices by a constant corresponds to a change in the numeraire.) As a matter of fact, the problems as stated do not yet guarantee uniqueness.

It is easy to show that unity is an eigenvalue for right-hand eigenvectors of A. Let e be the n-element column vector where all elements are unity. Since the rows of A all add up to unity, the following equation must hold:

A e = e

So unity is an eigenvalue of A. (This proof relies on the property that the set of eigenvalues for left-hand eigenvectors of A is the same as the set of eigenvalues for right-hand eigenvectors of A.) Non-negativity and uniqueness, when it obtains are less obvious.

4.2 Irreducible Matrices
The left-hand eigenvector P^T corresponding to the eigenvalue unity contains all positive elements if A is irreducible. Furthermore, if A is irreducible, the left-hand eigenvector P^T is unique, up to a multiple. A matrix is irreducible, obviously, if it is not reducible. To explain this, I need to define what it means for a matrix to be reducible.

Suppose A is transformed by interchanging a pair of rows and then interchanging the corresponding columns. Any permutation of rows and columns can be performed by repeating this operation for an appropriate sequence of pairs of row and column indices. In the economics case, such a sequence of operations corresponds to selecting a different ordering of the industries in which to express A. In the case of page ranks, such a sequence consists in taking a different ordering for the (unranked) pages. In both cases, the ordering is arbitrary, so no problem arises here.

The non-negative matrix A is reducible if there exists such a sequence of operations that transform A into the block structure form:

A1,1	A1,2
0	A2,2

where A_1,1 is a square non-negative irreducible matrix.

I think the meaning of reducibility in the two problems is suggested under the special case where:

• All the elements of A_1,2 are zero, and
• A_2,2 is irreducible (as well as A_1,1)

The economics problem would then correspond to two non-trading islands, each in a self-replacing state with no surplus. The web pages would consist of two islands of web pages, in which links can be used to get from any one page on an island to any other page on that island, but with no path between these islands of pages.

Unity would be a repeated eigenvalue for a reducible A. One solution vector P^T has strictly positive prices for the industries corresponding to A_1,1 and zero prices for the remaining industries. The other solution has zero prices for the industries corresponding to A_1,1 and strictly positive prices corresponding to industries for A_2,2. It seems reasonable to me to assume in the economics model one is considering a single economy. I don't see why in the page rank case, some set of pages cannot be partially isolated in some sense from the remaining pages. A page ranking algorithm needs to address this possibility.

I might as well mention a condition for an interesting generalization of the economics problem. Let A be a non-negative, reducible matrix with no row sums that exceed unity. Suppose the maximum eigenvalue of A_1,1 exceeds the maximum eigenvalue of A_2,2. Then A is a Sraffa matrix. I'm not sure if the definition of a Sraffa matrix requires some of the elements of A_1,2 to be non-negative so that this input-output matrix hangs together to describe a single economy. Some such condition makes sense to me for an analysis of an economy with a surplus.

4.3 Perron-Frobenius Theorems
I state a theorem, or rather, a combination of eight theorems:

Theorem: Let A be an irreducible non-negative nxn matrix. Then:

1. λ_m, the maximum eigenvalue of the matrix A is bounded below by the minimimum row-sum of A and is bounded above by the maximum row-sum of A.
2. The maximum eigenvalue of A is a continuous, increasing function of the elements of A.
3. Let μ = 1/ν be strictly positive. If μ > λ_m, then all the elements of the matrices (μ I - A)^-1 and (I - ν A)^-1 are strictly positive.
4. Any eigenvalue α of A is bounded above in modulus by the maximum eigenvalue of A:

|α| ≤ λ_m

5. The maximum eigenvalue of A is associated with a left-hand eigenvector p^T whose elements are strictly positive:

p^T A = λ_m p^T

p_i > 0, for i = 1, 2, ..., n,

6. The maximum eigenvalue of A is associated with a right-hand eigenvector q whose elements are strictly positive:

A q = λ_m q

q_i > 0, for i = 1, 2, ..., n,

7. To each eigenvalue α of A different from the maximum eigenvalue λ_m there corresponds a non-zero left-hand eigenvector which has at least one negative component.
8. To each eigenvalue α of A different from the maximum eigenvalue λ_m there corresponds a non-zero right-hand eigenvector which has at least one negative component.

I deliberately included more Perron-Frobenius theorems above than I need for this problem. Perron-Forbenius theorems of a slightly different form have also been stated for reducible matrices.

Anyways, from the first condition, one sees that unity is the maximum eigenvalue for an irreducible A in both the economics and page rank problems. From the fifth conditon, it follows that there exists a set of strictly positive prices, in the economics case, or of strictly positive page ranks in the other case. And by the seventh condition, I guess, this is an unique solution (up to a multiple of the eigenvector).

5.0 References

• Kurt Bryan and Tanya Leise, "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google"
• Luigi L. Pasinetti (1977) Lectures on the Theory of Production, Columbia University Press
• Piero Sraffa (1960) Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, Cambridge University Press

Two Problems, One Mathematics (1 of 2)

"Besicovitch insists that I publish; the fact that I was able to forsee interesting mathematical results shows that there must be be something in the theory." -- Piero Sraffa (Diary entry, 31 May 1958)

1.0 Introduction
In this post, I derive the same equation for two completely different problems. One is an economics model. The other is a simplified presentation of how Google might automatically calculate page ranks to determine the order in which web pages are presented to a user on completion of his search. I could have complicated my exposition by considering a third problem: the steady state probability distribution in a Markov chain.

2.0 Prices for Simple Reproduction
Consider an economy in which n commodities are produced. Each commodity is produced in a process in which it is the only output. In other words, no joint production, such as of wool and mutton, occurs in this economy. n processes are in use, each producing one of the n commodities, and all commodities are produced by one of these processes. Each production process requires a year to complete and uses up all its inputs.

Let a_i,j denote the quantity of the ith commodity used in the production of the jth commodity. Quantities are measured in normalized units, such that the output of each process is one unit of the respective commodity. The nxn matrix A is the Leontief input-output matrix of interindustry quantity flows for this economy. Each element of A is non-negative.

Assume that this economy is undergoing simple reproduction. That is, the output of each process is exactly equal to the total inputs of that commodity used across all processes. (If it helps, one might think of the inputs to each process as including the commodities consumed by the workers operating that process. Labor inputs are not shown in the representation of this economy being considered here.) Anyways, this assumption implies that the sum for each row in A is unity.

Suppose each process is operated by a separate firm. The firm own ats the end of each year a single (normalized) unit of a single commodity. For the firm to continue in operation, it must trade this commodity for an appropriate amount of each of its inputs in all-around markets. Let p^T denote the row vector of the prices in these markets. The condition that the economy continue in operation implies the following equation for prices:

p^T A = p^T

This characterization of prices is a non-neoclassical idea. Markets have not been modeled here as including any sort of maximization process. Nor have these prices been presented as a (stable?) limit point of some sort of dynamic process. Sraffa describes these prices as follows:

"There is a unique set of exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated; such values spring directly from the methods of production." -- P. Sraffa (1960)

3.0 Google Page Ranks
I now consider a re-definition of all of my symbols. Suppose n web pages have been identified, perhaps by a web-crawler. We want to rank these pages in some way.

These web pages contain links, including to one another. In ranking them, perhaps a page in which a high proportion of the links on other pages goes to that page should have a high rank. But ratios of the proportion of links on other pages that go to that page should be weighted by the ranks of those other pages. These ideas can be formalized.

Let m_i,j be the number of links on the ith web page to the jth web page, for i unequal to j. Let m_i,i be zero. Let m_i be the total number of links on the ith page, excluding links to itself and to pages outside the pages being ranked.

a_i,j = m_i,j/m_i, i = 1, 2, ..., n; j = 1, 2, ..., n

I have now defined a nxn matrix A, where each element is the proportion of the links on a page within a web that go to another specified page in that web. Each element in A is non-negative, and each row adds up to unity. Also, the principal diagonal of A is zero, although that property is not used in the following mathematics.

Let p^T denote the row vector of page ranks. Page ranks satisfy the following system of equations:

p^T A = p^T

In the next part, I consider conditions under which a solution exists and is unique.

5.0 References

• Kurt Bryan and Tanya Leise, "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google"
• Piero Sraffa (1960) Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, Cambridge University Press

Letters From Soros

Last month, I noted resemblances between Soros' concept of "reflexivity" and Davidson's use of non-ergodicity to formalize the notion of a model economy set in historical time. Davidson drew this point to Soros' attention over a decade ago. Soros has commented on this resemblance.

The following letter has an Open Society Institute letterhead:

February 28, 1997

Professor Paul Davidson
Holly Chair of Excellence in Political Economy
The University of Tennessee Knoxville
College of Business Administration
Department of Economics
Stokely Management Center
Knoxville, Tennessee 37996-0550

Dear Professor Davidson,

Thank you for sending me your book Economics for a Civilized Society. I found your comments on Samuelson's ergodic hypothesis very pertinent.

Yours Sincerely,

George Soros

From the 15-21 March 1997 issue of The Economist:

Sir - In "Palindrome repents" (January 25th) you accuse me of ignorance of economic theory. In particular, you say that my "claim that economics is inherently flawed on some deep epistemological level is just embarrassing." Is it?

Economics aspires to the status of a hard science. Specifically, it seeks to establish universally valid laws similar to 19th-century physics. For this purpose it relies on the concept of equilibrium, similar to the resting place of the pendulum, which is the same irrespective of any temporary perturbation. Paul Samuelson, an economist, called this the "ergodic hypothesis" and considered it indispensable to making economics a hard science.

The trouble is that economics cannot be made into a hard science, because of the reflexive interaction between the participants' thinking and the actual state of affairs. The interaction does not have a determinate outcome, because the outcome is contingent on the participants' expectations, and the participants' decisions do not merely passively discount the future but also actively help to shape it. There is a two-way feedback mechanism that does not lead to a predetermined resting place, but keeps a historical process in motion. Economic theory can protect the false analogy with 19th-century physics only by eliminating reflexivity. It does so by assuming demand and supply as independently given. The result is an axiomatic system that has little relevance to the real world.

You are correct to claim that, in practice, economists have learnt this, in order to deal with the real world. Alan Greenspan's recent Humphrey-Hawkins testimony is a brilliant exercise in reflexivity. But the theory has never been discarded and it serves as the scientific underpinning for the prevailing belief in the magic of the marketplace.

You are also right to claim that markets do not reign supreme; but you cannot deny that there is a powerful body of opinion that passionately believes that they should. You are plain wrong in asserting that I do not know the "big difference" between laisser-faire and totalitarian ideologies. I stated it explicitly in my Atlantic Monthly article and have been guided by it in my philanthropic activities. I can tolerate personal attacks but I must object when they are used to obfuscate valid arguments.

New York
George Soros

Will Notre Dame Be Serious In Teaching Economics?

Apparently some members of the Department of Economics and Policy Studies would still like to teach classes and hire colleagues. If Notre Dame is serious about educating their students, shouldn't they be taught of the existence of the full range of views on economics? After all Notre Dame has some excellent scholars, including some great historians of economics. (I'm not sure that Esther-Mirjam Sent is still at Notre Dame.)

An on-line petition has been put up in support of these wild ideas. (I haven't yet signed it.)

Hat tip to shagan at daily Kos.

Update: I have now signed the petition. Christopher Hayes comments.