Wednesday, February 27, 2008

I Stared At This For A Good Five Minutes

Referee Report on "Some Capital-Theoretic Fallacies of Austrian Economics"
January 2008

Summary: This paper challenges some of the very premises of the Austrian theory of the business cycle, via a criticism of Mengerian/Böhm-Bawerkian/Hayekian capital theory. In particular, the author challenges the standard Austrian claim that a reduction in the rate of interest leads to a deeper, more roundabout capital structure. To prove that such a claim is false in the general case, the author draws on the reswitching debate from the Cambridge Capital Controversy (CCC).

Recommendation: I must advise that the current paper is not suitable for publication in the RAE in its present form. If I have understood it, the paper is basically saying, "The reswitching examples that surfaced in the CCC demonstrate that the starting point of ABCT is wrong. As Sraffa and his followers showed, entrepreneurs can switch from one technique to another, and then back again to the first, as interest rates fall. This means it is clearly impossible to rank objective capital structures in terms of their roundaboutness."

However, if this is indeed the author’s contribution (and if it isn’t, then s/he needs to rewrite the paper to make the true thesis much clearer!), then it is not novel. Paul Samuelson's famous "A Summing Up" (1966 Quarterly Journal of Economics) article - in which he comes as close to admitting he was wrong as Paul Samuelson ever does — presents a beautiful illustration of the flaws in the basic Böhm-Bawerkian "fable" (Samuelson’s term). The numbers in Samuelson's example are nice round ones, making the issue far easier to grasp than the complicated fractional numbers chosen by the current author. Moreover, historians of economic thought understood the implications as well: In his Economic Theory in Retrospect, Mark Blaug says that the possibility of reswitching proved the "final nail in the coffin" for Böhm-Bawerkian capital theory.

Therefore, economists have been well aware of the vulnerability of orthodox Böhm-Bawerkian capital theory to the reswitching examples. What's more, the Austrians themselves have responded. Ironically, the present author cites Garrison's 2006 work - which John Hicks apparently told Garrison was the best response to the reswitching issue—but doesn’t deal directly with Garrison's responses, except for a short quote questioning the empirical relevance of reswitching. A novice who read the present paper would have no idea that Garrison (or any other Austrian) had tried to grapple with the theoretical challenges posed by reswitching. In fact, when the author claims on page 6 that "this paper is the first to look at Hayekian triangles in light of the CCC," the novice reader would probably consider this entire critique as a new challenge to ABCT.

My recommendation is for the author to first, read the Samuelson paper. Then, if s/he is willing, a new paper could be written, demonstrating to the Austrian reader that reswitching is not merely a theoretical curiosity, but a real-world phenomenon. I personally have not read the empirical literature to which the author alludes on page 14 (in response to Garrison). So a new paper might be acceptable for the RAE, if it (a) started out with a very quick summary of the reswitching controversy, and used a simple example such as Samuelson's, then (b) presented the major Austrian responses, and finally (c) used the empirical literature and/or theoretical arguments to show why the responses quoted in (b) are unsatisfactory.

Let me end this section by disclosing my identity as Robert Murphy, because I am going to recommend some of my own work as background (and I don’t want to be coy about it). The following online article gives a quick summary of Samuelson’s piece (and my own response):

Some other of my articles that may interest the writer are another online article about Sraffa: I also have two formal expositions of Böhm-Bawerkian capital theory in The Journal of the History of Economic Thought. The first is "Dangers of the One-Good Model: Böhm-Bawerk's Critique of the 'Naïve Productivity Theory of Interest'" (Vol. 27, No. 4 (December 2005), pp. 375-382), and "Interest and the Marginal Product of Capital: A Critique of Samuelson" (December 2007).

Please note that I am NOT saying the above articles need to be cited in a future RAE submission. It's just that it is very rare for economists to write articles that deal with both Sraffian and Austrian concerns, and so I want the author (who belongs to this select club) to be aware of them.

Specific Comments: Below I offer some minor comments on the draft for the author.

Page 2, bottom quote from Garrison: It seems that this particular statement is OK, even with reswitching.

Page 4, top: The citation says Lewin 1991, but no such work is in the bibliography. I think the year is wrong?

Page 4, first full paragraph: I didn't really understand the Lewin argument described here. Is he simply talking about learning by doing, or something else?

Page 7, table: I don't understand why these numbers are so complicated. Would it hurt anything to multiply through by 49? Or by some higher number in order to make it consistent with Table 3? If the fractions are used simply to allow for a surplus of one unit of corn, I’d recommend increasing the surplus in order to make the inputs integers.

Page 8, Table 2: I stared at this for a good five minutes and couldn’t figure it out - and I'm familiar with such diagrams from Hayek, Rothbard, Garrison, and even Samuelson. It should be explained more thoroughly if it is to be retained.

Page 9, middle: "Consistency…ensures…the existence of a maximum above which the interest rate cannot rise in the ERE." The author doesn't take this any further, but it seems s/he is saying that the standard Austrian story wouldn’t "work" in this case, because an increase in time preference couldn’t raise the interest rate above the ceiling set by physical constraints. However, this is only because the author has assumed that certain production processes will be carried out indefinitely, à la Sraffa. There is no reason that these processes would be carried out - thus "determining" the rate of interest - if consumer preferences changed in certain ways.

Page 15, Paul Davidson entry: I think the title is incorrect. Should it be "The Economics of Ignorance OR Ignorance of Economics?"?

Sunday, February 24, 2008

Wittgenstein to Sraffa

The March 2008 issue of Harper's Magazine reports that a new edition of Wittgenstein's letters in Cambridge is being published by Blackwell. They include the following 31 January 1934 letter:
Dear Sraffa,

The following are some remarks I've put down on the topic of our last conversation. I hope they won't be too disconnected and that you'll read them to the end.

You said, "The Austrians can do most of things the Germans did." I say, How do you know? What circumstances are you taking into account if you say they can? "This man, Austria, can remove the wedding ring from his finger." True, it's not too heavy and doesn't stick to his finger. But he may be ashamed of doing it, hiw wife may not allow it, etc.

You say, "Learn from what happened in Italy." But what should I learn? I don't know exactly how things happened in Italy. So the only lesson I can draw is that things one doesn't expect sometimes happen.

I ask, How will this whose face I can't imagine in a rage looks when he gets into a rage? And can he get into a rage? What shall I say when I see him in a rage? Not only, "Ah, so he can get into a rage after all," but also, "So this is the way he can be in a rage; so this is how it connects up with his former appearance."

You say to me, "If a man is in a rage, the muscles a, b, c of his face contract. This man has the muscles a, b, c, so why shouldn't they contract? If you, Wittgenstein, wish to know what he will look like in a rage, just imagine him with those muscles contracted. What will Austria look like when it turns Nazi? There will be no Socialist Part, there won't be Jewish judges, etc., etc., etc. That's what it'll look like."

I reply, This gives me no picture of a face; apart from the fact that I don't know enough about the workings of things to know whether all these changes that you point out will happen together. For I understand what it means to say that the muscles a, b, c will contract, but what will become of the many muscles, etc., between them? Can't the contraction of the one in this particular face prevent the contraction of the others? Do you know how in this particular case things interact?

You may say, "Surely the only way to tell the future physiognomy is to know more and more exactly the contractions, etc., of all, not only the main, muscles."

I say, I don't think this is the only way; there is another one, although the two ways meet. I may ask a physiologist what the face will be like, but also a painter. The two will give different answers - the painter by drawing the angry face - although if they both are correct they will agree. Of course, I know that painters have to study anatomy. I want to know the painter's answer, and I also want to know what the physiologist can tell me to check the painter's answer.

I am interested to know what phrases the Austrians will use when they'll have turned Naze. Supposing their patriotism is only talk, then I'm just interested in their future talk.

I wish to say one more thing. I think that your fault in a discussion is this: YOU ARE NOT HELPFUL! I am like a man inviting you to tea in my room, but my room is hardly furnished; one has to sit on boxes, and the teacups stand on the floor, and the cups have no handles, etc., etc. I hustle about fetching anything I can think of to make it possible that we should have tea together. You stand there with a sulky face, say that you can't sit down on a box and can't hold a cup without a handle, and generally make things difficult. At least that's how it seems to me.


Ludwig Wittgenstein

Monday, February 18, 2008

Capitalism Advocates Undressed

I find this amusing. I suppose I should be grateful that somebody with a more popular blog than mine cites me.

Sunday, February 17, 2008

Jesse Larner On Friedrich Hayek

I bought the Winter 2008 edition of Dissent just to read Jesse Larner's article, "Who's Afraid of Friedrich Hayek?". This article has the intriguing subtitle, "The Obvious Truths and Mystical Fallacies of a Hero of the Right". I did not learn much, if anything, from this article since I had accepted Larner's main points years ago.

Larner argues that Hayek is not nearly as extreme as some of his fans in contemporary political debates make him out to be. I take Larner's main examples to be:
  1. Hayek, in, for example, Chapter 9 of The Road to Serfdom, states that important social democratic ideas are compatible with his principles. Among these are the state guaranteeing a minimum standard of life, organizing a comprehensive system of social insurance, and combating economic flucuations.
  2. Hayek offers no principled limitation on the size of government.
  3. The socialist calculation argument, including in Hayek's formulation, is an argument exclusively against a thorough-going central planning. It is not an argument for laissez faire inasmuch as it does not address all sorts of interventionist policies in a mixed economy and, for example, anarcho-syndicalism.
Although Larner doesn't mention it, a Hayek obituary in Commentary made his second point. Larner quotes Keynes on The Road to Serfdom:
"In my opinion it is a grand book... Morally and philosophically I find myself in agreement with virtually the whole of it; and not only in agreement with it, but in a deeply moved agreement." -- John Maynard Keynes
That blurb is on the back cover of the edition on my bookshelf.

I started reading Hayek in the mid 1980s before I realized how he was claimed by the right. I took the dedication in the Road seriously: "To the socialists of all parties." I now have some questions about this book. I doubt that historians accept Hayek's thesis about specific ways german socialists paved the way for the nazis. I don't read it as a slipperly slope argument, but rather as a jeopardy argument. If english socialists were to implement their policies after the war, they should be made aware of the risks. In this way, they could implement them in the best way possible. They might even have been persuaded to moderate some of these policies.

I think Individualism and Economic Order was the first book I read by Hayek. I still think this an extremely insightful book. I wish I could find off-hand the bit where Hayek characterizes the mixed economy as "interventionist chaos". An inability to analyze mixed economies is a defect. Another defect is the chapter on the Ricardo effect - but my views on Austrian business cycle theory have long been available. Hayek's strength, including in the socialist calculation controversy, is on the use of distributed tacit knowledge in an economy. (I thought interesting how Mirowski traces the influence of this Hayek argument on the Cowles Commission.)

Saturday, February 16, 2008

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.

  • 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.

Wednesday, February 13, 2008

Reaction to Rodrik

Thomas Palley has been reading Rodrik's book, One Economics, Many Recipes. Pallay's reaction is better expressed and better thought out than my reactions to some of Rodrik's posts. Palley says, "Most people are incredulous that economists could be so audacious as to enforce one view of economics."

I like that Jesus Felipe shows up in the comments when Rodrik raises the question, on his blog, of the purpose of growth accounting. I think of Felipe's cited work as extending Anwar Shaikh's argument on the humbug production function.

Monday, February 11, 2008

Pasinetti's Principles

Luigi Pasinetti, in his new book, Keynes and the Cambridge Keynesians: A "Revolution in Economics" to be Accomplished, summarizes what he takes to be characteristic features of the Cambridge school:
  1. Reality (and not simply abstract rationality) as the starting point of economic theory.
  2. Economic logic with internal consistency (and not only formal rigour).
  3. Malthus and the Classics (not Walras and the Marginalists) as the major inspiring source in the history of economic thought.
  4. Non-ergodic (in place of stationary, timeless) economic systems.
  5. Causality vs. Interdependence.
  6. Macroeconomics before Microeconomics.
  7. Disequilibrium and instability (not equilibrium) as the normal state of the industrial economies.
  8. Necessity of finding an appropriate analytical framework for dealing with technical change and economic growth.
  9. A strong, deeply felt social concern.

Sunday, February 10, 2008

Time that with this strange excuse Pardoned Kipling and his views

There was a certain political tendency in the United States around 1900. Historians call it the Progressive movement. I think it interesting how Kipling depicts "progressive" as almost a slang term in a novel he wrote around then:
"'Allus can, till we begin to dress daown. Efter thet, the heads and offals 'u'd scare the fish to Fundy. Boat fishin' ain't reckoned progressive, though, unless ye know as much as dad knows.'" -- Rudyard Kipling, Captains Courageous, 1897
"'I tell you, Harve, there ain't money in Gloucester 'u'd hire me to ship on a reg'lar trawler. It may be progressive, but, battin' that, it's the putterin'est, slimjammest business top of earth.'" -- ibid.
"'Dad's sot agin 'em on account o' their pitchin' an' joltin', but there's heaps o' money in em. Dad can find fish, but he ain't no ways progressive - he don't go with the march o' the times. They're chock-full o' labour-savin' jigs an' sech all.'" -- ibid.
"'We know it ain't, but there's no goin' in the teeth o' superstition. That's one o' the advantages o' livin' in a progressive country.'" -- ibid.
"'Why didn't that Eastport man bid, then? He bought his boots. Ain't Maine progressive?'" -- ibid.
"'Huh! I guess I'm as enlightened and progressive as the next man, but when it comes to a dead St. Malo deck-hand scarin' a couple o' pore boys stiff fer the sake of a thirty-cent knife...'" -- ibid.

Friday, February 08, 2008

Send A Letter

King’s College
14 March 1938

Dear Wittgenstein,

Before trying to discuss, probably in a confused way, I want to give a clear answer to your question. If as you say it is of “vital importance” for you to be able to leave Austria and return to England, there is no doubt – you must not go to Vienna. Whether you are a lecturer at Cambridge or not, now you would not be let out: the frontier of Austria is closed to the exit of Austrians. No doubt these restrictions will have been somewhat relaxed in a month’s time. But there will be no certainty for a long time that you will be allowed to go out, and I think a considerable chance of your not being allowed out for some time. You are aware no doubt that are now a German citizen. Your Austrian passport will certainly be withdrawn and then you will have to apply for a German passport, which may be granted if and when the Gestapo is satisfied that you deserve it.

As to the possibility of war, I do not know: it may happen at any moment, or we may have one or two more years of “peace”. I really have no idea. But I should not gamble on the likelihood of six months’ peace.

If however you decided in spite of all to go back to Vienna, I think: a) it would certainly increase your chance of being allowed out of Austria if you were a lecturer in Cambridge; b) there would be no difficulty in your entering England, once you are let out of Austria (of Germany, I should say); c) before leaving Ireland or England you should have your passport changed with a German one, at a German consulate: I suppose they will begin to do so in a very short time; and you are more likely to get the exchange effected here than in Vienna; and, if you go with a German passport, you are more likely (though not at all certain) to be let out again.

You must be careful, I think, about various things: 1) if you go to Austria, you must have made up your mind not to say that you are of Jewish descent, or they are sure to refuse you a passport; 2) you must not say that you have money in England, for when you are there they could compel you to hand it over to the Reichsbank; 3) if you are approached, in Dublin or Cambridge, by the German Consulate, for registration, or change of passport, be careful how you answer, for a rash word might prevent you ever going back to Vienna; 4) take care how you write home, stick to purely personal affairs, for letters are certainly censored.

If you have made up your mind, you should apply at once for Irish citizenship – perhaps your period of residence in England will be counted for that purpose: do it before your Austrian passport is taken away from you, it is probably easier as an Austrian than as a German.

In the present circumstances I should not have qualms about British nationality if that is the only one which you can acquire without waiting for another ten years’ residence: also you have friends in England who could help you to get it: certainly a Cambridge job would enable you to get it quickly.

I shall be in Cambridge till Friday: afterwards letters will be forwarded to me in Italy, so take care what you say, that you may be writing for the Italian censor.

My telephone is 3675: you will find me available before noon and in the evening after 10.

Piero Sraffa

Excuse this confused letter.

Wednesday, February 06, 2008

Profits Resulting From Exploitation Of Workers

1.0 Introduction
This post outlines a simple economic model. This model formalizes the claim that capitalists obtain their income from the exploitation of workers. The concept of exploitation illustrated in this model is supposed to formalize at least some of Marx's results in Capital.

I present results here without proof. Michio Morishima calls the theorem with which I conclude the "Fundamental Theorem of Marxism". In the 1970s, Ian Steedman showed the theorem does not apply to models with joint production, under a natural generalization of labor values. On the other hand, Morishima argues the theorem does apply to joint production under a different way of defining labor values in that case.

2.0 The Data and Quantity Relationships
I assume an economy in which n commodities are produced. Each commodity is produced from inputs of labor and produced commodities. Define ai,j to be the quantity of the ith commodity used to produce one unit of the jth commodity. The nxn input-output matrix A contains these coefficients of production. By assumption, all commodity inputs are used up in a single production cycle (a year). That is, this is a circulating capital model. Assume the input-output matrix A is irreducible.

The net or gross quantities of commodity outputs of this economy are among the model's data. Let y be the column vector of net outputs (also known as the surplus), and let q be the column vector of gross outputs. Net and gross outputs are related by the following equation:
y = q - A q = (I - A)q
Assume A is such that all elements of y are strictly non-negative and at least one element is strictly positive. That is, in this economy, the circulating capital goods are reproduced, with some output left over. The assumptions allow one to invert the above relationship, thereby obtaining:
q = (I - A)-1 y
The inverse is known as the Leontief inverse. It exists under these assumptions by a Perron-Frobenius theorem.

Assume the quantity of any type of labor can be expressed as a known ratio of simple (unskilled) labor. For example, one hour of a nurse's labor might be expressed as five hours of simple labor, to pick a ratio at random. Let a0, j denote the hours of (simple) labor expended in producing one unit of the jth commodity. The n-element row vector a0 is composed of these labor coefficients. The labor force employed to produce the observed surplus is then a0 (I - A)-1 y.

Finally, the real wage is among the data of the model. Suppose wages are expended on a commodity basket of known proportions. Let the column vector c be in these proportions. If c is also the numeraire, the real wage is wc, in terms of numeraire-units per labor hours.

Assume wages are advanced. Some of the fomulas below are usefully expressed in terms of the augmented input-output matrix A(w). The augmented input-output matrix is defined as:
A(w) = A + c a0w
The coefficients of the augmented input-output matrix are the commodities advanced per unit output, where these commodities are needed both as inputs to production and to sustain the workers during a production cycle.

3.0 Labor Value Accounting
Let ej be the jth column of the identity matrix. Suppose the net output of the economy were to consist of one unit of the jth commodity. Then ej would be a column vector denoting the net output. The gross output of the economy would be (I - A)-1 ej. One could then calculate the labor time to produce at these levels of operation of each industry in the economy:

Definition: The labor value of the jth commodity, vj is:
vj = a0 (I - A)-1 ej
In words, the labor value of a commodity is the amount of labor time that would be required, if Constant Returns to Scale prevailed, to increase the net output of the economy by one unit of that commodity. Some refer to the labor value of a commodity as the amount of labor embodied in that commodity.

The row vector of labor values of all commodities is easily seen to be:
v = a0 (I - A)-1
The labor value of any quantities of commodities is calculated by premultiplying the column vector representing those quantities by the row vector of labor values. This observation allows one to make sense of a further definition:

Definition: The rate of exploitation, e is defined by:
e = [v(I - A - c a0 w)q]/(v c a0 q w)
In words, the rate of exploitation is the ratio of the labor embodied in the surplus not paid out in wages to the labor embodied in the commodities purchased out of wages.

4.0 The Price System for the Maximum Wage
The maximum wage, w*, arises when the entire net output (also known as the surplus) is paid out to the workers and the rate of profits is zero. The stationary row vector of prices, p*, consistent with the maxiumum wage satisfies the following equation:
p* [A + c a0 w*] = p*
p* A(w*) = p*
That is, an eigenvalue of unity exists for the augmented input-output matrix calculated for the maximum wage, and the prices comprise the corresponding left-hand eigenvector. The existence of unity as the eigenvalue follows from a Perron-Frobenius theorem. It also follows that the prices corresponding to the maximum wage are strictly positive.

These prices are proportional to labor values:

Theorem: There exists a k > 0 such that:
p* = k v

5.0 The Price System in General
Under the assumptions, a stationary price vector p satisfies the following equation:
p A(w) (1 + r) = p
where r is the rate of profits. (The question of the usefulness of these prices of production for understanding the dynamics of market prices is known as the "realization problem".) The following is an equivalent equation:
p A(w) = 1/(1 + r) p
1/(1 + r) is then an eigenvalue of the augmented input-output matrix, and the price vector is the corresponding left-hand eigenvector. Some manipulation yields an nth-degree polynomial equation for 1/(1 + r):
Determinant[ 1/(1 + r) I - A(w) ] = 0
For a wage less than the maximum wage, the maximum root of this equation is real and has a corresponding left-hand eigenvector with positive elements. (This claim also follows from a Perron-Frobenius theorem.) The price level is picked out by the condition that the price of the numeraire be unity:
p c = 1
Suppose that w < w*. That is, not all of the surplus is paid out in wages. Furthermore, assume that the organic composition varies among industries. ("Organic composition of capital" is Marxist jargon roughly equivalent to "capital-intensity".) Then there does not exist a k > 0 such that:
p = k v
That is, prices in the general case are not proportional to labor-values. In this sense, a simple labor theory of value usually does not hold.

(Have I left out any other freak cases? Is there possibly a left-hand eigenvector for the input-output matrix such that all of its elements are positive and that eigenvector is associated with some other eigenvalue that the Frobenius root of the input-output matrix? I'd look for other freak cases where the vector of direct-labor coefficients is some such eigenvector, if such exists.)

6.0 Conclusion

Definition: Labor is exploited if and only if e > 0.

In words, labor is exploited if the labor-hours embodied in the commodities workers buy is less than the labor-hours the workers expend to earn the wages with which they buy those commodities.

Theorem: r > 0 if and only if e > 0.

In words, the rate of profits is positive in a system of stationary prices consistent with smooth growth of the economy if and only if labor is exploited. In other words, the positive returns provided to ownership of capital come from paying workers less than the value they contribute to production.

As far as I am concerned, this is solid mathematics.

Tuesday, February 05, 2008

Problems Mount In Application of Free Market Theory

As a footnote in a discussion of anomalies in a paradigm, in the sense of Thomas Kuhn, Pasinetti writes:
"It seems to me significant that Kenneth Arrow, himself a major contributor to the clear formalisation of the present dominant paradigm based on the Walrasian exchange model of General Economic Equilibrium analysis, would write a short newspaper article (rather than an article in a scientific journal)... While giving a proud statement of the exchange paradigm, Ken Arrow frankly gives at the same time a long list of its major points of weaknesses and downright failures, implying that the number and the seriousness of these failures are continually mounting." -- Luigi L. Pasinetti, Keynes and the Cambridge Keynesians: A "Revolution in Economics" to be Accomplished, Cambridge University Press (2007)
Pasinetti refers to:
  • Kenneth Arrow, "Problems Mount in the Application of Free Market Theory", in the rubric "Debate" in The Guardian, 4 January 1994.
I could not find this article on-line by using search tools. I'm curious what Arrow could have written. Could he have explained the Sonnenschein-Debreu-Mantel results in that forum? The difficulty of developing something more realistic than the tâtonnement process?

Update (6 February 2008): I thank an anonymous commentator for posting Arrow's article in the comments.

Sunday, February 03, 2008

Hyman Minsky: Man of the Moment

There has been quite a bit of talk about Hyman Minsky recently, and for good reason. In particular, this week's New Yorker leads off with an article by John Cassidy about Hyman Minsky.

Minsky was a Post Keynesian economist who I read years ago. I think in particular of his book John Maynard Keynes, which I thought quite good. I do not recall the five business-cycle stages John Cassidy mentions (displacement, boom, euphoria, profit taking, and panic). The elements I do recall lie elsewhere. I'm currently reading a couple of articles to help my recollection.

As I recall, Minsky emphasizes that Keynes' General Theory was set in a business cycle context. He thinks this context important in understanding Keynes' idea of an unemployment equilibrium. Minsky also points out the tendency under capitalism to continually evolve new financial instruments and new markets for trading in second-hand debt. (Thus, a regulatory regime will also need to evolve if a recurrence of debt-deflation is to be avoided.) In a sense, Minsky's view is that the supply of money is endogenous and non-neutral in the long run.

Minsky makes a tripartite distinction among types of finance:
  • Hedge Finance: The returns to an investment both cover interest charges and allow the principal to be paid off.
  • Speculative Finance: The returns cover interest charges, but the principal must be rolled over when it comes due.
  • Ponzi finance: The returns do not even cover interest charges and one must take on a growing burden of debt.
Businesses take on finance for leverage.

As memories of the last downturn fade, pressure grows to become more highly leveraged. Speculative and ponzi finance grow at the expense of hedge finance. Notice that unexpected events can convert hedge finance to speculative finance and speculative finance to ponzi finance. The returns to an investment might not be as expected. Perhaps an institution from which you were expecting a cash flow goes bankrupt. So if returns were previously expected to cover more than interest charges, one might now find that returns can only be expected to cover interest charges. Or perhaps the interest rate is higher than expected when the principal comes due. A speculator can only roll over the principal in the hope that later refinancing will improve his situation. At any rate, the financial system is endogenously unstable.

Do these observations speak to the current mortage problems and their potential for affecting the broader economy?

On-Line References

Saturday, February 02, 2008

A Third Way

The post title could refer to a third alternative. It has been years since I read Dutt and Amadeo's book. Their title is taken from a Keynes' quotation:
"Those, who are strongly wedded to what I shall call 'the [neo]classical theory', will fluctuate, I expect, between a belief that I am quite wrong and a belief that I am saying nothing new. It is for others to determine if either of these or the third alternative is right." -- John Maynard Keynes, The General Theory of Employment Interest and Money

In politics, the "third way" is used to refer to another possibility between a laissez-faire night watchman state and Stalinist central planning. The failure of "actually existing socialism" does not imply "there is no alternative." The third way takes in a lot of possibilities. I think Sweden was referred to decades ago as embodying a third way. Likewise, the label is used to refer to ideas associated with Tony Blair and Bill Clinton. (I have not read Giddens.)

Cambridge-Italian economists constitute a school of thought within economics. They have a constructive agenda - to demonstrate an integration of classical political economy with Keynes' theory. Classical political economy refers to the approach of, for example, Adam Smith and David Ricardo. Keynes himself envisioned what he called a "monetary theory of production."

Heinrich Bortis has argued that this classical-Keynesian political economy is the socioeconomic theory of the third way. "In the Keynesian third-way view there is no automatic co-ordination of individual actions." And, he argues, the destructive criticism developed in the Cambridge Capital Controversy fits into this argument:
"...Specifically, it must be shown that under ideal conditions, i.e. perfect competition and absence of disturbing elements like uncertainty and money, one or more markets do not function properly so that, even in the long run, no tendency towards full employment exists: the problem is not about possible market failures, but about principles.

This task has been accomplished by the capital-theory debate, the main economic implications of which are set out in Garegnani (1970), Kurz (1985) and Pasinetti (1974, pp. 132-42; 1977, pp. 169-77); a comprehensive and easily understandable presentation of the crucial issues is Harcourt (1972).

...As a consequence, no regular (downward-sloping) associations between profit rates, on the one hand, and capital and output per worker and the capital-output ratio, on the other hand, exist. These relationships are, in fact, totally irregular. Since the 'capital market' does not function in the neoclassical sense and since factor markets are supposed to be interrelated, regular long-period relationships between 'factor prices' and 'factor quantities' cannot exist in general, i.e. there are no 'factor markets' at all if the long run is considered. This is the main result of the capital-theory debate...

...The fact that there are no regular relationships between 'factor prices' and 'factor quantities' is extremely damaging for equilibrium theory: the market cannot produce a tendency towards some postulated long-period equilibrium to solve the central economic problems, i.e. value, distribution and employment....

...These references to the history of the capital-theoretic discussion show that it is a discussion about fundamentals. The basic question is whether there are regular relationships between 'factor prices' and 'factor quantities' or not, i.e. normally functioning factor markets. Examining this question seriously will inevitably shape an economist's vision in a decisive way. The capital-theoretic debate is a theoretic watershed dividing two different views of looking at socioeconomic phenomena, i.e. neoclassical equilibrium theory which emphasizes behavior and classical-Keynesian political economy which starts from the functioning of the socioeconomic system, the question being which approach is more appropriate to tackle fundamental socioeconomic problems, such as value, distribution and employment. Therefore, as Geoffrey Harcourt was one of the first to perceive, the Cambridge controversies are 'not merely about the measurement of capital...but about the scientific status of neoclassical (equilibrium) theory' (Dixon 1988, pp. 251-2)...." -- Heinrich Bortis, Institutions, Behaviour and Economic Theory: A Contribution to Classical-Keynesian Political Economy (1996)