Reflections On "Sraffian Economics (New Developments)"

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

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

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

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

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

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

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

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

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

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

No Thanks, Alessandro. I'm Full.

Alessandro Roncaglia has written a book, Piero Sraffa, for Palgrave's "Great Thinkers in Economics" series. (This is the same series containing Paul Davidson's John Maynard Keynes, available in hardcover and paperback.) I have always enjoyed Roncaglia's take on Sraffa, but I think I'll pass for now. I've seen quite a bit of what he has had to write in the past.

• Alessandro Roncaglia (1978) Sraffa and the Theory of Prices, John Wiley & Sons.
• Alessandro Roncaglia (1979) "The Sraffian Contribution", in A Guide to Post-Keynesian Economics (edited by Alfred S. Eichner), M. E. Sharpe
• Alessandro Roncaglia (2000) Piero Sraffa: His Life, Thought and Cultural Heritage, Routledge
• Alessandro Roncaglia (2001) "Production of Commodities by Means of Commodities Between Criticism and Reconstruction: The Given Quantities Assumption", in Piero Sraffa's Political Economy: A Centenary Estimate (edited by Terenzio Cozzi and Roberto Marchionatti), Routledge
• Alessandro Roncaglia (2005) The Wealth of Ideas: A History of Economic Thought Cambridge University Press

On Austrian Business Cycle Theory, Recently

Brad DeLong offers an empirical criticism based on order of magnitude estimates. For some reason, John Quiggin's blog crashes this browser on this platform. So I look to Mark Thoma to echo Quiggin, who doesn't seem to understand the (failed) concepts. Quiggin doesn't mention Wicksell, the idea of a natural rate of interest, or capital structure, for example. DeLong's post was in response to Roger Garrison. Peter Boettke adds a post. In comments to some of these posts, I link to a recent iteration of my critique, which may have some influence on Roger Koppl.

Is Utility Theory Tautological? An Old Argument

"What does [Jevon's theory] really amount to? In my apprehension to this, and no more - that value depends upon utility, and that utility is whatever effects value. In other words, the name 'utility' is given to the aggregate of unknown conditions which determine the phenomenon, and then the phenomenon is stated to depend upon what this name stands for." -- J. E. Cairnes, Some Leading Principles of Political Economy (1874) (quoted by G. Myrdal in The Politcal Element in the Development of Economic Theory)

"...that value was determined by the conditions which determine it - an announcement, the importance of which, even though presented under the form of abtruse mathematical symbols, I must own myself unable to discern." -- J. E. Cairnes, Some Leading Principles of Political Economy (1874) (quoted by G. Myrdal in The Politcal Element in the Development of Economic Theory)

An Intervention By Kurt Gödel Into Economics

Kurt Gödel attended Karl Menger’s colloquium in Vienna in the 1930s. Sraffians should be interested in this colloquium since Von Neumann, in 1937, presented his classically-inspired economics model to the attendees. (Von Neumann had previously presented an earlier version to a Princeton mathematics seminar.) The later English translation of Von Neumann’s terse article is accompanied by a note from David Champernowne with the following acknowledgement.

"This note is the outcome of conversations with Mr. N. Kaldor, to whom many of the ideas in it are due. I am also indebted to Mr. P. Sraffa of Cambridge and to Mr. Crum of New College, Oxford, for instruction in subjects discussed in this article" -- D. G. Champernowne

Gödel’s published comment, however, was part of a discussion of a marginalist model. Walras’ models of the exchange of several commodities for one another and of production contain equations in which the quantity demanded of each good is a function of prices:

q₁ = d₁(p₁, ..., p_n)

q_n = d_n(p₁, ..., p_n)

Abraham Wald, in 1934, presented to the colloquium a sort of inverse or dual model, building on a paper from Karl Schlesinger. This model contains equations expressing the prices at which the quantities of commodities are demanded:

p₁ = d₁(q₁, ..., q_n)

p_n = d_n(q₁, ..., q_n)

I gather this model also contained inequalities, an important development in the theory of general equilibrium. At any rate, Kurt Gödel commented:

"Actually, for each individual entrepreneur the demand also depends on the price of factors of production. One can formulate an appropriate system of equations and investigate whether it is solvable." -- Kurt Gödel

According to John Dawson, Jr., Gödel’s remark is not well-taken; there is no obvious way to introduce prices of factors of production in this "inverse" model with many consumers. By contrast, when Gödel decided to say something about relevatistic physics, his remarks about rotating universes and world-lines traveling into the past, I guess, challenge physicists even decades later.

I stumbled on Gödel’s remark last week by noticing E. Roy Weintraub (1983) referenced in the first volume of Gödel’s collected works and wondering why that should be. I now see that Weintraub also quotes Gödel's remark, and Dawson is concurring with Weintraub.

References

• D. G. Champernowne (1945-1946). “A Note on J. v. Neumann’s Article on ‘A Model of Economic Equilibrium’”, Review of Economic Studies, V. 13, N. 1: 10-18
• S. Feferman et al (editors) (1986). Kurt Gödel: Collected Works: Volume 1: Publications 1929-1936, Oxford University Press
• J. v. Neumann (1945-1946). “A Model of Economic Equilibrium”, Review of Economic Studies, V. 13, N. 1: 1-9
• E. Roy Weintraub (1983). “On the Existence of a Competitive Equilibrium: 1930-1954”, Journal of Economic Literature, V. 21, N. 1 (March): 1-39

He Might As Well Have Said He Was Hungry

"Maureen: (getting less confused and quite interested): You mean to say that Socrates talks philosophy, knowing that he is going to die?

Leslie: Weird! A professor who talks and talks although he knows that the executioners are waiting for him, right outside his classroom. How does it all hang together?

Seidenberg (excited): Not only that. The two main characters of the dialogue Professor Cole wants to read with us, Theaetetus and Theodorus, were historical figures, both outstanding mathematicians. And Theaetetus, it says in the introduction, has been severly wounded in a battle and shortly after died from dysentery... there is an 'existential dimension' as one might call it - the way in which the entire conversation is inserted into extreme situations of real life. I feel this is very different from large parts of modern philosophy where you analyse only the logical properties of concepts and think that is all that can be said about them.

David (hesitatingly): I have read the dialogue because I wanted to be prepared for this class. I, too, wondered about the ending. But I don't see that it has any effect on the debate. The debate sounds very much like a philosophy class I just had; there is somebody who says that knowledge is experience...

Dr Cole: Perception...

David: ...well, that knowledge is perception, somebody else has counter-examples and so on. True, the dialogue is a little long-winded - but one doesn't notice anything about death in it. At the end Socrates suddenly says he has to go to court. He might as well have said he is hungry and wants to have dinner. At any rate, this seems just to be added for effect, it doesn't give any existential dimension to the concepts." -- Paul Feyerabend, Three Dialogues On Knowledge (1991)

I have some books written in prison. Antonio Negri's Marx Beyond Marx: Lessons on the Grundrisse, including the 1991 author's preface to the English translation, are written in circumstances beyond my understanding of Italian politics. The book, apparently, is based on lectures Negri gave in the mid 1970s to the École Normale in Paris. He was there at the invitation of Louis Althusser, in exile from Italy, under charges of having incited a riot in Padua.

This is, I gather, before Althusser murdered his wife by running her over. I never got much out of Althusser's For Marx. It seemed to me all methodological preliminaries, never illustrating or demonstrating that these preliminaries were worthwhile.

Negri's later introduction to the English edition is written from prison. I gather he was found guilty of having conspired with the Red Brigades to have kidnapped and murdered Aldo Moro, an Italian ex-prime minister. Negri's group was Potere Operaio (Worker's Power), not the Red Brigades.

I might as well summarize my understanding of the point of Autonomia. For Negri, previous Marxisms depicted workers as objects reacting to the machinations of capital, never as subjects initiating history themselves. Negri emphasizes the subjectivity of workers imprisoned throughout their lives, not just during their work time. Subjectivities will be organized around, for instance, ethnicity and gender, not just class. You can see how this is relevant to debates over Marx's outlines for Capital, whether he ever abandoned his plan for a volume on wages, and just did not get around to that volume. But I don't fully understand either Marx Beyond Marx or the more recent Empire.

Why Oh Why Can't We Have Better Mainstream Economists?

The answer to the question in the post title is obvious to a certain extent. Mainstream economists are part of a larger system that is served by obfuscation. If (some) economists become too penetrating in their examination of a capitalist economy, their colleagues simply purge them from the profession. (I seem to recall reading somewhere that Fred Lee is indeed writing a book.)

Anyways, I want to know whether mainstream economists, such as Brad DeLong, understand price theory - never mind whether they understand Karl Marx (which they don't). Consider this passage:

"Marx believed that capital is not a complement to but a substitute for labor. Thus technological progress and capital accumulation that raise average labor productivity also lower the working-class wage. Hence the market system simply could not deliver a good or half-good society but only a combination of obscene luxury and mass poverty. This is an empirical question. Marx's belief seems to me to be simply wrong." -- Brad DeLong

I see here an incorrect belief that income can be determined by technical relationships. Given DeLong's reference to complements and substitutes, he is, I think, drawing on his (mis)understanding of marginalism. He probably believes something like the following: in a market economy, agents receive (or should receive) the value of the marginal products of the services of the factors or production that they own. (By mentioning ownership, I am already being more careful than many might be; capitalists do not have a marginal product, even if the services of capital goods were to each have one.) To reinforce my point that some believe this, I quote some comment on a blog somewhere:

"And then you can have a simple theory of exploitation where it happens if somebody somewhere doesn't get their marginal product." -- Radek

I have pointed out before that marginal productivity, when correctly stated, is a theory of the choice of technique, not a theory of distribution. And, by quoting Duncan Foley, I acknowledged the unoriginality of my understanding. I now take the opportunity of my recent exposition of a reswitching example to re-iterate the non-existence of the marginal productivity theory of distribution. Figure 1 illustrates that example, and it is consistent with all correctly formulated conditions on marginal products for the example.

Figure 1: Wage-Rate Of Profits Curves

I want to consider what data about production the observing economist must know to calculate the value of marginal products. First, suppose he knows the technique in use. In each (non-vertically integrated) industry, the inputs purchased by each firm and the outputs are known. In a circulating capital model of competitive markets, this data determines wage-rate of profits surfaces, of which two are shown in the figure. But the observing economist cannot use this data to determine the equilibrium distribution; any point on the surface corresponding to the observed technique is consistent with the data.

But marginal products are defined in terms of counterfactual experiments. Accordingly, suppose an economist knows all available production processes, as well as the technique in use. One can use this data to construct the wage-rate of profits frontier, which is the outer envelope of the wage-rate of profits curves constructed for each technique. For the sake of argument, suppose an uncountably infinite number of techniques happen to exist, and these techniques vary continuously along the frontier. So the frontier contains no switch points, where more than one technique is cost minimizing. Nevertheless, if the rate of profits (or wages) varies an infinitesimal amount from the value corresponding to a location on the frontier, a different technique would be cost-minimizing in a long-run equilibrium.

Reswitching shows this data is not necessarily enough to determine distribution. In the example, the alpha technique corresponds to two discrete ranges of equilibrium wages. It may be that if wages were set to a completely different level, firms would want to employ the same number of people, purchase the same resources, and use the same processes in production. The quantity flows within the firms would be unchanged, although who would purchase what on consumption markets could be vastly different. And yet for some level of wages between these two values, firms would want to adopt other processes. Thus, one's income in a capitalist economy cannot be a reward for physical productivity. The belief that income rewards productivity in a capitalist economy is an element of vulgar political economy, contradicted by rigorous price theory.

"...one who believes technology to be ... like my 1966 reswitching example ... will have a more sanguine view about how successful militant power by organized labor can be in causing egalitarian shifts in the distribution of income away from property even in the long run." -- Paul A. Samuelson, "Steady-State and Transient Relations: A Reply on Reswitching", Quarterly Journal of Economics, V. 89, N. 1 (Feb. 1975): 46

Suppose you run into an economist who refers to the marginal product (or the value of the marginal product) of some factor of production, perhaps in explaining why, regrettably, wages for somebody cannot easily be made higher. That economist simply does not know what he is talking about.

Qu'Est-Ce Que La Propriété? C'Est Le Vol.

When I think of P. J. Proudhon, I think of two works: What is Property? and The Philosophy of Poverty. Apparently, System of Economical Contradictions; or, the Philosophy of Misery is a translation of the latter's full title. And I "know", from Karl Marx's The Poverty of Philosophy, it is a very badly argued book.

The Project Gutenberg collection for Proudhon consists of exactly those two books. The formats plain text, sometimes html, Mobi pocket, and other protable formats, but no PDF.

Shawn Wilbur recently announced annouced the New Proudhon Library. I found the organization of the wiki confusing. This page has external links, but not to the Project Gutenberg texts. I guess this page has links to the original French.

Yet Another Cambridge Controversy (YACC) Example

1.0 Introduction
This is another example of reswitching and capital reversing. In this example, a capital good can only be used with a fixed quantity of labor in producing the single consumption good. If entrepreneurs would like to employ a different quantity of labor per unit output of the consumption good, they must use the services of some other capital good. In other words, this is an example of fixed coefficients, in some sense. But the existence of reswitching and capital-reversing are compatible with variable coefficients and the possibility of marginal adjustments. I think many economists may be confused on this point.

This example can also be seen as an illustration of a generalization of Paul Samuelson's "Surrogate Production Function" model. Samuelson assumed that alternative processes for producing the consumption good each require the use of a different capital good. But Samuelson required the special-case assumption that, for a given capital good, the desired ratio of physical units of the capital good to labor was invariant among processes producing the consumption good and producing the capital good. As Garegnani pointed out, this special case effectively collapses Samuelson's model to a one-good model. And so Samuelson's attempted defense of the aggregate production function fails.

2.0 The Technology and Quantity Flows
Consider a firm whose managers are aware of the technology shown in Table 1. Each column defines a Constant-Returns to Scale process for producing the output indicated by the column heading. The managers know of two processes for producing corn, a good used only in consumption. Steel and labor are each used in producing either more steel or in producing corn. Similarly for tin. Each process requires a year to complete, and the capital good is totally used up in producing the output. In the jargon, this is an example with no fixed capital; all capital is circulating capital.

Table 1: The CRS Technology

Inputs	Steel Industry	Tin Industry	Corn Industry
			Alpha	Beta
Labor (Person-Years):	1/3	1/2	1	3/2
Steel (Tons):	1/6	0	1	0
Tin (Tons):	0	1/4	0	1/4
Corn (Bushels):	0	0	0	0
Output (Various):	1	1	1	1

Two techniques are available for the vertically-integrated firm to produce corn. Each technique consists of two processes operated in parallel. The first technique, called the alpha technique, consists of the steel-producing process and the first of the two corn-producing processes. Suppose these processes are operated at a scale to produce 6/5 tons of steel gross and one bushel corn. Of the output of the steel-producing process, 1/5 tons replaces the steel inputs used up in producing the steel. The remaing ton replaces the steel used up in producing the corn. Thus, at this scale, the net output of the vertically-integrated firm consists of one bushel corn. Since 7/5 person-years are used across both processes, the ratio of the capital-inputs in physical terms to worker is 6/7 tons steel per person-year. Output per worker consists of 5/7 bushels per person-year.

The second technique, called the beta technique, consists of the tin-producing process and the second corn-producing process. When these processes are used to produce 1/3 tons tin gross and one bushel corn, the net output consists of one bushel corn. At this scale of operations, 5/3 person-years are employed. The ratio of the capital-inputs to worker is 1/5 tons tin per person-year. Output per worker is 3/5 bushels per person-year.

The alpha technique produces more output per worker. In the traditional and incorrect neoclassical analysis of the production function, greater output per worker for a known technology is achieved by the use of more capital per worker. Firms choose to use a less labor-intensive process, in this incorrect analysis, when consumers choose to save more and the interest rate (called the rate of profits below) consequently falls. Notice that one cannot tell from the above arithmetic with the example whether the capital-to-labor ratio is higher in the alpha or in the beta technique. The units of comparison so far are incommensurable.

3.0 Prices
The adoption of each technique in a steady-state competitive capitalist economy specifies certain relationships among price variables.

3.1 The Alpha Technique
If the alpha technique is cost-minimizing, the following equations must hold:

(1/6) p_s (1 + r) + (1/3) w = p_s

p_s (1 + r) + w = 1

where p_s is the price of steel in units of bushels corn per ton steel, w is the wage in units of bushels corn per person year, and r is the rate of profits. These equations incorporate the assumption that wages are paid out of the surplus at the end of the year. This system of equations shows that the same rate of profits is earned in producing both steel and corn.

This is a system of two equations in three variables. As Sraffa notes, it has one degree of freedom. Two of the variables can be found in terms of the third. I take the rate of profits as the independent variable. The wage is then:

w_α(r) = (5 - r)/(7 + r)

And the price of steel is:

p_s(r) = 2/(7 + r)

The wage-rate of profits curve is a declining function in the first quadrant of the wage-rate of profits space (Figure 1). Since this is a model of the production of commodities by means of commodities, the wage-rate of profits curve cuts both axes. The maximum rate of profits in the alpha system, found when the workers live on air, is r = 500%. The maximum wage, where the capitalists receive none of the surplus, is 5/7 bushels per person-year.

The price of steel can be used to evaluate the capital goods used per worker in the alpha technique:

I_α(r) = 12/[7 (7 + r)] bushels per person-year

The price Wicksell effect is the variation, given the technique, in the value of capital per worker with the rate of profits.

Figure 1: Wage-Rate Of Profits Curves

3.2 The Beta Technique
The price equations for the beta technique consist of:

(1/4) p_t (1 + r) + (1/2) w = p_t

(1/4) p_t (1 + r) + (3/2) w = 1

where p_t is the price of tin in units of bushels corn per ton tin. The solution of this system of equations is:

w_β(r) = (3 - r)/(5 - r)

p_t(r) = 2/(5 - r)

The maximum rate of profits in the beta system is r = 300%, which is lower than the maximum in the alpha system. The maximum wage in the beta system is 3/5 bushels per person-year, which is also lower than in the alpha system. The value of capital per worker is:

I_β(r) = 2/[5 (5 - r)] bushels per person-year

3.3 Switch Points
The technique with the highest wage, at a given rate of profits, is the cost-minimizing technique at that rate of profits. The wage-rate of profits frontier in models like the example is the outer envelope in Figue 1 of all wage-rate of profits curves. The alpha technique is cost-minimizing both for rates of profits between 0% and 100% and for rates of profits between 200% and 500%. The beta technique is cost minimizing for rates of profits between 100% and 200%.

At a switch point, more than one technique is cost minimizing. In the example, switch points are at (r, w) = (100%, 1/2) and at (200%, 1/3).

3.4 Selected Consequences for Capital and Labor "Markets"
The analysis of the choice of technique allows one to graph the value of capital per worker in a steady state versus the rate of profits (Figure 2). The graph displays a combination of price and real Wicksell effects. Consider the horizontal lines at the rate of profits of 100% and 200% for the switch points. The real Wicksell effect is the variation in the in the value of capital per worker with the technique at a rate of profits for a switch point. The price Wicksell effect is shown by the curves not being vertical between switch points. In Figure 2, the switch point with a positive real Wicksell effect is indicated. The example demonstrates the logical invalidity of traditional neoclassical theory, in which real Wicksell effects are always negative.

Figure 2: Investment Function

The analysis of the choice of technique also allows one to graph the level of employment firms offer at each wage, given the level of net output. Figure 2 indicates the switch point around which firms will attempt to hire more labor if the wage is increased.

Figure 3: Labor Employed per Unit Net Output as a Function of Wages

As an aside, I wonder if the following quotation includes an allusion to the Cambridge Capital Controversy:

"For output in goods-producing industries to increase, the quantity of intermediate goods used to produce the output must also be increased (e.g. cloth to produce a shirt, ham to produce a ham sandwich, etc.). However, the concept of the marginal product of labor (or capital) requires that as the input of labor (or capital) is increased, all other inputs must be held constant. But this is not possible for intermediate inputs in goods-producing industries. Therefore, the concept of the marginal product of labor (or capital) is not possible when there are intermediate goods in the production function. Again, we prefer not to teach such logical errors to our students." -- Bernard Guerrien and Emmanuelle Benicourt (2008)

4.0 Conclusions
So much for the logical validity of typical arguments for improved labor market flexibility and for the belief that minimum wages cause unemployment.

Bibliography

• Bernard Guerrien and Emmanuelle Benicourt (2008) "Is Anything Worth Keeping in Microeconomics?" Review of Radical Political Economics, V. 40, N. 3 (Summer): 317-323
• P. Garegnani (1970) "Heterogeneous Capital, the Production Function and the Theory of Distribution", Review of Economic Studies, V. 37, N. 3 (July): 407-436.
• Paul A. Samuelson (1962) "Parable and Realism in Capital Theory: The Surrogate Production Function", Review of Economic Studies, V. 29, N. 3 (June): 193-206

Michal Kalecki: Economics Is The Science Of Confusing Stocks With Flows

J. R. Hicks invented the IS/LM model to compare and contrast his interpretation of Keynes' General Theory with "classical economics". Franco Modigliani later appended a supply and demand model of the labor market. Even later, John Hicks rejected this model.

Offhand, I can think of three issues with the IS/LM model:

• The LM curve shows a stock equilibrium, while the IS curve shows a flow equilibrium. Thus, it is not clear to me that they can be graphed on the same diagram.
• Both curves are drawn for a given set of expectations. If one curve shifts, the expectations upon which the other is drawn can hardly remain constant. Thus, both curves must shift and the equilibrium point becomes indeterminate.
• The curves replicate the separation between nominal and real values that Keynes was trying to transcend with his monetary theory of production. Thus, the model cannot be a valid representation of the theory Keynes was so laboriously trying to express.

The first point challenges the internal validity of the model. The second suggests the model cannot empirically predict. The third is a point about the history of economic thought and would be expressed better if I remembered better some of Keynes post-General Theory work.

Cavalry Tactics At The Battle Of Austerlitz

"To explain why people allocate time to a particular activity - like unemployment - we need to know why they prefer it to all other activities."-- Robert Lucas, , Basil Blackwell (1987): 54

Yes, why do people choose to be without a job?

(The title of this post is an allusion to a joke from Robert Solow.)

Knight Wins - No, Hayek Wins The Cambridge Capital Controversy

The best understanding of the Cambridge Capital Controversy is still an unresolved question, without a consensus having been reached. This presents an opportunity for fans of any long departed economist writing on capital theory. They can declare him or her the victor in the CCC avant le letter.

I barely recall Santiago Valiente (1980). But I seem to remember somebody declaing Knight the winner of the CCC.

On the other hand, Jack Birner argues that Hayek should be considered the winner:

"If the article [Hayek 1934] had been more widely known and understood, there would never had been a Cambridge debate. [Footnote:] Co. for instance [Hayek 1934], note 2 on pp. 212-13, which explains why there is not always a one-to-one correspondence between the rate of interest and the value of capital. Hayek's highly sophisticated analysis of the relations between input and output through time makes use of the same three-dimensional diagrams that seven years later were to constitute the core of [The Pure Theory of Capital]. Not only is the model of 1934 taken over almost unchanged in PTC, it is used there to analyze the most complicated of the various cases Hayek distinguishes, the one with durable capital goods." - Jack Birner (1999)

Some ironies arise here. Hayek and Knight opposed one another in the second great capital controversy in neoclassical economics. I think Birner is correct in arguing that Hayek thought of his triangles and the analysis in Prices and Production as a simplified and incomplete version of his more advanced capital theory. But that simplified version is itself a rejection of the even simpler Austrian theory associated with Böhm Bawerk and the "average period of production".

Anyways, my refutation of Garrison's version of Austrian Business Cycle Theory has been rejected by the Cambridge Journal of Economics. One of the reviewers stated that I need to rewrite it in view of Birner's article. I intend to take this advice.

So in the process of responding to reviews, I have retreated from arguing that ABCT is mistaken to arguing merely that Garrison's version of ABCT is mistaken. Garrison's version is the most prominent among scholars. I'll leave open whether an internally valid ABCT can possibly be constructed on Hayek's Pure Theory of Capital and "Ricardo effect" analysis. I am hardly alone, however, in doubting that it can be:

"The book [PTC] could not achieve its aim, because of Hayek's lack of formal and mathematical skills and the impossibility of the task itself [Footnote:] as taught by the outcome of the Cambridge capital controversies" -- Hansjörg Klausinger (2006)

"Whether or not Hayek's discussion of the Ricardo effect is refuted by arguments made in the Cambridge capital debates will be left aside in this paper." -- Theodore Burczak (2001: 64)

Bibliography

• Jack Birner, "The Place of the Ricardo Effect in Hayek's Economic Research Programme", Revue d'Économie Politique, V. 106, N. 6 (Nov-Dec 1999): 803-816
• Theodore A. Burczak "Profit Expectations and Confidence: Some Unresolved Issues in the Austrian/Post-Keynesian Debate", Review of Political Economy, V. 13, N. 1 (Jan. 2001): 59-80.
• F. A. Hayek "On the Relationship between Investment and Output", Economic Journal (1934)
• Hansjörg Klausinger "'In the Wilderness': Emigration and the Decline of the Austrian School", History of Political Economy, V. 38, N. 4 (2006): 617-644.
• Wilfredo Santiago Valiente (1980) "Is Frank Knight the Victor in the Controversy between the Two Cambridges?" History of Political Economy, V. 12, N. 1: 41-64

Novel By Ivan Turgenev

What do the following economists have in common?

Clark, Friedman, Galbraith, Keynes, Mill, Walras, Weintraub

Answer in the first comment.

The Sociology Of Mainstream And Non-Mainstream Economics

"I admit that my criteria of falsifiability does not lead to an unambiguous classification. Indeed, it is impossible to decide, by analyzing its logical form, whether a system of statements is a conventional system of irrefutable implicit definitions, or whether it is a system which is empirical in my sense; that is, a refutable system. Yet this only shows that my criterion of demarcation cannot be applied immediately to a system of statements - a fact I have already pointed out... The question whether a given system should as such be regarded as a conventionalist or an empirical one is therefore misconceived. Only with reference to the methods applied to a theoretical system is it at all possible to ask whether we are dealing with a conventionalist or an empirical theory. The only way to avoid conventionalism is by taking a decision: the decision not to apply its methods. We decide that if our system is threatened we will never save it by any kind of conventionalist stratagem." - Karl Popper (1968): 81-82

John Davis (2009) distinguished between two ways of dividing economists up: based on the content of their theories and based on more sociological criteria of citation networks, conference attendance, professional society membership, textbooks, etc. I think Davis' taxonomy remains of interest even if one does not agree with his views on trend in the economics profession.

Davis distinguishes between orthodox and heterodox economics on the basis of the substances of their theories. In the last column of Table 1, I have listed some distinguishing precepts of orthodox economics. The last three precepts roughly correspond to the opposite of the distinguishing features, according to Davis, of heterodox economics around 1980. I think one could also call orthodox economics "neoclassical". Heterodox economics rejects some combination of the precepts of orthodox economics. For Davis, mainstream economics is a sociological category. The first two columns of Table list some examples. Mainstream heterodox economics may become orthodox in time, with game theory perhaps already having succeeded, at least partially. At any rate, mainstream heterodox economists have access to the leading journals, a presence in the graduate schools generally rated to be the top, and so on.

Table 1: Divisions Among Economists

Non-Mainstream Economists	Mainstream Economists
Heterodox Economics		Orthodox Economics
Marxism Radical political economy Institutionalism Post Keynesianism Austrian school Regulation schools Circuitists Feminist economics	Game theory(?) Behavioral economics Experimental economics Evolutionary economics Neuroeconomics Complexity economics	Formal models Atomistic, non-socially embedded individuals Equilibrium models set out of historical time Methodological individualism, social structures explained by aggregation over individuals

Both mainstream and non-mainstream heterodox economics can be broken down further. This can be seen in the table. The first two columns each contain more than one school of thought as an exemplar of that category. Davis makes further schematic distinctions. One is between an inward or outward orientation of heterodox economists. Another is among differents ways schools of economists can become heterodox. With these distinctions, Davis argues that the content and understanding of mainstream, non-mainstream, orthodox, and heterodox economics has been evolving over time.

Davis argues that non-mainstream economists should work harder to engage mainstream heterodox economists and that mainstream economists are more open to theoretical innovation than some non-mainstream economists claim. Without such engagement, he thinks, mainstream economists might be excessively conservative, with consequences that mainstream economists will continue to fail to incorporate worthwhile insights of non-mainstream heterodox economists. In the present historical conjuncture, I think, the odds of mainstream economics being suddenly swept away have increased. If so, Davis's strategy might be unnecessary, though I am not very optimistic either way.

By the way, I could have cited previous work by Davis for this post. I wanted to mention that Davis's is the second essay I've read in Fullbrook (2009). McFarling (2009), which is at least a stretch for me, is the first essay I read in this book. So far, I find in the little I've read in this book a broad agreement that heterodox economists reject the orthodox overemphasis on social explanations from atomistic, non-socially embedded individuals.

References

• John B. Davis (2009) "The Nature of Heterodox Economics", in Fullbrook (2009)
• Edward Fullbrook (editor) (2009) Ontology and Economics: Tony Lawson and His Critics, Routledge
• Bruce R. McFarling (2009) "Finding a Critical Pragmatism in Reorienting Economics", in Fullbrook (2009)
• Karl R. Popper (1968) The Logic of Scientific Discovery, Revised edition, Harper

"Truth!" Said Pilate. "What Does That Mean?"

Alfred Tarski's 1944 essay, "The Semantic Conception of Truth and the Foundations of Semantics" has been put up on a Web site. Tarksi's problem is to formulate a definition of truth for an object language. According to Tarski, a definition of truth is materially adequate only if condition T holds for all true sentences "p" in the object language:

(T): X is true if and only if p,

where X is the name of the sentence "p", and p is the translation of the sentence "p" into the metalanguage in which condition T is expressed.

Maybe I should explain a litte about a metalanguage and the names of sentences. The object language is merely the language for which truth of sentences is defined. It is a formal language, and some mechanism (e.g., a grammar in Backus-Naur form) is available for determining what strings are sentences in the language and what are not. Predicate calculus with quantification ("for all" and "there exists") of variables taken over natural numbers provides an example. The grammar specifies the syntax of the language, but not the semantics.

The metalanguage is merely a (formal) language in which to talk about expressions and sentences in the object language. My title provides an easy example of named sentences. "John 18:38" is the name of those sentences. Notice that "John 18:38" does not appear in the New Testament, although the verse with the name "John 18:38" does. Likewise, the names of sentences presumably do not appear in the object language.

In this informal exposition, Tarski waves his hands at a couple of points, most notably in (not) explaining what it means for the metalanguage to be "essentially richer" than the object language. The metalanguage contains translations of every sentence "p" in the metalanguage, as well as additional sentences. But this is not enough for the metalanguage to be richer. Tarski points to Bertrand Russell's theory of types and says something about the metalanguage being able to include sentences about higher types.

I'll have to study more if I really want to understand "essential richness". It occurs to me that any sentence in the metalanguage has a Gödel number. So sentences in the object language can include variables taking on a number expressing a sentence in the metalanguage. But Gödel numbering operates only on the level of syntax. I guess the idea of essential richness is to prevent the formulation of a relation like T(GN(X), GN(p)) in the object language, where this relation somehow encodes condition T and GN(X) and GN(p) are the Gödel numbers of X and p, respectively. If one could formulate a relation like this, the possibility arises of creating a sentence that says that it itself is false, under the obvious interpretation. (Footnote 11 in Section 8 of Tarski's paper provides a neat formulation of the paradox of the liar.)

I find it amazing that Tarski can relegate a proof of Gödel's incompleteness theorem to a couple of footnotes. Part of why he can do this is that he presumes all the technical machinery Gödel used to demonstrate that one can assert the provability of a sentence in the object language within the object language (given an object language in which arithmetic can be expressed). Since Tarski has shown that one cannot assert the truth of a sentence in the object language, the non-equivalence of provability and truth falls out. And all provable sentences in the object language are true. So the existence of true but unprovable sentences in the object language follows, even though Tarski, unlike Gödel, doesn't construct one.

I have some questions:

1. Would at least some authors of the committe that developed the Web Ontology Language be extremely well-versed in Tarski's work, including semantics and model theory? Would the same be true of at least some developers of the semantic web?
2. Is there a good book on model theory available and downloadable on the Web?

Greek To Me

1.0 Introduction
I previously described, in an abstract way, a model in which individuals choose rationally even though they may not have a complete transitive preference relation. In that post, I relied heavily on a paper by S. Abu Turab Rizvi. Searching on some of Turab Rizvi's references, I stumbled upon Jeanne Peijnenburg's doctoral thesis, Acting Against One's Best Judgement: An Enquiry into Practical Reasoning, Dispositions and Weakness of Will. Reading some of this thesis inspired me to revisit my model by presenting a somewhat more concrete example.

2.0 Background
I learned a new word from Peijnenburg's thesis. Acting against one's own best judgement is called "akrasia". Peijnenburg shows that discussion of being divided in mind goes back, at least, to debates among Socrates, Plato, and Aristotle. She provides some amusing quotes about akrasia:

"I do not do what I want to do but what I hate... What happens is that I do, not the good I will to do, but the evil I do not intend." -- Romans 7:15 and 7:19

"The mind orders the body and is obeyed. But the mind orders itself and meets resistance." - Augustine

"Two souls, alas, do dwell within this breast" - Goethe

"Faust complained that he had two souls in his breast. I have a whole squabbling crowd. It goes on as in a republic." -- Otto von Bismarck

3.0 The Example
Consider an individual choosing among three actions. This person foresee an outcome for each action. For my purposes, it is not necessary to distinguish between an action and the outcome the individual believes will result from the action. Accordingly, let A, B, and C denote either the three actions or the three outcomes, depending on context.

3.1 Tastes
Suppose that the individual cares about only three aspects of the outcome. For example, if the action is obtaining an automobile of one of three brands, one aspect of the outcome might be the fuel efficiency obtainable from the car. Another might be the roominess of the car interior. And so on.

In the example, the individual has preferences among these three aspects of the outcomes, but not over the outcomes as a whole. "Preferences" are here defined as in neoclassical economics, that is, as a total order. Let the individual order the actions under each aspect as shown in Table 1. For example, under the first aspect, this person prefers A to B and B to C. Since a total order is transitive, one can conclude that this individual prefers A to C under the first aspect. The individual prefers C to A, however, under either of the other two aspects. (This example has the structure of a Condorcet voting paradox, but as applied to an individual.)

Table 1: Preferences Over Aspects of Outcomes

Aspect	Preference Over Aspect
1st	A > B > C
2nd	B > C > A
3rd	C > A > B

3.2 The Choice Function
The individual is not necessarily confronted with a choice over all three actions. Mayhaps only two of the three needed automobile dealers have franchaises in this person's area. The specification of the example is completed by displaying possible choices for each menu of choice with which the individual may be confronted. That is, I want to specify a choice function for the example:

Definition: A choice function is a map from a nonempty subset of the set of all actions to a (not necessarily proper) subset of that nonempty subset.

The domain of a choice function is then the set of all nonempty subsets of the set of all actions. Informally, the value of a choice function is the set of best choices on a menu of choices with which an agent is confronted. (The above definition is a variation on the one I gave in my previous post.)

Table 2 gives the choice function for this example. The first three rows show that in a menu consisting of exactly one action, the individual chooses that action. In a menu consisting of exactly two actions, the individual is willing to choose only one of those actions. And in a menu with three actions, the individual is willing to choose any of the three.

Table 2: The Choice Function

Choices on the Menu	Best Choice(s)
{A}	{A}
{B}	{B}
{C}	{C}
{A, B}	{A}
{A, C}	{C}
{B, C}	{B}
{A, B, C}	{A, B, C}

3.3 The Conditions of Arrow's Impossibility Theorem
I intend the above example as an illustration of application of Arrow's impossibility theorem to a single individual. The choice function given above is compatible with the conditions of Arrow's impossibility theorem:

• No Dictator Principle: For each aspect, some menu exists in which the choice function specifies a choice in conflict with preferences under that aspect. For example, the choice from the menu {A, C} conflicts with the individual's preferences under the first aspect of the outcomes.
• Pareto Principle: This principle is trivially true in the example. No menu with more than one choice exists in which preferences under all aspects specify the same choices. So the choice function cannot be incompatible with the Pareto principle when it applies, since it never does apply.
• Independence of Irrelevant Alternatives: I think this principle is also trivially true.

In compatibility with Arrow's impossibility theorem, the existence of a single preference relation is not possible for the above choice function. A preference relation applies to all possible pairs of actions, and it must be transitive. But a transitive relation cannot be constructed for the three menus consisting of exactly two actions. So I have defined a choice function, but preferences (one total order) does not exist.

4.0 Conclusions
Neoclassical economists tend to equate rationality with the existence of a unique preference relation for an individual. In other words, rationality for an individual is identified with the existence of one total order (that is, a complete and transitive binary relation) over a space of choosable actions. The example suggests this point of view is mistaken. An orthodox economist can either assert that the individual in the example is not rational or accept that he has been learning and teaching error.

A choice function is a generalization of preferences, as neoclassical economists understand preferences. If such preferences exist for an individual, then a choice function exists for that individual. But individuals can have choice functions without having such preferences, as is demonstrated by the above example. It is up to those asserting the existence of preferences to state their special-case assumptions, to show that models with those assumptions can provide falsifiable predictions about society, and to provide empirical evidence. The evidence from experimental economics, though, is systematically hostile to neoclassical economics. The phenomenon of menu-dependence is particularly apposite here.

So much for prattle about competitive markets yielding efficient outcomes.

If I Read Italian...

...I suspect I would find this amusing. (I get glimmers thanks to Google language tools.) Notice the contributions from Fabio Petri in the comments below that post, and Boldrin's complaint about their incomprehensibility, format, and length. I offer cool water to contrast to the heat of those exchanges:

Fontana con tritone, da Bernini a Roma

Wiener On Economics As A Cargo Cult

I've seen this quote referenced from time to time:

"The success of mathematical physics led the social scientist to be jealous of its power without quite understanding the intellectual attitudes that had contributed to this power. The use of mathematical formulae had accompanied the development of the natural sciences and become the mode in the social sciences. Just as primitive peoples adopt the Western modes of denationalized clothing and of parliamentatism out of a vague feeling that these magic rites and vestments will at once put them abreast of modern culture and technique, so the economists have developed the habit of dressing up their rather imprecise ideas in the language of the infinitesimal calculus." -- Norbert Wiener (quoted by Joan Robinson in Freedom and Necessity)

Looking at the last chapter in his Cybernetics: or Control and Communication in the Animal and the Machine (John Wiley & Sons, 1948) provides some insight into Wiener's attitude. That chapter is titled "Information, Language, and Society". He looks at society as an organization, the elements of which are themselves small organizations. He looks at communication between these elements as being an application of cybernetic theory, now days more commonly known as C³I. And Wiener makes such observations as:

"In connection with the effective amount of communal information, one of the most surprising acts about the body politic is its extreme lack of efficient homeostatic processes. There is a belief, current in many countries, which has been elevated to the rank of an official article of faith in the United States, that free competition is itself a homeostatic process: that in a free market, the individual selfishnesses of the bargainers, each seeking to sell as high and buy as low as possible, will result in the end in a stable dynamics of prices, and with rebound to the greatest common good. This is associated with the very comforting view that the individual entrepreneur, in seeking to forward his own interest, is in some manner a public benefactor, and has thus earned the great rewards with which society has showered him. Unfortunately, the evidence, such as it is, is against this simple-minded theory." -- p. 185

Wiener also comments on those those who

"consider the main task of the immediate future is to extend to the fields of anthropology, of sociology, of economics, the methods of the natural sciences..."

He thinks they "show an excessive optimism, and a misunderstanding of the nature of all scientific achievement." He thinks the social sciences do not have the requisite "degree of isolation of the phenomenon from the observer."

So it seems the prodigious Norbert Wiener considered cybernetics to encompass an alternative to neoclassical economics and was concerned about the proper methodology of applying his theories to society.

Business As Sabotage

Over at Boing Boing, Dan Gillmor praises some comments of Thorstein Veblen on the media. (One of these days I might read Robert McChesney.) I did not recall the passage Gillmor quotes, but I was amused by the following passage from earlier in the same book:

"It was then still true, in great measure, that the undertaker was the owner of the industrial equipment, and that he kept an immediate oversight of the mechanical processes as well as of the pecuniary transactions in which his enterprise was engaged; and it was also true, with relatively infrequent exceptions, that an unsophisticated productive efficiency was the prime element of business success. A further feature of that precapitalistic business situation is that business, whether handicraft or trade, was customarily managed with a view to earning a livelihood rather than with a view to profits on investment...

...The economic welfare of the community at large is best served by a facile and uninterrupted interplay of the various processes which make up the industrial system at large; but the pecuniary interests of the business men in whose hands lies the discretion in the matter are not necessarily best served by an unbroken maintenance of the industrial balance. Especially is this true as regards those greater business men whose interests are very extensive. The pecuniary operations of these latter are of large scope, and their fortunes commonly are not permanently bound up with the smooth working of a given sub-process in the industrial system. Their fortunes are rather related to the larger conjunctures of the industrial system as a whole, the interstitial adjustments, or to conjunctures affecting large ramifications of the system. Nor is it at all uniformly to their interest to enhance the smooth working of the industrial system at large in so far as they are related to it. Gain may come to them from a given disturbance of the system whether the disturbance makes for heightened facility or for widespread hardship, very much as a speculator in grain futures may be either a bull or a bear. To the business man who aims at a differential gain arising out of interstitial adjustments or disturbances of the industrial system, it is not a material question whether his operations have an immediate furthering or hindering effect upon the system at large. The end is pecuniary gain, the means is disturbance of the industrial system, - except so far as the gain is sought by the old-fashioned method of permanent investment in some one industrial or commercial plant, a case which is for the present left on one side as not bearing on the point immediately in hand. The point immediately in question is the part which the business man plays in what are here called the interstitial adjustments of the industrial system; and so far as touches his transactions in this field it is, by and large, a matter of indifference to him whether his traffic affects the system advantageously or disastrously. His gains (or losses) are related to the magnitude of the disturbances that take place, rather than to their bearing upon the welfare of the community.

The outcome of this management of industrial affairs through pecuniary transactions, therefore, has been to dissociate the interests of those men who exercise the discretion from the interests of the community. This is true in a peculiar degree and increasingly since the fuller development of the machine industry has brought about a close-knit and wide-reaching articulation of industrial processes, and has at the same time given rise to a class of pecuniary experts whose business is the strategic management of the interstitial relations of the system. Broadly, this class of business men, in so far as they have no ulterior strategic ends to serve, have an interest in making the disturbances of the system large and frequent, since it is in the conjunctures of change that their gain emerges. Qualifications of this proposition may be needed, and it will be necessary to return to this point presently.

It is, as a business proposition, a matter of indifference to the man of large affairs whether the disturbances which his transactions set up in the industrial system help or hinder the system at large, except in so far as he has ulterior strategic ends to serve. But most of the modern captains of industry have such ulterior ends, and of the greater ones among them this is peculiarly true. Indeed, it is this work of far-reaching business strategy that gives them full title to the designation, 'Captains of Industry.' This large business strategy is the most admirable trait of the great business men who with force and insight swing the fortunes of civilized mankind. And due qualification is accordingly to be entered in the broad statement made above. The captain's strategy is commonly directed to gaining control of some large portion of the industrial system. When such control has been achieved, it may be to his interest to make and maintain business conditions which shall facilitate the smooth and efficient working of what has come under his control, in case he continues to hold a large interest in it as an investor; for, other things equal, the gains from what has come under his hands permanently in the way of industrial plant are greater the higher and more uninterrupted its industrial efficiency.

An appreciable portion of the larger transactions in railway and 'industrial' properties, e.g., are carried out with a view to the permanent ownership of the properties by the business men into whose hands they pass. But also in a large proportion of these transactions the business men's endeavors are directed to a temporary control of the properties in order to close out at an advance or to gain some indirect advantage; that is to say, the transactions have a strategic purpose. The business man aims to gain control of a given block of industrial equipment - as, e.g., given railway lines or iron mills that are strategically important - as a basis for further transactions out of which gain is expected. In such a case his efforts are directed, not to maintaining the permanent efficiency of the industrial equipment, but to influencing the tone of the market for the time being, the apprehensions of other large operators, or the transient faith of investors. His interest in the particular block of industrial equipment is, then, altogether transient, and while it lasts it is of a factitious character.

The exigencies of this business of interstitial disturbance decide that in the common run of cases the proximate aim of the business man is to upset or block the industrial process at some one or more points. His strategy is commonly directed against other business interests and his ends are commonly accomplished by the help of some form of pecuniary coercion. This is not uniformly true, but it seems to be true in appreciably more than half of the transactions in question. In general, transactions which aim to bring a coalition of industrial plants or processes under the control of a given business man are directed to making it difficult for the plants or processes in question to be carried on in severalty by their previous owners or managers. It is commonly a struggle between rival business men, and more often than not the outcome of the struggle depends on which side can inflict or endure the greater pecuniary damage. And pecuniary damage in such a case not uncommonly involves a setback to the industrial plants concerned and a derangement, more or less extensive, of the industrial system at large.

The work of the greater modern business men, in so far as they have to do with the ordering of the scheme of industrial life, is of this strategic character. The dispositions which they make are business transactions, 'deals,' as they are called in the business jargon borrowed from gaming slang. These do not always involve coercion of the opposing interests; it is not always necessary to 'put a man in a hole' before he is willing to 'come in on' a 'deal.' It may often be that the several parties whose business interests touch one another will each see his interest in reaching an amicable and speedy arrangement; but the interval that elapses between the time when a given 'deal' is seen to be advantageous to one of the parties concerned and the time when the terms are finally arranged is commonly occupied with business manoeuvres on both or all sides, intended to 'bring the others to terms.' In so playing for position and endeavoring to secure the largest advantage possible, the manager of such a campaign of reorganization not infrequently aims to 'freeze out' a rival or to put a rival's industrial enterprise under suspicion of insolvency and 'unsound methods,' at the same time that he 'puts up a bluff' and manages his own concern with a view to a transient effect on the opinions of the business community. Where these endeavors occur, directed to a transient derangement of a rival's business or to a transient, perhaps specious, exhibition of industrial capacity and earning power on the part of one's own concern, they are commonly detrimental to the industrial system at large; they act temporarily to lower the aggregate serviceability of the comprehensive industrial process within which their effects run, and to make the livelihood and the peace of mind of those involved in these industries more precarious than they would be in the absence of such disturbances. If one is to believe any appreciable proportion of what passes current as information on this head, in print and by word of mouth, business men whose work is not simply routine constantly give some attention to manoeuvring of this kind and to the discovery of new opportunities for putting their competitors at a disadvantage. This seems to apply in a peculiar degree, if not chiefly, to those classes of business men whose operations have to do with railways and the class of securities called 'industrials.' Taking the industrial process as a whole, it is safe to say that at no time is it free from derangements of this character in any of the main branches of modern industry. This chronic state of perturbation is incident to the management of industry by business methods and is unavoidable under existing conditions. So soon as the machine industry had developed to large proportions, it became unavoidable, in the nature of the case, that the business men in whose hands lies the conduct of affairs should play at cross-purposes and endeavor to derange industry. But chronic perturbation is so much a matter of course and prevails with so rare interruptions, that, being the normal state of affairs, it does not attract particular notice." -- Thorstein Veblen (1904). The Theory of Business Enterprise, Chapter 3.

CCC Not Exclusively About Aggregate Theory

I thought I might point out what some others say the Cambridge Capital Controversy is about:

"It is also worth noting that Samuelson...assesses the relevance of capital reversing mainly in terms of the beehavior of the interest rate consequent upon a change in saving behavior: a decrease in current consumption may entail a new steady-state equilibrium in which the interest rate is higher rather than lower than initially. This was indeed unexpected in conventional theory, but its ramifications are rather more serious than Samuelson lets on. The conventional relation between consumption and the interest rate emerges from the operation of the substitution mechanisms that underlie the downward-sloping factor demand functions of the marginalist theory; it is the latter distribution theory that capital reversing undermines." -- Gary Mongiovi, 2002. "Classics and Moderns: Sraffa's Legacy in Economics", Metroeconomica, V. 53, N. 3: 223-241.

"...one must conclude that at present there is no defensible neoclassical theory (in the sense of explanation) of prices and distribution. The onus is on the neoclassicals to show that this is not so. Unless and until they succeed, it seems reasonable to turn to different, non-neoclassical approaches to value and distribution (and employment and growth)." -- Fabio Petri, 1999. "Professor Hahn on the 'neo-Ricardian' Criticism of Neoclassical Economics", In Value, Distribution and Capital: Essays in Honour of Pierangelo Garegnani, Routledge.

"After the stirring, contentious debate over the theory of capital generated by the discovery of the phenomenon of re-switching in the 1960s, one has surprisingly witnessed, in the economic literature, within the course of only a few years, the sudden, one might even say abrupt, disappearance of all discussions on such themes.

The phases through which this state of affairs has come about are themselves an interesting phenomenon, from the view point of the history of economic science, and deserve careful consideration, even at the cost of a brief digression.

The first reaction to the discovery of re-switching was one of uneasy fastidiousness. The intuitive conjecture prevailed that it should be an odd, weird, bizarre or rare case of no empirical relevance whatsoever. The economists who nevertheless originally had to admit it did so with instinctive reluctance, as it clashed with their inherited way of thinking. They used a variety of terms for it, ranging from 'paradoxical' and 'perverse' to 'exceptional', 'inconvenient' and 'anomalous'; a case that 'intuition suggests is unrealistic', and so on (see the numerous quotations in Pasinetti 1966, p. 515, and also Pasinetti 1978). Charles Ferguson, as reported above, was more explicit and candid. He reasserted his instinctive confidence in the neoclassical production function, but admitted that his trust was 'a statement of faith'.

There followed a second phase in which there was a painstaking search for specifying the conditions that could be sufficient to exclude the re-switching phenomenon (on the subject see, for example, Franklin Fisher 1971, Sato 1974, Burmeister 1980). There was moreover a substantial effort to re-interpret the rate of interest as at least expressing the rate of return for society as a whole, when the economic system was changing the proportions between two equally profitable techniques (Solow 1963 and 1967). However, all these efforts did not lead very far. On the one hand the conditions that would be needed in order to avoid the re-switching of techniques proved to be so extremely restrictive as to leave no reasonable possibility of relying on them. On the other hand, in a critique of Solow's attempt to revive Irving Fisher's concept of the 'rate of return', Pasinetti investigated a general discontinuity property of the conception of spectrum of techniques, showing that the vicinity, even an infinitesimal vicinity, of any two techniques on the scale of variation of the rate of profits does not entail at all any vicinity of such techniques (as marginal productivity theory would require) on the scale of variation of their degree of capital-intensity (capital/output, or capital/labour ratios). Capital-intensity might in fact remain quite far apart for the two techniques involved (Pasinetti, 1969). These discontinuity properties have been analysed in detail by J. Barkley Rosser Jr. (1991, ch. 8: 'Discontinuity and Capital Theory'). Thus, new analytical investigation could bring no help for the traditional views; quite the contrary.

Yet there finally came a third very curious phase, which should appear rather strange, given its weak theoretical and empirical underpinning, but which was greeted with relief by the theorists of mainstream economics. The essence of this third phase can be summed up with the following proposition: the criticisms of the traditional theory of capital raised by the phenomenon of re-switching (and consequent reverse capital-deepening) are valid, but only with reference to the neoclassical model conceived in aggregate terms. They do not apply to the neoclassical case of the general economic equilibrium model, conceived in disaggregated terms and based on the behaviour of individuals maximising inter-temporal functions of profits and of utility.

This proposition actually has no objective foundation: phenomena of non-convexity, re-switchings of techniques and badly-behaved production functions, to take an expression that has been widely used ('behaving badly' meaning simply that they behave in a way as not to obey the assumptions of neoclassical economics), are not ­ as has been amply demonstrated ­ a consequence or a characteristic of any particular process of 'aggregation'. They may occur at any time and in any context, aggregated or disaggregated. Various authors have continued to demonstrate this point (e.g. Kurz 1987, Schefold 1997, Garegnani 1998, and others). But so things go. The contrary conviction had taken root and has continued to spread. Above all, the proposition cited above has been trundled out again and again, with no proof, but simply referring back to other sources, which in turn are either insufficient or inconsistent.

The principal one of these sources is represented by an incredibly polemical and dogmatic paper by Frank Hahn (1982), explicitly intended to heap discredit on those economists whom he calls 'the Neo-Ricardians'. With undeniable rhetorical and dialectical skill, Hahn shifted the bases of the whole debate. He admits, without mincing words, that the entire version of neoclassical theory of capital and income distribution, based on aggregate production functions (basically, the whole neoclassical stream of thought descending from Böhm-Bawerk, Wicksell and John Bates Clark) has to be scrapped as inconsistent and incorrect. He then goes on to argue that the correct and relevant version of the neoclassical theory is not that of Böhm-Bawerk, Wicksell and Clark, and not even that of Marshall, but rather the theory that stems from the Walrasian scheme of general economic equilibrium; a scheme which in its modern version is represented by the Arrow-Debreu formulation (Arrow and Debreu 1954, Debreu 1959, Arrow-Hahn, 1971). In this version, the scheme appears as a very general one. Although, in its essential terms, the scheme is a pure exchange model (i.e. a scheme of given resources, which the 'agents' exchange among themselves on the basis of the postulate of maximisation of utility), it can also be reinterpreted in inter-temporal terms, by associating with each resource a quantity index and a time index. In this version, the phenomenon of production becomes a phenomenon of inter-temporal exchange. Thus a framework can be traced out containing a whole range of heterogeneous capital goods. At any given moment of time, the postulates of maximisation (of utility and of profit) by the 'agents' (consumers and entrepreneurs) lead the system to positions of 'temporary equilibrium', generating an overall system of prices for all resources, present and future.

According to Hahn, this framework also includes Sraffa's model as a very special case; namely, as the case where the original heterogeneous goods in the given initial set are exactly in those proportions that generate a uniform rate of profits. But, in general, the 'equilibrium prices' generated by the system will imply rates of interest (and of profit, taken to coincide with the rates of interest) differing from any one (heterogeneous) capital good to another. This does not matter in the Walrasian model à la Arrow-Debreu, given that this model is a price determining model (a point which will be taken up again in the following section). Indeed, the non-uniformity of interest rates is proudly pointed out as a sign of the generality of the model. Hahn admits that the framework might show cases and problems of lack of uniqueness and/or lack of stability of the solutions. However, Hahn claims that the scheme should be immune to the criticisms prompted by the re-switching phenomenon.

But how? The point is precisely here. According to Hahn, in a system with manifold production techniques, equality would still hold between the return on each capital good and the derivative of its production with respect to its input, namely the 'marginal productivities' (in physical terms), although no causal relation could ever be asserted, since all the solutions emerge from a system of simultaneous equations. Hahn admits that there might, of course, be some 'non-convexities' and 'badly-behaved' production functions, in other words that cases of re-switching might occur. So Hahn admits cases of re-switching after all! But here is the ruse: while admitting such cases, Hahn relegates them to the category of difficulties concerning the zones of 'instability'. Now, zones of instability of the system can always occur, in models with heterogeneous capital goods, even in the case of perfectly convex and well-behaved production functions. Indeed, Hahn himself had demonstrated precisely this in an earlier article of his (Hahn 1966) ­ an article, it is to be it noted, written as a critique of dominant theory. Here is therefore how the confusion has been generated ­ a confusion between two different phenomena, namely: a) instabilities, that can in general arise in all neoclassical models with heterogeneous capital goods, and b) the particular phenomenon of re-switching, which ­ by being re-classified as generating instability (a characteristic which is not incorrect, since, among other things, re-switching also generates instability in the capital goods market) is restrictively associated (and confused) with the case previously considered by Hahn.

The paradoxical outcome has been that, instead of taking up Hahn's first finding (1966), which is critical and negative with reference to all the multi-sector models of neoclassical theory, mainstream literature has used Hahn's second article (1982) to assert that the difficulties connected with instability were already well-known.

Conclusion: re-switching had nothing new to tell us. As if the difficulties, when they are already known could, by this very fact, acquire a justification for being ignored, no matter whether they crop up in a different context, where they are reiterated and extended! Surprisingly enough, however, this is precisely what has happened.

Hahn has certainly been very careful not to stress his previous findings ­ strictly logical and negative. Instead, he has adopted the familiar expedient of saying that, of course, there are difficulties; of course these difficulties call for further research; hopefully further research will settle them in the future.

And here we finally come to the non sequitur of the conclusion: the 'Neo-Ricardians' could safely be ignored.

Mainstream economists could not have asked for better. The effect has been to give re-switching the air of an obsession vexing others, and to induce dominant economic theorists not to talk of it any more. The debate soon flagged; in the major economics journal it has been forgotten.

But something even more interesting and intriguing has happened. After only a few years, even the admissions initially made no longer found any mention. Aggregate production functions have made their untroubled re-appearance in the macroeconomic textbooks, without the slightest hint as to their earlier (recognised) logical inconsistencies. It has taken only a few years for them to reappear in papers published in the major journals of dominant economic theory, which at the same time have begun systematically to reject all articles dealing with re-switching as unpublishable. The same authors, who had for two decades been asserting the need to scrap the aggregate neoclassical production functions are now using them quite normally. The typical economics student entering university from the 1980s onwards has heard nothing of the re-switching difficulties involved in the neoclassical theory of capital and income distribution.

It is as if the debate on the choice of techniques had never taken place. Amnesia on such a vast scale can only be explained by more appropriate terms, such as 'suppression' or 'repression' or 'removal'. This is, perhaps, one of the most interesting examples of that process described by Kuhn (1962), through which dominant 'normal' science suppresses, and thus ignores, the cases of contradiction and anomaly it bears within." -- Luigi L. Pasinetti, "Critique of the Neoclassical Theory of Growth and Distribution", 200?

A Manhattan Project For Economics?

Last December, Mike Brown, Stuart Kauffman, Zoe-Vonna Palmrose, and Lee Smolin discussed "Can Science Help Solve the Economic Crisis?" They suggest that what we need now is an economics Manhattan project. And by the way, neoclassical economics is not completely correct. (The Edge seems like an interesting place, whatever you think of this article.)

I vaguely know something about two of these authors. I read Stuart Kauffman's At Home in the Universe a number of years ago. I had previously read something about the Santa Fe Institute, including some of Brian Arthur's papers. But the idea of mathematical biology, with an emphasis on cross-disciplinary work from computer science was new to me.

I have been struggling through Peter Woit's Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law for a month or so now. The algebra is tough going for me. Maybe I would have been better off with Lee Smolin's book on the same topic. And I have Smolin's paper "Time and Symmetry in Models of Economic Markets" to read. Barkley Rosser, Jr., suggests that Smolin should read some more economics, but it seems to me Smolin is quite modest about the potential of his work. I think Rosser and Smolin and his colleague approach some harmony in the comments in that thread.

Hat Tip: New York Times

The First Thing We Do, Let's Kill All The Lawyers

Paul Samuelson seems to be aware of the possibility of hostile, sometimes politically-motivated, readings of works in economics:

"Piero's was a subtle mind, which had thought long and hard on these (mathematical) relationships. His pen writes as if a lawyer were at hand to ensure that no vulnerable sentence appears. I honour him for that, and with my own students felt obligated to point out the subtelty of the text..." -- Paul A. Samuelson (2000) "Sraffa's Hits and Misses", in Critical Essays on Piero Sraffa's Legacy in Economics (ed. by Heinz D. Kurz), Cambridge University Press

"For some reason that I have no understanding of, the virulence of the attack on Tarshis was of a higher order of magnitude than on my book, but there were plenty of attacks on my book, and there was a lot of work done by people. Also I wrote carefully and lawyer-like so that there were a lot of complaints that Samuelson was playing peek-a-boo with the Commies. The whole thing was a sad scene that did not reflect well on conservative business pressuring of colleges."-- Paul A. Samuelson (quoted in David Colander and Harry Landreth, "Political Influence on the Textbook Keynesian Revolution: God, Man, and Laurie Tarshis at Yale")

Some Links

• "A Progressive Program for Economic Recovery & Financial Reconstruction" from the Universiy of Massachusetts Amherst's Political Economy Research Institute (PERI), the New School's Schwartz Center for Economic Policy Analysis (CEPA), and others
• "Capitalism Beyond the Crisis", by Amartya Sen, in The New York Review of Books
• "Ivory Tower Unswayed by Crashing Economy", Patricia Cohen, New York Times, 4 March 2009
• "Sold Out: How Wall Street and Washington Betrayed America"

Paul Lewis On Unproven Justifications For Flexible Labor Markets

Many who do not understand economics, such as many mainstream economists working at the OECD, the IMF, the World Bank, and other powerful institutions, think less unemployment would result from more "flexible" labor markets. Flexibility is a code-word for eliminating unions, lowering the real value of minimum wages, and otherwise decreasing standards in labor markets. I have pointed out some reasons why this push for labor market flexibility is theoretically and empirically unjustified.

There is more to Paul Lewis' recent paper than this echo of my favorite argument:

"One rationalisation of F[lexible] L[abour] M[arkets] rests upon neoclassical economic theory, in particular M[arginal] P[roductivity] T[heory]. A key feature is optimisation of the quantity of each factor employed so that its price equals its marginal productivity. To fit with the trade and technology hypotheses this neoclassical model must contain a minimum of two homogeneous categories of labour - low and high skilled - and two types of 'capital' - advanced high-skill complementary and low-skill complementary equipment.¹...

...What results from these labour market conditions at a macro level is the natural rate of unemployment, or N[on]-A[ccelerating] I[nflation] R[ate] of U[nemployment] as it has come to be known. This is a long-run equilibrium, a consequence of supply and demand in the labour market, in this case largely constituted by the market for the low-skilled. It is consistent with firms having zero net profit,³ which corresponds with a 'warranted wage' for labour (Blanchard, 2006, p. 13).

¹ I consider the arguments for F[lexible] L[abour] M[arkets] rest upon the following neoclassical assumptions. (i) Capital refers to the physical means of production, which has to be homogeneous in its inherent productive features, (ii) it is quantifiable independently of its price, which allows it to be optimised in production. This characterisation of capital was shown to be nothing more than a 'neoclassical parable' as Samuelson put it, with no grounding in reality (see Blaug, 1997; Hodgson, 1997; Hunt, 2002). However, this shortcoming has not prevented its continued use as a foundation of mainstream microeconomics.

³ A condition of perfect competition in the product markets. The outcome of zero profits in equilibrium is a further example of the inability of M[arginal] P[roductivity] T[heory] to model common features of real economies." -- Paul Lewis, "(How) Do Flexible Labour Markets Really Work? The Role of Profitability in Influencing Unemployment, Cambridge Journal of Economics, V. 33 (2009): pp. 51-77

No Need For Greed Or Hunger, A Brotherhood Of Man

Last month, I compared and contrasted "socialism" and "social democracy". A discussion on Crooked Timber inspired me here.

I now find John King has a working paper, "Socialist Democratic and Socialist Policies", intended for publication in the International Encyclopedia of Public Policy. I haven't fully absorbed this, but I see King goes back before Eduard Bernstein and his Marxist revisionism.

Freeing Oneself From The Ideas Of Some Academic Scribbler Of A Few Years Back

I have just begun reading James Galbraith's The Predator State. I like this passage:

"What, then, is a reality-based person to do? Many people appear to believe that the best they can do under the circumstances is to hedge and qualify, at the margins. That is, they can aver that the market may be imperfect, that under certain conditions it may fail, that it might function better given the aid of fuller information or certain constraints on behavior. And this position, deeply rooted in academic economics and therefore at least somewhat defensible on the public stage, has become the 'liberal' position in debates over markets, linked to the slogan 'making markets work.'

The problem with this compromise is that it depends on a misreading of the academic economics on which it is based. The underlying idea appears to be that markets exist but sometimes have problems: a bit of monopoly power, some kinks in the flow of information, a few side effects, maybe a little difficulty predicting the future. But in fact, the modern currents of academic economics are far more devastating than that. Each of the problems just mentioned is not incidental; rather they are pervasive. Taken together, they raise serious doubts about the idea that markets can work at all. To state that again: taken together, they form an overwhelming critique of the very concept of the market.

In the purest version of the theory that underlies the conservative version of the perfect market, economic man is a machine to whom whimsy and evolution are unknown. In practice, man is inconsistent; changeable; sometimes, though not consistently, irrational; his judgments biased and distorted and influenced by his peers. Modern behavioral economics has begun - but only begun - to notice this, seeking by experimental methods to show whether the actual behavior of presumptively competent people corresponds to the predictions of the rationalist theory. The findings, associated with the Nobel Prize-winning work of the Princeton psychologist Daniel Kahneman, are that they are not. Ordinary, intelligent people appear consistently unwilling, or unable, to calculate the consequences of their decisions in a manner predicted by the view that they are responding purely to the market. Instead, they act as social beings, concerned about their standing with their peers, about the fairness of the deal they are being offered, and other matters quite irrelevant to the utility of the object or money on offer. These are remarkably subversive findings, for they suggest that even if there were no monopoly, no externalities, perfect information, and perfect foresight, markets composed of real people would still not perform as the conservative vision requires.

But of course there are easier ways to reach the same conclusions, and behavioral economics is of interest mainly because it speaks to market-obsessed academics from within all the mind-boggling restrictions that they habitually impose on their analyses in order to make the problems appear capable of solution. The real world is a different place altogether." -- James K. Galbraith, The Predator State: How Conservatives Abandoned the Free Market and Why Liberals Should Too, Free Press (2008): pp. 21 -22

I'm not sure that Galbraith contains much of that spontaneous wit that his father generally put in in about the fifth draft.

A Plague of Economists

What do economists think about Keynesian ideas, such as deficit spending in the midst of a great depression? Oliver Staley and Michael McKee report, "[James] Tobin's stamp is on the $787 billion stimulus signed by President Barack Obama, former students and colleagues say. His philosophies are influencing Austan Goolsbee, a former Tobin student advising Obama, and Ben S. Bernanke, head of the Federal Reserve. Unlike Friedman, Tobin provides guidance for today’s problems, said Paul Krugman, a Princeton University economist." Furthermore, "Bernanke cited Tobin’s 1969 essay on monetary theory in a 2004 paper discussing options available to the Federal Reserve for stimulating the economy when interest rates approach zero."

So economists are for it.

On the other hand, Will Wilkinson interviews Edward Prescott and Edmund Phelps. The idiot savant Edward Prescott says, "Stimulus is not part of the language of economics... There is an old, discarded theory that's been tried and failed spectacularly, which is where that language of stimulus comes from".

So economists are against it.