## Finding equilibrium

5 Feb, 2015 at 12:32 | Posted in Economics | 5 Comments

Finding Equilibriumexplores the post–World War II transformation of economics by constructing a history of the proof of its central dogma—that a competitive market economy may possess a set of equilibrium prices. The model economy for which the theorem could be proved was mapped out in 1954 by Kenneth Arrow and Gerard Debreu collaboratively, and by Lionel McKenzie separately, and would become widely known as the “Arrow-Debreu Model.” While Arrow and Debreu would later go on to win separate Nobel prizes in economics, McKenzie would never receive it. Till Düppe and E. Roy Weintraub explore the lives and work of these economists and the issues of scientific credit against the extraordinary backdrop of overlapping research communities and an economics discipline that was shifting dramatically to mathematical modes of expression.Based on recently opened archives,

Finding Equilibriumshows the complex interplay between each man’s personal life and work, and examines compelling ideas about scientific credit, publication, regard for different research institutions, and the awarding of Nobel prizes. Instead of asking whether recognition was rightly or wrongly given, and who were the heroes or villains, the book considers attitudes toward intellectual credit and strategies to gain it vis-à-vis the communities that grant it.Telling the story behind the proof of the central theorem in economics,

Finding Equilibriumsheds light on the changing nature of the scientific community and the critical connections between the personal and public rewards of scientific work.

Although I find Düppe’s and Weintraub’s book a well-researched and interesting reading , I still can’t get rid of the feeling that all these efforts at modeling a world full of agents behaving as economists — “often wrong, but never uncertain” — and still not being able to show that the system under reasonable assumptions converges to equilibrium (or simply assume the problem away), is a gross misallocation of intellectual resources and time.

Almost a century and a half after Léon Walras founded neoclassical general equilibrium theory, economists still have not been able to show that markets move economies to equilibria.

We do know that — under very restrictive assumptions — equilibria do exist, are unique and are Pareto-efficient. After reading Franklin M. Fisher’s masterly paper The stability of general equilibrium: results and problems one however has to ask oneself — what good does that do?

An extremely prominent economist [Milton Friedman – LPS] long ago remarked to me in passing that the study of stability is unimportant because it is obvious that the economy is stable and, if it isn’t, we are all wasting our time. I pass over the question of whether it really is obvious that the economy is stable and observe that the issue of time-wasting by economists is not one of whether the economy is stable but rather of whether the theory is. A principal reason for studying general equilibrium in the first place is to examine the consistency of partial equilibrium analyses. Having powerful theories of the firm, the household, and the market, may not be very useful if all those theories cannot be true at the same time.

Clearly, the heart of this important consistency question lies in the existence of general equilibrium, and existence theory, fortunately, is a subject which is in pretty satisfactory shape. Nevertheless, there is a sense in which the consistency question cannot be regarded as settled with- out a satisfactory analysis of stability. It is no use knowing that there exist points at which all partial equilibrium propositions can be jointly true, if such points are not attainable. Hence the question of the stability of general competitive equilibrium is a vital one for economic theorists, particularly if the economy is stable, but not only then. If general equilibrium turns out to be stable only under a very restrictive set of assumptions, then, indeed, we will all have been wasting our time, for there will be something wrong with the partial theory that we think we understand.

As long as we cannot show, except under exceedingly special assumptions, that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is negligible. As long as we cannot really demonstrate that there are forces operating — under reasonable, relevant and at least mildly realistic conditions — at moving markets to equilibria, there cannot really be any sustainable reason for anyone to pay any interest or attention to this theory.

A stability that can only be proved by assuming “Santa Claus” conditions is of no avail. Most people do not believe in Santa Claus anymore. And for good reasons. Santa Claus is for kids, and general equilibrium economists ought to grow up.

And then, of course, there is Sonnenschein-Mantel-Debreu!

So what? Why should we care about Sonnenschein-Mantel-Debreu?

Because Sonnenschein-Mantel-Debreu ultimately explains why “modern neoclassical economics” — New Classical, Real Business Cycles, Dynamic Stochastic General Equilibrium (DSGE) and “New Keynesian” — with its microfounded macromodels are such bad substitutes for real macroeconomic analysis!

These models try to describe and analyze complex and heterogeneous real economies with a single rational-expectations-robot-imitation-representative-agent. That is, with something that has absolutely nothing to do with reality. And — worse still — something that is not even amenable to the kind of general equilibrium analysis that they are thought to give a foundation for, since Hugo Sonnenschein (1972) , Rolf Mantel (1976) and Gerard Debreu (1974) *unequivocally *showed that there did not exist any condition by which assumptions on individuals would guarantee neither stability nor uniqueness of the equlibrium solution.

Opting for cloned representative agents that are all identical is of course not a *real solution* to the fallacy of composition that the Sonnenschein-Mantel-Debreu theorem points to. Representative agent models are — as I have argued at length here — rather an *evasion* whereby issues of distribution, coordination, heterogeneity — everything that really defines macroeconomics — are swept under the rug.

Instead of real maturity, we see that general equilibrium theory possesses only pseudo-maturity. For the description of the economic system, mathematical economics has succeeded in constructing a formalized theoretical structure,

thus giving an impression of maturity, but one of the main criteria of maturity, namely, verification, has hardly been satisfied. In comparison to the amount of work devoted to the construction of the abstract theory, the amount of effort which has been applied, up to now, in checking the assumptions and statements seems inconsequential.

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A man at equilibrium is dead. An engine at equilibrium does no work. A system at equilibrium is dead.

I would argue that the economists with their thermodynamics analogies have been able to bring the world damn close to equilibrium.

Comment by Martin Kullberg— 5 Feb, 2015 #

Simply forget it

Comment on ‘Finding equilibrium’

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It is a rather old problem with these savants:

“These savants, as Galileo put it, first decided how the world should function in accordance with their preconceived principles. … He openly criticized scientist and philosophers who accepted laws which conformed to their preconceived ideas as to how nature must behave.” (Kline, 1982, p. 48)

Equilibrium, or by implication disequilibrium, is a nonentity. However, it is a fact — not only in the realm of science — that people have a strong proclivity to occupy themselves with nonentities. As J. S. Mill put it:

“Mankind in all ages have had a strong propensity to conclude that wherever there is a name, there must be a distinguishable separate entity corresponding to the name; …” (2006, p. 756)

The inexcusable methodological blunder with equilibrium is this:

“… you shouldn’t find the fixed equilibria first and then see if an economy converges to it; rather, the convergence process will itself constitute the equilibrium, if any exist.” (Mirowski, 1989, p. 459)

In brief, it is inadmissible to put assumptions like equilibrium, decreasing returns, perfect competition etcetera into the premises (2014). This mistake is known since antiquity as petitio principii and J. S. Mill, the founder of economic methodology, dealt with it at length in his System of Logic.

Equilibrium economists have not solved anything.

“It is utopian, as a matter of economics, because in effect it simply assumes from the outset a perfect solution to the very problem that an economic system is supposed to solve.” (Nelson, 2006, p. 62)

Therefore, the title of the book is, to begin with, misleading. Economists have not found equilibrium but simply put it into the hat. Economic methodologists who overlook this constructive defect, and there are many, are not up to their task.

What follows from all this?

Students of economics can gain a wealth of time by immediately stopping to read an article or a book as soon as the concept of equilibrium is introduced. Even better, with immediate effect journals do no longer accept papers that apply equilibrium.

Identifying nonentities is one of the defining activities of science. The discussions among physicists became enormously productive just by no longer applying concepts like perpetual motion machine or epicycle because they refer to nonentities. It is perfectly analogous with equilibrium.

The representative economist does not understand what Aristotle already understood.

“When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” (Resume of Aristotle’s Posterior Analytics) http://en.wikipedia.org/wiki/Posterior_Analytics

Equilibrium is neither a certain, true nor primary premise. To cling any longer to equilibrium is self-disqualifying.

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Egmont Kakarot-Handtke

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References

Kakarot-Handtke, E. (2014). Objective Principles of Economics. SSRN Working

Paper Series, 2418851: 1–19. URL http://papers.ssrn.com/sol3/papers.cfm?

abstract_id=2418851.

Kline, M. (1982). Mathematics. The Loss of Certainty. Oxford, New York, NY:

Oxford University Press.

Mill, J. S. (2006). A System of Logic Ratiocinative and Inductive. Being a Connected

View of the Principles of Evidence and the Methods of Scientific Investigation,

volume 8 of Collected Works of John Stuart Mill. Indianapolis, IN: Liberty Fund.

(1843).

Mirowski, P. (1989). The Rise and Fall of the Concept of Equilibrium in Economic

Analysis. Louvain Economic Review, 55(4): 447–468. URL http://www.jstor.org/

stable/40723905.

Nelson, R. H. (2006). Economics as Religion: From Samuelson to Chicago and

Beyond. Pennsylvania, PA: Pennsylvania State University Press.

Comment by Egmont Kakarot-Handtke— 5 Feb, 2015 #

The equilibrium assumption, also suggest a method for decisionmaking, it conditions behavior of large institutions and creates a mathematically determined course of action that seek out equilibrium (death of economy).

Mathematical reductionism is not a universally legitimate assumption. It is a very good way to create black holes. This is exactly what mathematical reductionism does in economy. The mathematics that these economists use, has a logical end point, where everything is gathered on a single entity, an entity that at that point will own everything and also be bankrupt. Ofcourse it falls apart long before that, in costly market convulsions, where massive institutions own enormous amount of property, yet are bankrupt.

Comment by Martin Kullberg— 11 Feb, 2015 #

What does a market really look like?

Comment on Martin Kullberg on ‘Finding equilibrium’

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Equilibrium is a nonentity. For theoretical economics follows that the familiar supply-demand-equilibrium depiction of the textbooks has to be replaced. This presupposes an entirely new approach because equilibrium is an indispensable element of the orthodox research program.

“Thus it is an organizing feature of any theory in the program that there must be a well-defined idea of equilibrium present; that equilibrium notion is to be intrinsic to any model or theory that exists in the protective belts.” (Weintraub, 1985, p. 148)

In order to replace Orthodoxy the correct market theory has to be developed. This is the make-or-break challenge for Heterodoxy (2015).

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Egmont Kakarot-Handtke

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References

Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: The Market. SSRN Working Paper Series, 2547098: 1–10. URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2547098.

Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal. American Economic Review, Papers and Proceedings, 75(2): 146–149. URL http://www.jstor.org/stable/1805586.

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For the correct depiction of the product market see here

Comment by Egmont Kakarot-Handtke— 11 Feb, 2015 #

Chill out, Egmont.

LPS, I want to know how you know that Franklin Fisher was speaking of Milton Friedman. Got a link, maybe?

Comment by The Arthurian— 8 Feb, 2015 #