## General equilibrium theory — still dead after all these years

from **Lars Syll**

Raphaële Chappe has written a very interesting article about the value of general equilibrium theory, concluding in the following words:

For a student of real world markets, general equilibrium theory appears strangely distant. It is not surprising that a highly abstract framework consisting of hyper-rational agents might be ill equipped to provide a sufficiently credible account of markets in modern capitalism. What is more surprising is that despite these obvious limitations (some even claim that general equilibrium has been “dead” since the Sonnenschein-Mantel-Debreu results in the 1970s) the framework is still central to the Ph.D. curriculum, and continues to play a preeminent role in the high theory of economics. To the extent it shows the limits of the way of thinking, this is fair enough, but that is not how the subject is approached, by Mas-Colell/ Whinston/Green or any other major text. Is this an example of the greater importance given in our ‘science’ to the rites of justification than to the task of explanation? When a way of thinking limits our thinking then it’s time, with due appreciation for those who built it, to ‘throw away the ladder’.

The economist considering general equilibrium since the SMD results dead, is Frank Ackerman, and this is what he has to say on general equilibrium:

General equilibrium is fundamental to economics on a more normative level as well. A story about Adam Smith, the invisible hand, and the merits of markets pervades introductory textbooks, classroom teaching, and contemporary political discourse. The intellectual foundation of this story rests on general equilibrium, not on the latest mathematical excursions. If the foundation of everyone’s favourite economics story is now known to be unsound — and according to some, uninteresting as well — then the profession owes the world a bit of an explanation.

Almost a century and a half after Léon Walras founded general equilibrium theory, economists still have not been able to show that markets lead economies to equilibria. We do know that — under very restrictive assumptions — equilibria do exist, are unique and are Pareto-efficient. But after reading Ackerman’s and Chappe’s articles one has to ask oneself — what good does that do?

As long as we cannot show that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is nil. 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.

Continuing to model 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. As Ackerman writes:

The guaranteed optimality of market outcomes and laissez-faire policies died with general equilibrium. If economic stability rests on exogenous social and political forces, then it is surely appropriate to debate the desirable extent of intervention in the market — in part, in order to rescue the market from its own instability.

Equilibrium is stone dead — and now?

Comment on Lars Syll on ‘General equilibrium theory — still dead after all these years’

Frank Ackerman resumes: “If the foundation of everyone’s favourite economics story is now known to be unsound — and according to some, uninteresting as well — then the profession owes the world a bit of an explanation.”

Heavens no! Nobody needs pointless excuses of why things got messed up. The one interesting question is how to get out of the mess as fast as possible. But here is the crux of the matter: “There is another alternative: to formulate a completely new research program and conceptual approach. As we have seen, this is often spoken of, but there is still no indication of what it might mean.” (Ingrao et al., 1990, p. 362)

Economists know quite well that equilibrium is an inadmissible concept. The schizophrenia consist in the fact that equilibrium is firmly built into the axiomatic foundations. Orthodoxy is defined by these hard core propositions:

HC1. There exist economic agents.

HC2. Agents have preferences over outcomes.

HC3. Agents independently optimize subject to constraints.

HC4. Choices are made in interrelated markets.

HC5. Agents have full relevant knowledge.

HC6. Observable economic outcomes are coordinated, so they must be discussed with reference to equilibrium states. (Weintraub, 1985, p. 109)

The methodological blunder that suffices to make this axiom set forever unacceptable is that HC3 and HC5 introduce nonentities and that HC6 is a petitio principii.

So, the microfoundations approach as defined by HC1/HC6 is dead. In fact, it has already been dead in the cradle since Jevons/Walras/Menger. In their bottomless incompetence and ignorance economists busily produce SS-DD-equilibrium models as one-size-fits-all explanation since more than 140 years.

ALL articles in peer-reviewed quality journals that contain the concepts equilibrium/disequilibrium are scientific rubbish. What does this tell you about the quality of economic quality journals? Or their editors and reviewers? Or the smartness of authors and readers?

Keynes made an attempt to switch from microfoundations to macrofoundations but he, too, failed methodologically. Note well, that Post Keynesians, too, busily apply equilibrium (2011).

The paradigm shift in economics requires the switch from behavior-centered bottom-up, i.e. subjective microfoundations, to structure-centered top-down, i.e. objective macrofoundations.

The most elementary configuration of the economy consists of the household and the business sector which in turn consists initially of one giant fully integrated firm and is given by these three objective structural axioms:

A1. Yw=WL wage income Yw is equal to wage rate W times working hours L,

A2. O=RL output O is equal to productivity R times working hours L,

A3. C=PX consumption expenditure C is equal to price P times quantity bought/sold X.

The investment good sector comes in at a later stage. So, what we have with the minimalist and equilibrium-free set A1 to A3 is the pure consumption economy as the most elementary economic structure. This structure is the core of what Keynes called the monetary theory of production and it fully replaces silly real exchange models, silly Walrasian equilibrium models, and silly Post Keynesian models.

Economists are unable to get their heads around the fact that economics is a system science. A system can be unambiguously defined. This is the indispensable condition to do science. Walrasians, Keynesians, Marxians, and Austrians are like house flies which bang their heads incessantly against the window without ever changing the modus operandi. Nothing else than the fly swatter can bring this pathetic spectacle to an end.

Never ask stupidity to explain itself.

Egmont Kakarot-Handtke

Good post.

The only general equilibrium is death. As long as a system is actively increasing entropy (by using energy) it can’t be in equilibrium. SMD conditions imply a steady state rather than an equilibrium, but that implicitly assumes infinite (and unchanging) energy sources. Even if you buy that, SMD did not address stability. Unless a complex system is exactly at a point attractor it will never settle on one.

As Kauffman showed (Origins of Order) any complex system that is capable of remaining in a steady state is incapable of any form of change. One would have to be a pretty poor economic historian to believe that of a modern economy.

Basically GE theory in any or all of its guises is mumbo-jumbo, hocus-pocus, or any other form of distraction used by con men as their accomplices pick your pocket.

I guess I can’t imagine studying economics at any level (eg a single general undergrad or even high school course or a full PhD curriculum) without getting some presentation of general equilibrium theory. Every physics student will get a presentation of the derivation of the second law of thermodynamics usually following the boltzmann statistical mechanical or ideal gas approach (from very elementary ones —eg pictures of gas molecules in boxes—to very advanced ones —maybe using von neumann/birkhoff proofs based on ergodic theory) even though its pretty much totally innapplicable to most real systems people study.

It is unfortunate that sometimes (as when I took undergrad physics) more complex systems were not much discussed—KAM theorem, FPU experiments, chaos theory, self-organizing systems—all of which result from modifications of the ideal gas model (eg throwing out the idea of perfectly elastic, frictionless collisions, that the system is closed—rather its open and nonequilibrium, and there are multiple constraints in space and time).

The ideal gas model is analogous to general equilibrium of arrow, hahn, etc. Its a logical place to start. Just as in probability theory you may start studying the statistics of flipping a perfect coin or dice, and maybe translating it into a random walk. Then you start using biased coins or dice, and non-markov processes with memory (which actually should be called higher oder markov pracesses) in which your next coin flip or step in a random walk depends on where you are and where you have been, add barriers, etc.

One also typically looks for rather than equilibria, ‘quasi-equilibria’ or ‘metastable’ or transient states or attractors. Formally or mathematically these can be written to look almost identical to the equilibrium solutions but the terms have a different interpretation or are in different coordinates. I find this intuitive. My own world to an approximation can ne modeled as an increase in entropy to a local maximum. Similarily, standard utility maximization under a budget constraint, within a microsociety, is a reasonable description of my daily life (though i dont exactly write down the equations for it—-i just have a reasonable idea of my resources, my needs and preferences, and my environment —including the needs and preferences around me).

I also view SMD actually to be fully compatible with and a logical outcome of GET (though I’d have to look again carefully at the assumptions—eg i forget if the kind of if i recall ‘neothetic preferences’ are disallowed in the original Arrow (or Walras for that matter) GET model (i think not). The situation reminds me of Godel’s theorem—people thought once they had axiomatized math, basically the situation was done —every problem had a solution. This was Hilbert’s program. They got more than they asked for. (There was an earlier result I think by mantel—also a founder of GET—he almost immediately found a counterexample, although i think his model did have a slight modification of GET axioms (basically slightly non-continuous , discrete preferences). (His model is very similar to one in population genetics where they have an analogue of the 2nd law—-fisher’s fundamental theorem of population genetics—-alot of people assumed this was universally true but people found very simple genetic systems which didnt reach equilibrium —or rather , it reached a different kind of equilibrium).

The FPU (fermi-pasta-ulam) experiments were designed to prove the 2nd law in the 40’s or 50’s—one of the first uses outside of the atom bomb project of then new computers (maybe eniac). They set up a simulation of a kind of ideal gas system (though again it was a slight modification) and ran it on the computer to watch it reach equilibrium. It didn’t. Rather they discovered, chaos and precursor of KAM theorems. Nowadays these are viewed as different kinds of equilibrium solutions, and much more applicable.