L’équilibre général depuis Sonnenschein-Mantel-Debreu

8 Aug, 2019 at 15:10 | Posted in Economics | 4 Comments

La question est de savoir si, partant toujours d’une situation qui n’est pas un équilibre, la variation des prix amène à un équilibre … Les théoriciens de l’équilibre général ont fait apparaître, dans les années 1970, les difficultés rencontrées dans la formalisation du processus supposé mener à un équilibre et ont abouti à un résultat négatif : il n’est pas possible d’affirmer, même dans le modèle de concurrence parfaite, que le processus est stable, c’est-à-dire qu’il conduit effectivement à l’équilibre …

pignolLes théoriciens de l’équilibre général ont donc formulé la question de la stabilité dans les termes suivants : peut-on élaborer des hypothèses sur les agents dont on puisse déduire des propriétés sur les fonctions de demande nette agrégée qui garantiraient la stabilité de l’équilibre ? La réponse est négative. Le théorème établi par Hugo Sonnenschein en 1973, et généralisé par Rolf Mantel et Gérard Debreu, montre qu’on ne peut établir aucune propriété des demandes nettes agrégées qui assure la stabilité de l’équilibre. Les hypothèses sur les fonctions de demande nette agrégée nécessaires à la stabilité (par exemple, l’hypothèse de substituabilité brute) ne sont pas fondées microéconomiquement. On peut certes énoncer des conditions qui assurent la stabilité, mais elles sont arbitraires : on ne peut les déduire de l’axiomatique des comportements individuels.

La conclusion est que l’on n’a aucune idée de la manière dont un mécanisme de prix concurrentiel peut mener à l’équilibre. La théorie de l’équilibre général ne fournit aucun résultat appuyant l’idée selon laquelle un système de libre concurrence, dans lequel les prix sont flexibles et varient selon la loi de l’offre et de la demande, converge vers l’équilibre. Même en acceptant toutes les hypothèses, la théorie de l’équilibre général n’a pas démontré la capacité du système des prix à coordonner efficacement les décisions des agents économiques.

Claire Pignol / Alternatives Economiques

I can’t but agree with Pignol here. You could, of course, as Brad DeLong has asserted, consider modern mainstream economics to be in fine shape “as long as it is understood as the ideological and substantive legitimating doctrine of the political theory of possessive individualism” and if you manage to put a blind eye to all the caveats to its general equilibrium models — markets must be in equilibrium and competitive, the goods traded must be excludable and non-rival, etc, etc. The list of caveats soon becomes impressively large — and not very much value is left of modern mainstream economics if you ask me.

Still — a century and a half after Léon Walras founded neoclassical general equilibrium theory — modern mainstream economics hasn’t been able to show that markets move economies to equilibria.

We do know that — under very restrictive assumptions — equilibria do exist, are unique and Pareto-efficient. One, however,​ has to ask oneself — what good does that do?

It’s strange that mainstream macroeconomists still stick to a general equilibrium paradigm more than forty years after the Sonnenschein-Mantel-Debreu theorem — devastatingly showed that it is​ an absolute non-starter for building realist and relevant macroeconomics.

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.

Stability​ that can only be proved by assuming Santa Claus conditions is of no avail. 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.

4 Comments »

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  1. If the system can’t be shown to converge to equilibrium, aren’t you left with something like Black’s analysis, that prices are noisy and administered and essentially arbitrary? If prices are arbitrary, should inflation be a constraint on public policy? Or can we ignore economists and print money at least as fast as prices rise to guarantee access to vast superabundance?

  2. The utter debilitation of general equilibrium theory as a theory of macroeconomics is the assumption of full employment.

  3. Henry,
    Long before the SMD theorem, Malthus and Keynes emphasised the possibility of general gluts and deficient aggregate demand for labour.
    However, Keynes’ views contrast starkly with the negative tendencies of your comment and Prof. Syll’s post.
    Keynes argued that (neo-)classical general equilibrium theory is still very relevant and important when generalised to include government policies.
    Conversely, and contrary to Prof.Syll, it is the SMD theorem which is​ now “an absolute non-starter for building realist and relevant macroeconomics”
    See Keynes’ General Theory, Chapter 24: “Concluding Notes on the Social Philosophy Towards which the General Theory Might Lead”, Section III.
    .
    “if our central controls succeed in establishing an aggregate volume of output corresponding to full employment as nearly as is practicable, the classical theory comes into its own again from this point onwards. If we suppose the volume of output to be given, i.e. to be determined by forces outside the classical scheme of thought, then there is no objection to be raised against the classical analysis of the manner in which private self-interest will determine what in particular is produced, in what proportions the factors of production will be combined to produce it, and how the value of the final product will be distributed between them.
    .
    “apart from the necessity of central controls to bring about an adjustment between the propensity to consume and the inducement to invest, there is no more reason to socialise economic life than there was before.”
    .
    “the modern classical theory has itself called attention to various conditions in which the free play of economic forces may need to be curbed or guided. But there will still remain a wide field for the exercise of private initiative and responsibility. Within this field the traditional advantages of individualism will still hold good.”
    .
    “… no obvious case is made out for a system of State Socialism which would embrace most of the economic life of the community. It is not the ownership of the instruments of production which it is important for the State to assume. If the State is able to determine the aggregate amount of resources devoted to augmenting the instruments and the basic rate of reward to those who own them, it will have accomplished all that is necessary.”

    • Kingsley,
      .
      My comment is not at odds with the quotes you have provided from Keynes.
      .
      I understand Keynes’ views on the applicability of Classical Theory at full employment. At full employment, the main economic problem (aside form inflation) is the optimal allocation of resources, which classical/neoclassical theory (C/NCT) can account for.
      .
      At below full employment, where real world economies spend a good deal of time, C/NCT is inapplicable. C/NCT cannot explain how an economy can move from underemployment to full employment, only Keynesian theory has been able to do this.
      .
      My comment above is merely making the point that C/NCT only applies at full employment, which is what Keynes argued.


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