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Finding equilibrium

from Lars Syll

book-equilibrum-till-duppeFinding Equilibrium explores 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 Equilibrium shows 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 Equilibrium sheds 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.kornai 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.


  1. Macrocompassion
    February 8, 2015 at 12:35 pm

    Are equilibrium and stability so similar? Equilibrium is a condition that the social system continuously seeks (but never quite achieves due to a series of external disturbances often being introduced at random); whilst stability is the rate of change toward equilibrium that the system inherently possesses. Thus stability is the aggregate and rate of change of the variable of the function for equilibrium.

  2. February 8, 2015 at 1:14 pm

    The obsession with equilibrium can easily waylay the learner of economics. To the lay person, it appears that the whole purpose and wisdom of markets is to discover clearing prices for commodities and that that function is, if not all that economics studies, its crowning achievement.

    It takes determination to discover that these ideal markets with one commodity, one price, and neatly intersecting supply and demand curves rarely exist outside of textbooks. High-tech markets are dominated by network effects that work opposite to a textbook supply curve: Selling more smartphones makes them cheaper.

    Energy markets have different and incommensurate prices for wholesale than for individuals. Regional differences in retail prices suggest these are dominated by policy (taxes), monopoly, and cost of sales effects rather than commodity clearing prices. Even for crude, recent volatility demonstrates that price is affected by politics and futures concerns at least as plausibly as spot supply and demand.

    Then there is the stock market, which is a fine thing but certainly not in equilibrium. The trend for the US stock market is to ever increase in value at a linear rate, fuelled by new money from QE, buybacks, and margin debt. The stock market only falls when there’s a debt crunch. It’s a good wealth concentrator, but a funny kind of equilibrium for sure.

    Perhaps the biggest failing of economic teaching is to view markets as simple price regulators, sort of like a steam governor (http://en.wikipedia.org/wiki/Governor_%28device%29). Markets and economies deserve more than that. Markets are vibrant!

    The purpose of a market, and Adam Smith’s invisible hand, is not to connect marginal producers and consumers of potatoes to determine the clearing price of potatoes. It’s to connect pin makers and cobblers, potato consuming doctors, farmers who need legal advice, bored scholars, and bawdy entertainers to produce things that none of them individually could orchestrate. Making things that have unforeseen uses is the achievement, not equilibrium.

    The market is a bazaar, not an intersection of two curves. The economy is a network that constantly makes and tears down connections, not a steam engine to be kept in equilibrium. What is this classical obsession with equilibrium? Economics is a celebration of complexity!

    • Larry Motuz
      February 9, 2015 at 6:54 pm

      What a superb comment!

      I think the central problem has to do with value-in-use :: actual benefits from consumption as use, whether by ‘consumers’ as users or ‘producers’ as users :: having dropped out of economics in favor of value-in-exchange with its emphasis on money benefits.

      For instance, if I need 2500 calorie-units (or other nutritional units) every day (or multiples over longer ‘periods’) then it is this ‘benefit’ that I seek. If there were two goods, X and Y, with X providing 500 calories per unit consumed and Y providing 250, then my budgeting decision and my consumption would be subject to a lower bound calorie constraint: 2500 – 500X – 250Y = 0 and I would have to be able to budget for some position on or above this line given any price regime. [This also implies that we must drop the manna from heaven budget constraints common in micro-theory, and, in fact, construct objective measures of ‘utility’ and ‘dis-utility’ as use-value.]

      Such an approach does not lead to any kind of ‘equilibrium’ as such.

      And, yes, the ‘market’ is most certainly a bazaar.

  3. blocke
    February 8, 2015 at 2:22 pm

    “The economy is a network that constantly makes and tears down connections, not a steam engine to be kept in equilibrium. What is this classical obsession with equilibrium? Economics is a celebration of complexity”

    If this is so, then the regulator must be the knowledgeable expert state official not the supposed self regulation of markets.

    • Helge Nome
      February 9, 2015 at 4:33 pm

      The capitalist economy is akin to a paper airplane that has been incorrectly trimmed:
      It gains speed, and as it does, puts the nose up and stalls, nosedives and repeats the process.
      While doing so, assets are snapped up by then big guys from the small fry in debt.
      Economists who practice Newspeak describing the economy as a self correcting system
      are rewarded with Nobel Prizes.
      Long live Big Brother!

      • davetaylor1
        February 9, 2015 at 8:04 pm

        Exactly, Helge. In electronics we would liken it to a relaxation oscillator feeding a transformer inducing output voltages proportional to the slope, e.g. an auto spark generator. As energy accumulates in the magnetic field of the transformer, those on the up slope get a small positive output (of negative electrons), then at the flick of a switch and/or a breakdown of insulation the energy accumulating in the transformer is sucked out and sent rapidly the other way at a much higher voltage. Of course they don’t teach such revealing analogies in schools of economics.

  4. February 8, 2015 at 6:17 pm

    Sorry Edward, but the STARTING POINT of “autisme economy” and then the “post-autisctic” movement was that even if equlibrium exist, is unique, stable, optimal, it describes a CENTRALISED ECONOMY with price taking agents : nothing to do with market economies. IT IS NOT RELEVANT (different from “non realistic”).
    And representative agent models (RBC, DSGE) are NOT of the “general equilibrium” kind, as there is ONLY ONE person (Robinson Crusoe, representative agent or ‘social planner’, etc.) who decides.
    I do not understand why “heterodox” still continue to continue to speak about “markets” – like mainstream – concerning Arrow-Debreu and representative agent models. It is quite desperating.

    • February 8, 2015 at 7:28 pm

      From false to true
      Comment on Guerrien on ‘Finding equilibrium’

      All one needs to know about market theory is known:
      “There is little or nothing in existing micro- or macroeconomics texts that is of value for understanding real markets. Economists have not understood how to model markets mathematically in an empirically correct way.” (McCauley, 2006, p. 16)

      For Heterodoxy follows that the defunct theory of market interaction has to be replaced by the correct approach. For a start see (2015).

      Egmont Kakarot-Handtke

      Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: The Market.
      SSRN Working Paper Series, 2547098: 1–10. URL http://papers.ssrn.com/sol3/
      McCauley, J. L. (2006). Response to “Worrying Trends in Econophysics”. Econo-
      Physics Forum, 0601001: 1–26. URL http://www.unifr.ch/econophysics/paper/

  5. February 12, 2015 at 4:16 pm

    It still suprizes me why the Nobel prize is awarded for unimportant work as the general equilibrium theory.indeed economics is a celebration of complexity

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