Franklin Fisher on the Stability(?) of General Equilibrium

The eminent Franklin Fisher, winner of the J. B. Clark Medal in 1973, a famed econometrician and antitrust economist, who was the expert economics witness for IBM in its long battle with the U. S. Department of Justice, and was later the expert witness for the Justice Department in the antitrust case against Microsoft, currently emeritus professor professor of microeconomics at MIT, visited the FTC today to give a talk about proposals the efficient sharing of water between Israel, Palestine, and Jordan. The talk was interesting and informative, but I must admit that I was more interested in Fisher’s views on the stability of general equilibrium, the subject of a monograph he wrote for the econometric society Disequilibrium Foundations of Equilibrium Economics, a book which I have not yet read, but hope to read before very long.

However, I did find a short paper by Fisher, “The Stability of General Equilibrium – What Do We Know and Why Is It Important?” (available here) which was included in a volume General Equilibrium Analysis: A Century after Walras edited by Pacal Bridel.

Fisher’s contribution was to show that the early stability analyses of general equilibrium, despite the efforts of some of the most best economists of the mid-twentieth century, e.g, Hicks, Samuelson, Arrow and Hurwicz (all Nobel Prize winners) failed to provide a useful analysis of the question whether the general equilibrium described by Walras, whose existence was first demonstrated under very restrictive assumptions by Abraham Wald, and later under more general conditions by Arrow and Debreu, is stable or not.

Although we routinely apply comparative-statics exercises to derive what Samuelson mislabeled “meaningful theorems,” meaning refutable propositions about the directional effects of a parameter change on some observable economic variable(s), such as the effect of an excise tax on the price and quantity sold of the taxed commodity, those comparative-statics exercises are predicated on the assumption that the exercise starts from an initial position of equilibrium and that the parameter change leads, in a short period of time, to a new equilibrium. But there is no theory describing the laws of motion leading from one equilibrium to another, so the whole exercise is built on the mere assumption that a general equilibrium is sufficiently stable so that the old and the new equilibria can be usefully compared. In other words, microeconomics is predicated on macroeconomic foundations, i.e., the stability of a general equilibrium. The methodological demand for microfoundations for macroeconomics is thus a massive and transparent exercise in question begging.

In his paper on the stability of general equilibrium, Fisher observes that there are four important issues to be explored by general-equilibrium theory: existence, uniqueness, optimality, and stability. Of these he considers optimality to be the most important, as it provides a justification for a capitalistic market economy. Fisher continues:

So elegant and powerful are these results, that most economists base their conclusions upon them and work in an equilibrium framework – as they do in partial equilibrium analysis. But the justification for so doing depends on the answer to the fourth question listed above, that of stability, and a favorable answer to that is by no means assured.

It is important to understand this point which is generally ignored by economists. No matter how desirable points of competitive general equilibrium may be, that is of no consequence if they cannot be reached fairly quickly or maintained thereafter, or, as might happen when a country decides to adopt free markets, there are bad consequences on the way to equilibrium.

Milton Friedman remarked to me long ago that the study of the stability of general equilibrium is unimportant, first, because it is obvious that the economy is stable, and, second, because if it isn’t stable we are wasting our time. He should have known better. In the first place, it is not at all obvious that the actual economy is stable. Apart from the lessons of the past few years, there is the fact that prices do change all the time. Beyond this, however, is a subtler and possibly more important point. Whether or not the actual economy is stable, we largely lack a convincing theory of why that should be so. Lacking such a theory, we do not have an adequate theory of value, and there is an important lacuna in the center of microeconomic theory.

Yet economists generally behave as though this problem did not exist. Perhaps the most extreme example of this is the view of the theory of Rational Expectations that any disequilibrium disappears so fast that it can be ignored. (If the 50-dollar bill were really on the sidewalk, it would be gone already.) But this simply assumes the problem away. The pursuit of profits is a major dynamic force in the competitive economy. To only look at situations where the Invisible Hand has finished its work cannot lead to a real understanding of how that work is accomplished. (p. 35)

I would also note that Fisher confirms a proposition that I have advanced a couple of times previously, namely that Walras’s Law is not generally valid except in a full general equilibrium with either a complete set of markets or correct price expectations. Outside of general equilibrium, Walras’s Law is valid only if trading is not permitted at disequilibrium prices, i.e., Walrasian tatonnement. Here’s how Fisher puts it.

In this context, it is appropriate to remark that Walras’s Law no longer holds in its original form. Instead of the sum of the money value of all excess demands over all agents being zero, it now turned out that, at any moment of time, the same sum (including the demands for shares of firms and for money) equals the difference between the total amount of dividends that households expect to receive at that time and the amount that firms expect to pay. This difference disappears in equilibrium where expectations are correct, and the classic version of Walras’s Law then holds.

9 Responses to “Franklin Fisher on the Stability(?) of General Equilibrium”


  1. 1 Blue Aurora October 2, 2014 at 8:25 pm

    Out of curiosity, Dr. Glasner…has Franklin Fisher written anything on Alfred Marshall’s contributions to economics? Since he has written about Leon Walras on economic equilibrium…I would be surprised if it turned out that he hadn’t written anything about Alfred Marshall.

    On another note…I came across this old paper in the History of Economics Review, and thought of you:

    http://www.hetsa.org.au/pdf-back/30-A-3.pdf

  2. 2 dan October 3, 2014 at 5:17 am

    Rich.
    The best analysis is always that which illuminates rather than asserts (or worse advocates). It is the subtle difference between simple and simplistic.

    Equilibrium is obviously a useful modeling tool that helps illuminate an understanding of how the economy works, it rather obviously is not an immutable law with some set of parameters and values determined by pre-ordained laws of nature.

    Its always wonderful to have introductions to those economists who thought (think) deeply and to get a push in that direction with one’s own thinking.

    As an aside, Milton Friedman surely must be one of the great puzzles as an economist of his stature. While it seems he was unquestionably brilliant, the number of rather dumb and thoughtless quotes that are attributed to him is striking. Perhaps he was someone who was just too imbalanced, a genius who didn’t feel music deeply.

    dan

  3. 3 James J Wayne October 3, 2014 at 7:03 am

    Rich:

    I happen to agree with Milton Friedman’s comments on stability.

    It is very important to put the General Equilibrium (GE) Theory in a more broad context. GE model is a very poor description of how the economics really works.

    Take the current US economy as an example. We have lots of slacks in terms of unemployment and underemployment workers, and the spare capacities in the manufacture sectors. And we have business inventories. If there is inventories and lots of spare capacities, the aggregated supply and potential supply is always greater than the aggregated demand. Therefore, there is no Walras Equilibrium in reality. The Walras Equilibrium does not allow the slacks, unemployments, and inventories.

    If the GE model is a very poor description about what is happening in reality, it makes stability of GE model almost irrelevant and purely an academic excercise.

    If one insists on using the equilibrium model, the overall economy is much better described as the flow equilibrium in terms of flows of goods and money than a GE model. The stability of a flow equilibrium is decided by the size of shock-absorbing buffers, which are the business inventories.

  4. 4 Charles October 3, 2014 at 8:10 am

    Have you looked at Herbert Gintis’s work on this ? For example, Economic Journal 2007.

  5. 5 James J Wayne October 3, 2014 at 2:52 pm

    The Dynamics of General Equilibrium

    Herbert Gintis, Santa Fe Institute
    Abstract
    The Walrasian general equilibrium model is the centerpiece of modern economic theory. While the equilibrium properties of the model have been well known since the seminal work of Arrow and Debreu a half century ago, progress in understanding its dynamical properties has been meager. Some rethinking of Walrasian dynamics is in order. This paper shows that the instability of Walras’ tatonnement process is due to the public nature of prices, which leads to excessive correlation among the behaviors of economic agents. When prices are private information, a dynamic with a globally stable stationary state obtains in economies that are unstable in the tatonnment process. We provide an agent-based model of a multi-sector Walrasian economy with production and exchange, in which prices are private information. This economies is dynamically well-behaved.

    Suggested Citation
    Herbert Gintis. “The Dynamics of General Equilibrium” Economic Journal (2007).

  6. 6 MB. October 6, 2014 at 3:19 pm

    Dr Glasner, you might be interested in Andre Orlean’s book on the wlrasian general equilibrium model “the empire of value”. He offers a very interesting critic of the theory of value as utility.

  7. 7 dan October 7, 2014 at 5:58 am

    James J Wayne,

    I think my point on Friedman is a little different than your take.
    My problem with the Friedman quote is not whether or not he was right. Indeed, he was a formidable intellect and a brilliant economist. He’s more likely than not to be right.

    My problem is with his intellectual framework.

    I love Keynes because he was happy intellectually with contradictions. He didn’t (apparently) need absolutes. Every great truth is balanced by opposite and contradictory truths. Keynes at the very least communicated an extremely high comfort level with that, and dealt with it.
    Friedman, it seems to me, fought it. Friedman wanted consistency a rule to rule all others. He wanted his truths to be always and everywhere true.

    Obviously there is a world of difference between something being true, and something being ALWAYS true.

    Free markets produce optimal outcomes; markets need coordinating agents.


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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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