Fisher: Disequilibrium Foundations of Equilibrium Economics

Fisher, Franklin M. (1983). Disequilibrium foundations of equilibrium economics. Cambridge [Cambridgeshire] ; New York: Cambridge University Press. http://www.loc.gov/catdir/description/cam022/82025105.html
http://www.loc.gov/catdir/toc/cam026/82025105.html

What does equilibrium mean in an economic setting in any case? Why would the study of equilibrium be of interest? Some people say that the study is uninformative because if the economy is in some way in disequilibrium, then the study of economics is theoretically off the mark. We can say that a market is in equilibrium if we define equilibrium so narrowly that it doesn’t explain much of anything. We can also say that an economy is in equilibrium if we endow agents with quasi-omniscient abilities.

There is much more to this analysis that specifically explores the nature of economic modeling vis-à-vis economic stability, equilibrium and disequilibrium in the first chapter that will not be touched on in this abstract.

From the beginning of chapter 2: “In my view, there have been four major developments in the history of modern stability analysis. These are (1) the realization that the subject was one which had to be studied in a context with a formal dynamic structure; (2) the realization that global, rather than simply local, results could be obtained; (3) the introduction of non-tâtonnement processes; and (4) closely related to this, the insight that attention paid to specifying the disequilibrium processes involved could lead to far more satisfactory results than could be obtained by restricting the excess demand functions” (19).

In chapter 2, Fisher explores the concept of tâtonnement. Stability analysis began with Samulson and Hicks. These, “…observed that the subject could only be rigorously studied in a framework specifying the equations of motion of the system when not in equilibrium”. Hicks suggested that Walras’ theory of tâtonnement be formalized which was realized through, “…a set of price adjustment equations that formed the basis for nearly all later work” (20).

Fisher highlights problems with the basic equilibrium equation (20), and argues that there are flaws. For example, he believes that in reality, it is impossible to translate, for example, excess demand into efficient price changes. He goes on to claims that the auctioneer who adjusts prices according to the prevailing sentiment of the consumers in the room is, “…at best an inconvenient fiction” (21).

There is also embedded in the above equation assumptions about consumers wanting to take action when their demand doesn’t agree with the dictated price, as well as their ability to take action. “…so that, even though the excess demand involved may be for a good dated in the far future, 1990 toothpaste, for example, individuals who will want that good in the far future begin immediately to attempt to acquire it” (22). “I shall refer to this as the ‘Present Action Postulate.’ It is implicit in the entire stability literature, although seldom explicitly stated. Perhaps this is because it need not be faced explicitly as long as we remain in a world in which the adjustment of prices to equilibrium can be safely supposed to take place before the dates on any commodities…come due and all acquisitions must be made before any are needed for consumption or production – the Arrow-Debreu world in which all markets and trades occur at the beginning of time and never again. Elegant as such a model is, however, it is not truly satisfactory when applied to real economies developing over time” (22).

Tâtonnement: The Lyapounov Second Method is explored. It requires a rest point, which is, “…a point at which the process does not move. In the models we shall be considering, rest points are in one-to-one correspondence with points that are in some sense also economic equilibria…” (24). “A rest point is said to be globally stable if the system converges to it from every set of initial conditions. This, of course, is a very strong property. In particular, if there is more than one rest point, then no particular rest point can be globally stable in this sense since if the process begins at some other rest point it will never leave it” (24). The next term introduced is that of an adjustment process: “An adjustment process…is said to be globally stable if, for any set of initial conditions, there is a rest point to which the system converges. The difference, of course, is that it doesn’t have to be the same rest point for all initial conditions” (25). “Finally, it is useful to distinguish this from the definition of the quasi-stability of an adjustment process. For convenience of language, let us suppose that the variables involved are prices only…Starting with any initial condition, consider an infinite sequence of prices. Such a sequence may not have a limit…but it may nevertheless have one or more limit points (roughly, points to smaller and smaller neighborhoods of which the sequence keeps returning). If every limit point of every such sequence is a rest point of the adjustment process, then that process is said to be quasi-stable” (25).

The book moves to a non-tâtonnement trade model: “One such development was the abandonment of the tâtonnement assumption of no trading out of equilibrium which had wound up in a dead end and the introduction of what are rather inelegantly called ‘non-tâtonnement’ processes. Since that is not a very informative name, I shall refer to them as ‘trading processes.’ It is important to remember that, while this stage of development permits trading out of equilibrium, most of the work to be discussed does not permit consumption or production to take place until equilibrium has been reached. One must think of participants as swapping titles to commodity stocks while prices…adjust. Only after the music stops do people go home and enjoy what they have.” (25).

There is an examination of the Edgewood process, which is seen as being inadequate.

The Hahn Process is then explored. “The central assumption of the Hahn Process is as follows. At any one time, after trade has taken place, there may of course be either unsatisfied demand or unsatisfied supply for some commodity, say, apples. However, we suppose that markets are sufficiently well organized that there are not both. In other words, there may be people who wish to sell apples at the current prices and cannot or there may be people who wish to buy apples at the current price and cannot, but there are not, after trade, simultaneously both unsatisfied sellers and unsatisfied buyers” (31).

“Note the different roles played by utilities in the Edegeworth and Hahn Processes. In the Edgeworth Process, the utilities actually achieved by individuals…rise while trading is going on. In the Hahn Process, target utilities—the utilities which they would achieve if they could complete their transactions—fall out of equilibrium. One way of looking at it is to say that in disequilibrium plans are not all compatible and that, in the Hahn Process, the adjustment is such that people have to lower their expectations until equilibrium is reached and everyone can in fact attain the utility he anticipates” (32). One key assumption of the Hahn Process is that no one ever runs out of money.

It continues down the path of micro-economic analysis.

The book concludes that, when producers and consumers take their decisions in a state of market disequilibrium, the model will eventually fall into equilibrium (hence the title). This model avoids some of the crucial misgivings of other models, specifically the tâtonnement model which necessarily needs to make large cuts in demand, which is unrealistic.

I skipped much of the middle of this book, its focus on micro-analysis and the equations.