Disequilibrium Dynamics and Aggregate
Excess Demand: On a Homunculus
Fallacy in Economic Theory
Maarten Pieter Schinkel
Modern economic theory is predominantly a theory of equilibrium. The
question of how such positions of rest, in which all individual plans and
expectations match, come about in larger economies is rarely addressed.
The discipline has little more to offer on it than the metaphor of the “invisible hand,” the imposed “law of supply and demand,” which says that the
prices of goods and services rise when their demand exceeds their supply and fall otherwise until they are equal, or at best formalizations of
such price adjustments, carried out by an auctioneer-like central institution with information on aggregate excess demand. The auctioneer model
is hardly convincing as an explanation of the majority of market processes in which no such central coordinator is present. By appealing to
an outside entity, an “auctioneer,” with no objectives of its own, existing
disequilibrium theory is furthermore at odds with the microfoundations of
economics. It presupposes a level of coordination, whereas economics’
original research question is whether and how order arises in an unorchestrated society of people making their own individual plans. Moreover,
despite this considerable amount of structure, the approach was able to
This essay is in part based on my PhD thesis (Schinkel 2001). I am indebted to Manuel Luis
Costa, Franklin Fisher, Hans Maks, Jan Tuinstra, Michel De Vroey, and Roy Weintraub for
many stimulating discussions over the years. I also thank them, as well as Iwan Bos, Wade
Hands, Phil Mirowski, and participants at the 2005 HOPE conference, for comments on an
earlier version of this essay. Sander Nieuwenhuis has kindly advised me on homunculi in the
cognitive sciences. Errors and opinions are mine.
History of Political Economy 38 (annual suppl.) DOI 10.1215/00182702-2005-022
Copyright 2006 by Duke University Press
190 Maarten Pieter Schinkel
establish global stability of these processes only under special and highly
restrictive sufficient conditions on aggregate excess demand that do not
generally follow from individual choice theory, a lot of ad hoc structure
imposed on the organization of markets, or extended algorithmic instructions to the auctioneer that have little to do with the workings of actual
markets.
This state of affairs is not a direct heritage of the classics: questions of
disequilibrium adjustment were seen as fundamental by Adam Smith and
Léon Walras, for example, as well as, in fact, some of the later seminal
contributors to general equilibrium analysis, including Kenneth Arrow
and Frank Hahn. Yet in mainstream neoclassical economics such questions gradually stopped being asked. Disequilibrium theory has almost
disappeared from the authoritative textbooks.1 By relying on an auctioneer, the little modeling that remains presupposes most of the order it
aspires to explain. As a result, the widespread presumption that free and
competitive economies with rational agents will swiftly be driven to an
equilibrium with desirable properties is largely unfounded.
This is problematic for a number of reasons. Competitive markets have
been adopted as a proper basis for organizing society in applied economics and politics. Faith in its potential has led to deregulation, liberalization,
and active antitrust policies. Although we have fairly well-developed partial theories on what constitutes good competition in isolated markets,
these are not well embedded in a general equilibrium framework. Also,
the vast majority of economic policy recommendations are derived from
comparative statics analyses. Such analyses begin with a model in equilibrium and then predict what new equilibrium results from certain measures
that change the parameters of the model. No insight is offered into the
question of which new equilibrium is established and how. As a result,
there is no particularly good justification for advising one of many possible developments. Furthermore, disequilibrium processes that are an
intricate part of the model typically affect the set of potential equilibria,
because they consume resources, for example, or, more fundamentally,
require deviations from the model of perfect competition, such as monopolistic price setting.
1. The need to justify equilibrium theory by disequilibrium analysis is the organizing
principle in Newman 1965, in its time a widely read textbook. After Takayama 1973 and
1985, which still have extensive chapters on disequilibrium theory, the influential Varian [1978]
1984 and the currently authoritative Mas-Colell, Whinston, and Green 1995 offer decreasing
coverage of the subject.
A Homunculus Fallacy in Economic Theory 191
How can it be that the teachings of economic theory still rest today on
such soft foundations?2 Why do we lack a generally accepted theory of
disequilibrium? Several scholarly histories of economic thought, among
them Hands 1984, Weintraub 1991, and Ingrao and Israel 1990, have documented how the dominant attempt to model disequilibrium adjustment
processes and study the global stability of general equilibrium models—
that is, the theory of tâtonnement that relies solely on aggregate excess
demand for price adjustment—stranded in the early 1960s on Herbert
Scarf’s (1960) puzzling example of nonconvergence of the tâtonnement
process in an otherwise standard setting. Furthermore, in the early 1970s,
the Sonnenschein-Mantel-Debreu results in demand theory showed that
aggregate excess demand functions are not restricted much by individual choice theory (Sonnenschein 1972, 1973; Mantel 1976; Debreu 1974).
This established that Scarf’s counterexample was not a special nongeneric
finding but a manifestation of the fact that instead the theory of tâtonnement
is a special theory, as it requires special assumptions on aggregate excess
demand.3 This gradual insight that general results did not seem available
in tâtonnement adversely affected further initiatives to understand the
behavior of economies outside equilibrium. It left the field to degenerate and eventually be largely abandoned, despite the fact that its central
research question was still very much open, and alternative approaches, not
burdened by the SMD results, in particular the theory of non-tâtonne­ment,
were available for further development.
However insightful, these histories raise further questions. How is it,
for example, that disequilibrium theory set itself up to be as vulnerable
to the SMD theorem as it did? That is, why did it rely solely on aggregate
excess demand to drive disequilibrium adjustments? And why did the discipline not, when aggregate excess demand proved an impossible base,
extend more than it did on the alternative theories of out-of-equilibrium
behavior available? In this essay, I suggest that the reason for this is that
neoclassical economics largely fails to see—or to the extent it does, refuses
to accept—that it offers a homunculus explanation for the workings of the
market process by postulating what it endeavors to explain. The Walras­
ian auctioneer is the personification of this. As a consequence, economics
2. This is so, despite the fact that some influential economists, such as Frank Hahn at
Cambridge and Franklin Fisher at MIT, kept stressing the importance of hardening them.
See, for example, Hahn 1982a and Fisher 1983.
3. The relationship between the Scarf counterexamples and the SMD result seems to have
been established for the first time in Fisher 1976. See also Fisher 1983, 11.
192 Maarten Pieter Schinkel
did not embrace the few attempts that were made to understand disequilibrium processes with more specification of detail, which likely would
have advanced the science.
The remainder of this essay is organized as follows. The next section
sets out what a homunculus explanation is, and how in the cognitive sciences it was long ago exposed as deficient, extensively debated, and
eventually constructively embedded in that discipline’s methodology.
The cognitive sciences follow a progressive program of gradually eliminating homunculi with ever less-sophisticated functions. These insights
can help economics to revive the study of disequilibrium. How economics got its homunculus is set out in section 2. Some possibilities of shedding it, contributed over the history of economic thought but largely outside the mainstream, are presented in section 3. Section 4 concludes.
1. Homunculus Explanations
The object of study in the cognitive sciences is the human mind and its
inner workings. The mind is a complex phenomenon. Located in the brain,
it produces such diverse effects as reflexes, memories, sensations, and
emotions, as well as well-planned rational schemes and the occasional
brilliant idea. Early cognition theories, from the second half of the eighteenth century up until far into the 1900s, offered an understanding of
human thought as a more or less coherently structured system of ideas
based on a male-type “master of ceremonies,” who resided in the brain
and organized thinking. Rudimentary theories of the memory likewise
postulated a little librarian running around the corridors of the head, who
would deliver from his archives foregone observations and thoughts at the
request of the working intellect. Any coordinated impulse or action was
typically taken to be the responsibility of some miniature person, or several little men, pulling strings connected to the limbs. The picture below
illustrates these primitive origins of cognitive psychology.4
A complete office of executives in the “brain headquarters” situated in
the cerebrum takes in signals from the senses, forwarded by “camera
operators” or via the “air tubes to aerating room,” and interpreted by the
4. This particular picture, originally from a 1925 children’s encyclopedia (Mee 1925), is
discussed, reproduced, and modified in the introductions of several twentieth-century textbooks on cognition as an illustration of the humble beginnings of the science—see, for example, Restak 1995.
A Homunculus Fallacy in Economic Theory 193
Figure 1 A homunculus explanation of the human mind
“receiver of camera pictures,” the “tester of odour,” or the “tester of foods.”
The headquarters then coordinates appropriate action, which is subsequently taken by the “manager of speech” when something is to be said
or by the operators of various muscles and reflexes housed in the cerebellum when something has to be done.
Obviously, this model of the intelligent man is not very explanatory, for
the little librarians, operators, and managers supposedly each have brains
too. The proposition implies, therefore, that each executive would need
its own office workers, who in turn require assistant librarians and staff.
Naturally, each of these workers would need to have his or her own brain,
194 Maarten Pieter Schinkel
with its own staff of office workers and assistants, all of whom in turn need
to have their own brains, etc. This problem of infinite regress was recognized as unsatisfactory quite early on in the development of the sciences. It
is referred to as the homunculus fallacy: what is aspired to be accounted for
is really presupposed—as a metaphor—on a higher level of abstraction.
Homunculus explanations today still capture popular imagination.
The conscience, for example, often takes the form of a little angel on the
shoulder, whispering in one’s ear what is the right thing to do, while the
id, personified by a little devilish man-bull hybrid with an arrow-pointed
tail, advises otherwise. In the 1959 educational cartoon “Gateways to
the Mind,” stimulated senses make red lights flash on a television screen
in the brain, on which a little man pulls a lever to instigate the proper
reaction. Likewise, in Woody Allen’s 1972 film Everything You Always
Wanted to Know about Sex * * But Were Afraid to Ask, the main character’s troubles with his Manhattan sex life are borne by a whole army
of little men carrying out all sorts of partial bodily functions.
Although these amusing homunculus fallacies are obviously not taken
as a serious proposition for understanding ourselves, in cognition theory
homunculi are center stage in a methodological debate still. B. F. Skinner strongly condemned them and forwarded behaviorism as an alternative methodology, in which the central research program is to establish
revealed reactions to external stimuli, rather than seek to identify underlying principles of the working of the brain.5 A maintained interest in
the microfoundations of cognition, however, which was boosted by artificial intelligence research, led to a methodology in which homunculi have
a proper place.
Frederick Attneave (1961) pointed out that the problem of infinite
regress arises only if the acts performed by each homunculus are just
as complex as the behavior it is supposed to explain. When performing
only partial psychoneural functions as intermediate steps in complex
explanations, the homunculus fallacy does not necessarily apply, since
more is offered than just a full replication. Postulating homunculi was further defended as constructive by Daniel Dennett in a number of papers
originally published in the early 1970s that were collected in Brainstorms.
Dennett argued that deferring parts of the explanation of the mind to
subsequent levels of little men is a progressive research methodology if
the subsequent men are ever less intelligent. By breaking down the vari5. See Skinner 1964.
A Homunculus Fallacy in Economic Theory 195
ous complex tasks of the mind into ever more simple subtasks that eventually boil down to decisions of a zero/one type that can be handled by
nonintelligent binary decision units, cognition is founded in underlying
principles: “Homunculi are bogeymen only if they duplicate entire the
talents they are rung in to explain. . . . If one can get a team or committee
of relatively ignorant, narrow-minded, blind homunculi to produce the
intelligent behavior of the whole, this is progress. . . . One discharges
homunculi from one’s scheme by organizing armies of such idiots to do
the work” (Dennett 1997, 123–24; emphasis in original). Hence homunculi that perform complex unexplained partial functions are seen as both
inescapable and illuminating in the development of scientific understanding. However, any appeal to them must be logged for later correction. Den­
nett uses a banking analogy to convey this idea that the little men can
only be intermediaries in developing full theory, which should appeal to
economists:
Any time a theory builder proposes to call any event, state, structure,
etc., in any system (say the brain of an organism) a signal or message
or command or otherwise endows it with content, he takes out a loan
of intelligence. He implicitly posits along with his signals, messages, or
commands, something that can serve as a signal-reader, messageunderstander, or commander, else his “signals” will be for naught, will
decay unreceived, uncomprehended. This loan must be repaid eventually by finding and analyzing away these readers or comprehenders; for,
failing this, the theory will have among its elements unanalyzed mananalogues endowed with enough intelligence to read the signals, etc.,
and thus the theory will postpone answering the major question: what
makes for intelligence? (12; emphasis in original)
Working cognitive scientists have embraced these ideas. Allen Newell
(1980, 715), for example, contributed to the 1978 Attention and Performance symposium that “a major item on the agenda of cognitive psychology is to banish the homunculus (i.e., the assumption of an intelligent
agent (little man) residing elsewhere in the system, usually off stage, who
does all the marvelous things that need to be done actually to generate the
total behavior of the subject).”
Twenty years later, the editors of the proceedings of the 1998 meeting, Stephen Monsell and Jon Driver, made it the theme of that year’s
meeting to take stock of progress on this agenda item. In their introduction to the proceedings, titled “Banishing the Homunculus,” they write:
196 Maarten Pieter Schinkel
On the one hand, it is our impression that, far from leading the furtive
life of a fugitive, the homunculus has continued to parade about in
broad daylight, its powers largely intact . . . and flagrantly laying claim
to prime real estate in the frontal lobes. On the other hand, there has
been a substantial increase in research by neuroscientists, neuropsychologists, and experimental psychologists on “executive” functions,
and on interaction between endogenous (voluntary) and exogenous
(stimulus-driven) control of cognitive processes. We may now have a
sufficient database for a serious attack on the problem to which the
control homunculus has been the default solution. (Monsell and Driver
2000, 3–4)
After a further discussion of “homunculitis,” and a favorable reference
to Dennett’s ideas about productive homunculi, their subsequent survey
of the contributions to the bundle concludes: “We hope readers of this
volume will agree that the control homunculus is now an endangered spe­
cies, and that a variegated genus of control ‘idiots’ is beginning to colonize the vacated niches” (29).
2. The Auctioneer as a Loan of Coordination
In economics, the Walrasian auctioneer, the off-stage executive, the deus
ex machina, who hovers over the market, collecting disaggregate information on individual intentions to supply and demand, aggregating it and
attempting to make plans match by adjusting prices in the direction of
aggregate excess demand, is a homunculus explanation of the working of
markets. He is a loan of coordination. That neoclassical economics ran up
this debt undoubtedly had its benefits. By postponing answering the question of what makes up for coordination, general equilibrium theory could
develop as the foundation of microeconomics and the basis of an ongoing
process of extension and generalization that ties in many economic subdisciplines. Yet it also needs a theory of disequilibrium to complement it.
However, there seems to be little awareness that the auctioneer is a deferred
debt that at some point should be repaid if our understanding of economic
coordination is to be advanced and general equilibrium analysis closed.
Over the history of neoclassical economics the loan was extended, with
only a few isolated attempts to pay some of it back.
In line with his acknowledged proper method for the pure science of
political economy, the original auctioneer loan was taken out for the fifth
and eventually translated edition of Elements by Walras, to settle his
A Homunculus Fallacy in Economic Theory 197
struggle with the theory of tâtonnement over the book’s consecutive editions.6 The first part of Walras 1954 develops a multiproduct exchange
model in which existence of equilibrium is determined as a “theoretical
and mathematical solution.” The market process is then rather lightly perceived as a system that “finds” that exact same equilibrium price vector—
which, moreover, Walras (1954, 200) presumed to be unique:
What must we do in order to prove that the theoretical solution is identically the solution worked out by the market? Our task is simple: we
need only show that the upward and downward movements of prices
solve the system of equations of offer and demand by a process of groping [“par tâtonnement”]. (170; emphasis added)
In the exchange model subsequently developed, each market is sequentially equilibrated, under the assumption that disturbing “indirect influences” cancel each other out, so that the process “naturally” converges to
an equilibrium (172).7 The theory of tâtonnement with production, introduced in lessons 20 and 21, is more involved. Walras here realizes that the
transformation of commodities on the basis of disequilibrium prices would
change the composition of available commodities, in an essential and irreversible way, so that the process would not converge on the fixed equilibrium. Furthermore, he observes that production takes time, contrary to
exchange. Whereas in earlier editions of the book, Walras had presented a
rich theory of disequilibrium that allowed for production and trade at disequilibrium prices, in the fifth he ignores the time issue and solves the
irreversibility of disequilibrium production by introducing “tickets.”8 The
latter are notional production plans at disequilibrium prices that are communicated but not actually carried out. Accordingly, prices are adjusted
sequentially in the direction of aggregate excess demand, again assuming
that indirect price effects cancel each other out, so that the system moves
asymptotically “closer to equilibrium” (Walras 1954, 246).
The fact that Walras only recognized the need to assume away the
complications of disequilibrium production as late as the final edition,
and not already in the context of disequilibrium exchange, may explain
6. In part 1 of Elements, Walras (1954, 71) stated: “[Pure] sciences abstract ideal-type
concepts which they define, and on the basis of these definitions they construct a priori the
whole framework of their theorems and proofs. . . . The return to reality should not take place
until the science is completed and only then with a view to practical applications.”
7. This implicit assumption is now known as diagonal dominance—and not necessarily
sufficient for global stability; see Hahn 1982b.
8. See Patinkin 1956 and Walker 1996.
198 Maarten Pieter Schinkel
why there is no mention in Elements of what nevertheless later became
known as the “Walrasian auctioneer.”9 Although it may have escaped
Walras that his series of simplifying and neutralizing assumptions on the
market process implied an external person or institution responsible for
establishing equilibrium prior to the execution of plans, he did personify
the market, using the term “crying,” for instance, when he starts the iteration process described above: “Let p′b, p′c, p′d, . . . , of (B), (C), (D) . . . in
terms of (A) be the m − 1 prices cried in this way [i.e., in relative terms], at
random” (Walras 1954, 169; emphasis added). From this, the auctioneer
readily presented himself to complement the theory, most likely as an
invention by Joseph Schumpeter that, through his teachings at Harvard in
the late 1930s, got introduced into the literature by Paul Samuelson.
The debt was further incurred by twentieth-century interpretations of
Walras’s work. The influence of Elements was not immediate and indirect, however. To the extent that it was read in French, it was generally
considered overly formal and was not appreciated for the abstract framework of general equilibrium it offered. Instrumental in raising an interest
in general equilibrium theory among Anglo-American theorists was John
Hicks’s Value and Capital, which first appeared in 1939. Hicks (1946, 66)
did not develop an explicit theory of disequilibrium, however—which he
considered “an awkward business.” Rather, he assumed that markets
cleared instantaneously once a week on the “Monday” on which they
opened. Yet Hicks did discuss the local movement of prices that, on a
“slight movement away from the equilibrium position . . . sets up forces
tending to restore equilibrium” (62). For his generalization of Walras’s
local stability analysis of equilibrium to a multimarket setting, Hicks
introduced the concept of “perfect stability,” which meant that if “a rise in
the price of X will make supply greater than demand, (a) all other prices
given, (b) allowing for the price of Y being adjusted to maintain equilibrium in the Y-market, (c) allowing for the prices of Y and Z being adjusted,
and so on, until all prices have been adjusted” (66n).
In reaction to Hicks’s analysis, Samuelson subsequently formalized
over a number of papers that later were incorporated in Foundations,
published in 1947, how prices respond locally to small perturbations of
9. In fact, the only discussion that involves the term auctioneer explains how none is necessary for markets to work well: “It is a matter of daily experience that even in big markets
where there are neither brokers nor auctioneers, the current equilibrium price is determined
within a few minutes, and considerable quantities of merchandise are exchanged at that price
within half or three quarters of an hour” (Walras 1954, 106).
A Homunculus Fallacy in Economic Theory 199
equilibrium. It was to substantiate comparative statics analysis by the
“correspondence principle,” surely not to be a theory of market dynamics far removed from equilibrium.10 For this, he formulated the following
disequilibrium dynamics:
To test the necessity or sufficiency of these criteria [of Hicks’s perfect
stability] in terms of a more fundamental definition of stability of equilibrium let us make a natural generalization of the Walrasian conditions
of the following form: the price of any good will fall if its supply exceeds
its demand, these each being regarded as functions of all prices.
Mathematically,
i
i
pi = – H i qS – q D
i
i
= – H i q S p1, . . . , pn – qD p1, . . . , pn . Samuelson 1963, 270
Using linear approximations of these dynamic equations at equilibrium
prices, Samuelson showed that Hicks’s perfect stability was neither necessary nor sufficient for what Samuelson called “truly dynamic stability” of equilibrium (273). Hicks’s reaction to this came in an additional
note to the second edition of Value and Capital, in which Hicks claimed
that his sequential partial process had more economic content than Samuel­
son’s mechanics. In response, a literature developed that detailed the relationship between the Hicksian and the Samuelsonian conditions for local
stability, the latter taken to be formally sound, the former as having intuitive economic meaning.11
In a pair of papers in Econometrica, Arrow, Henry Block, and Leonid
Hurwicz would subsequently interpret Samuelson’s formalization of local
out-of-equilibrium price adjustment as “a formal dynamic model whose
characteristics reflect the nature of the competitive process” (Arrow and
Hurwicz 1958, 523). Intending to derive general conditions for global stability of the competitive general equilibrium model, and applying the
newly rediscovered second method of Lyapounov that allowed for bypassing an explicit analysis of the actual dynamic system by constructing a
summarizing function of the state variables of a system of (nonlinear)
10. See Samuelson 1963, 5.
11. Akira Takayama (1973, 315; 1985, 315) clearly takes this view and provides an extensive survey of this literature. Incidentally, Daniel McFadden (1968) shows that for a class of
dynamic processes Hicks may have envisioned when he wrote Value and Capital, the Hicksian local stability conditions are sufficient for dynamic stability, the practice of studying
Hicksian matrices is justified, and Samuelson’s conclusion on the meaning of Hicks’s analysis
is overly harsh.
200 Maarten Pieter Schinkel
equations, they state that “from among the many possible versions of the
market process we have chosen . . . the instantaneous adjustment process,
[since it] is well-known and is of particular interest because it is close to
the formulations of Walras, Hicks, and many other writers, and because
(comparatively) a great deal is known about it” (524).12
The market process thus becomes an autonomous system of simultaneous ordinary differential equations. For each commodity j its price pj
changes over time by a function given as
dpj
= k j fj p1, . . . , pm , k j > 0,
dt
j = 1, . . . , m ,
in which fj is the aggregate excess (net) demand function for the jth commodity, and kj the speed of adjustment (525).13
In this system, an equilibrium is a rest-point in which (dpj )/(dt) = 0 for
all j. Arrow and Hurwicz 1958 reports on a number of stability results for
equilibria. In Arrow, Block, and Hurwicz 1959, global asymptotic stability of the system as such is then considered under conditions imposed on
the system of aggregate excess demand functions that were also looked
at in demand theory to provide uniqueness of equilibrium, in particular
gross substitutability.14 This reintroduced the high ambitions Walras had
for the theory of tâtonnement as a theory of the market process—which
both Hicks and Samuelson had stayed away from. Yet it also reiterated
the (implicit) assumptions that Walras had needed to make the tâtonne­
ment process find the static equilibria of the model. Arrow, Block, and
Hurwicz offered little or no discussion of these crucial issues associated
with this choice of model. Instead, they were confident it represented competition as a process quite well:
None of the results so far obtained contradicts the proposition that under
perfect competition, with the customary assumptions as to convexity,
etc., the system specified is always stable. If the latter proposition turns
out to be true, Samuelson’s “correspondence principle” would then provide no information that could not be deduced from micro-economic
12. Roy Weintraub (1991) documents the rediscovery of the second method of Lyapounov
and its influence on global stability theory in detail.
13. This process, as well as those to follow, are presented in the original notation.
14. The results obtained on tâtonnement stability, which place sufficient conditions on the
system of aggregate excess demand functions, have since hardly been advanced. See chapter 9
of Arrow and Hahn 1971 on these conditions in demand theory and Fisher 1983 or Schinkel
2001 on their role in stability theory.
A Homunculus Fallacy in Economic Theory 201
considerations under competition, at least for the particular class of
adjustment processes considered. At the moment, however, the question
remains open. (Arrow and Hurwicz 1958, 530)
Their global stability results would not generalize, however, and the optimistic conjecture was soon proven false by Scarf’s counterexamples. When
the SMD result subsequently failed demand theory in the early 1970s, it
brought down with it global tâtonnement stability theory. Stability theories based on conditions of aggregate excess demand other than Walras’s
law, homogeneity of degree zero in prices, and continuity are special theories with no hope for generalization.
Further development of the theory of tâtonnement set out to specify the
auctioneer’s program into an explicit equilibrium search algorithm. In
Uzawa 1959, 184, the auctioneer becomes a secretary—surely not a conceivable description of the market process:
Let us interpret the competitive exchange economy as a game [in] which
R individuals and a fictitious player, say a Secretary of Market, play
according to the following rules:
(i) Secretary of Market announces a price vector.
(ii) Each individual submits to Secretary of Market a “ticket” on
which the quantity of demand and supply by the individual according
to the announced price vector is described.
(iii) Secretary of Market calculates the quantity of aggregate excess
demands from the tickets submitted to him by the individuals.
(iv) Secretary of Market announces a new price vector such that prices
of commodities which have positive excess demand will rise, and prices
of commodities which have a negative excess demand . . . will fall.
Moves (ii) and (iii) are repeated at the new equilibrium price vector.
Simultaneous and sequential price adjustment processes that formalize
this program are subsequently shown with a proper Lyapounov function to
be stable under the assumption that aggregate excess demand satisfies the
weak axiom of revealed preferences.15
With his counterexamples, Scarf (1960, 160) had suggested that perhaps “the price adjustment mechanism . . . is not correct.” He himself set
out to develop computational algorithms with which to find quickly and
15. Uzawa 1959, 184, 186, respectively. Michio Morishima (1960) derives similar results
for a (linear) production model of tâtonnement. See also Uzawa 1961.
202 Maarten Pieter Schinkel
efficiently equilibrium prices for arbitrary initial conditions in ever larger
models.16 These algorithms divide the price-simplex into subsimplices,
which are sequentially visited, following a rule that dictates direction,
until equilibrium is approximated. The approach has roots in a socialist
planning perspective on general equilibrium theory forwarded by Oskar
Lange (1936). It placed high hopes on the future development of computers to perform the necessary calculations.17 In their account of general
equilibrium theory, Arrow and Hahn (1971, 302–3) suggest a similar direction in a section titled “Some Other Auctioneer’s Rules,” which opens with
the following quote:
We have seen that it is by no means true that, in all situations, the two
[tâtonnement] rules we have examined will be successful in seeking
an equilibrium for the economy. If, for the moment, we think of the
auctioneer as a planner who is seeking the equilibrium by trial and
error and forget all about simulating market procedures, it is reasonable to enquire whether there is some other rule that would lead to an
equilibrium whatever the fine properties of the excess-demand functions might be.
One such rule uses local knowledge of the direction in which aggregate demand changes upon price changes to show that such a process
can be globally successful in finding an equilibrium (303–6). Along
these lines, Stephen Smale (1976a) established slightly relaxed stability
conditions with the global Newton method. To assume the auctioneer has
insight into the Jacobian of the aggregate excess demand system at
all prices adds substantially to his assumed local knowledge, however.
Yet this was subsequently established in Saari and Simon 1978 to be
required. Progressive models use less local information but need, for
example, a memory of past prices on the basis of which the auctioneer
makes larger and smaller relative price adjustments toward aggregate
excess demand.18 If anything, these findings emphasize how ill suited
the auctioneer model is for understanding economic phenomena outside
equilibrium. The understanding that the model once was so intended also
got lost along the way. To Gerard van der Laan and Dolf Talman (1987,
85), Walras’s theory of tâtonnement is a “little advanced” algorithm. And
Kehoe’s (1991, 2068) survey on computing equilibria presents tâtonne­
16. See Scarf 1973.
17. See Goodwin 1951, Lange 1967, and Scarf 1989.
18. See Laan and Talman 1987 and Herings 1997.
A Homunculus Fallacy in Economic Theory 203
ment processes as rather clumsy methods to do so, which, however, are
“popular in practice.”19
3. Elements for an Installment Plan
The auctioneer model clearly is a run-up debt to coordination. Moreover,
the model is a homunculus fallacy, because it is assumed to encompass
all there is to the coordination process. On his own, the little man was to
perform Walras’s “simple task” that puzzles mainstream disequilibrium
theory still today. Banishing the homunculus, therefore, seems a constructive step forward, indeed. It is only because of the persistent reliance on
aggregate excess demand as a basis for price adjustment that both the Sonnenschein-Mantel-Debreu result and the Saari-Simon result are the blow
to global stability analysis that they are. A more careful look at the microfoundations of auctioneer behavior would, furthermore, allow for lifting
the methodological dichotomy between equilibrium and disequilibrium
theory, the first being based on methodological individualism, the second
not. This, in turn, is essential for a proper qualification of equilibrium.
How could economics repay its loan on coordination? As explained
above, in the cognitive sciences, the research agenda is to take away elements of cognition from the homunculus and replace him by a number
of little homunculi that are each less than a full model of intelligence.
Economics’ homunculus embodies coordination. Hence a progressive
agenda for economics would be to take elements of coordination away
and replace the single auctioneer by several little auctioneers who are
each less organized. Some contributors to the discipline did indeed proceed in this way. They developed elements for an installment plan that is
yet to be executed by neoclassical economics.
An early literature on so-called non-tâtonnement or trading processes
did away with Walras’s “tickets” by allowing trade at disequilibrium prices.
It developed the Edgeworth process and the Hahn process. Reviewing
Walras’s Elements, Francis Ysidro Edgeworth had considered the theory
of tâtonnement cumbersome.20 In Mathematical Psychics, originally
19. See also Smale 1976b. An altogether different approach to get around the SMD result is
to establish distributions over individual characteristics that assure aggregate excess demand is
well behaved. In Hildenbrand 1983 and 1994 the shape of the conditional distribution of individual income and expenditures is qualified to that end. In Grandmont 1987 and 1992 similar
results are obtained by placing conditions on the distribution of preferences and choices.
20. For a discussion of Edgeworth’s critique of Walras’s theory of tâtonnement, see Walker
1996.
204 Maarten Pieter Schinkel
published in 1881, he offered an alternative theory, in which the market
process rests on a sequence of disequilibrium transactions of individual
traders who seek to better themselves in the process. Parties recontract
until a “final settlement” is reached (Edgeworth 1967, 313–14).21 In Uzawa
1962, this process takes the following form. Prices are adjusted in the
direction of aggregate demand. Simultaneously, at each price level, binding trades are made that redistribute commodities such that new bundles
weakly increase the utility of all consumers. Outside equilibrium, a rationing rule assures that all commodities are fully distributed. Using the negative of the sum of individual utilities as a Lyapounov function, global
asymptotic stability of the process on a Pareto efficient allocation is shown.
The equilibrium distribution of commodities depends on the “path of bartering” (Uzawa 1962, 226–27).
The payoff from moving away from tâtonnement is immediate: global
stability of the Edgeworth process does not need any special conditions
on aggregate excess demand. In fact, given time, the process will almost
always converge, irrespective of the behavior of prices. Whenever new
prices happen to be such that some advantageous trade can materialize, the Lyapounov function falls, and otherwise it remains stationary—
provided there is no consumption or production outside equilibrium.
Instead, it raises questions about how mutually beneficial trade agreements are formed. Some further work on coalition formation has extended
on this. In Green 1974, a sequence of nonbinding coalition proposals
and blocking proposals is shown to converge “almost surely”—that is,
for all possible solution paths of the disequilibrium process, but a subset
of measure zero—to a Walrasian equilibrium proposal that is then executed. Hurwicz, Roy Radner, and Stanley Reiter (1975a, 1975b) show that
if intermittent trades are actually carried out and irreversible, a random
process of coalition formation is globally asymptotically stable on a pathdependent core allocation. Yet the information requirements to form the
coalitions and match the individual bids within each one are large. Franklin Fisher (1989) generalizes earlier results by Paul Madden (1975, 1976)
to argue they are restrictively severe, especially when compounded trades
are required in the process.22
21. There is some dispute in the literature on whether Edgeworth thought of recontracting
as a sequence of binding agreements, or rather as nonbinding trade proposals. In the former
interpretation, equilibrium is path-dependent. In the latter, it is not. See Walker 1996.
22. On the role of money in this context, see Arrow and Hahn 1971 or Ostroy and Starr
1974.
A Homunculus Fallacy in Economic Theory 205
In the Hahn process, the order of markets is more explicit (Negishi
1961a; Hahn 1962; Hahn and Negishi 1962). The auctioneer adjusts
prices in the direction of aggregate demand. As long as individuals can
gain from doing so, they engage in disequilibrium trades at these prices
on a “first come first served” and “quid pro quo” basis—the latter assures
that trade does not change individual wealth. Once all trading opportunities are exhausted, prices are adjusted, so that new trading opportunities arise. Markets are assumed to be sufficiently “orderly” for all partners
with potential trades between them to find each other. As a result, every
individual excess demand for each commodity is, after all trade has settled, of the same sign as the aggregate excess demand for that commodity. Under these assumptions, the sum of the (indirect) utilities that individuals aspire to realize at disequilibrium prices—referred to as “target
utility”—as the process unfolds. It serves as a Lyapounov function to
show global stability of the process. That is, people are constantly (weakly)
disappointed over time, when they see the prices of the commodities
they planned on buying but were rationed to, going up, and the prices
of the commodities they in vain planned to sell going down. Although
orderly markets presuppose a considerable amount of coordination
again, the concept of falling target utility leaves room for various typical
disequilibrium phenomena, such as mismatches, irreversible actions like
consumption and production that are in hindsight suboptimal, and speculation with disappointing outcomes. In a series of extensions on the
Hahn adjustment process in the 1970s, Fisher explored these degrees of
freedom.23
Although these developments reveal that disequilibrium convergence
and stability can be had in models with considerable amounts of fleshedout disaggregated disequilibrium behavior, both trading processes still
rely on the auctioneer for adjusting prices and allowing supply and demand
to meet. As a result, although not necessarily to a Walrasian equilibrium,
both processes do converge to a core allocation. The reason for this is that
the advances were still made within the context of the model of perfect
competition. Robert Clower and Arrow in the 1950s made some early
suggestions instead to use elements of monopolistic competition to substantiate the auctioneer’s behavior. Clower (1955, 225) observed that “the
idea that there is something fundamentally different about a monopoly
23. This series of advances accumulated in Fisher 1983, which establishes the global stability condition of “No Favorable Surprise.” It is not a primitive assumption, but wholly independent of aggregate excess demand.
206 Maarten Pieter Schinkel
and a competitive market is . . . mistaken. It is a mere illusion which follows
from the failure to recognize that the marketee [whether ‘he’ is a person, a
committee, or a mechanical device] function must be undertaken by some
economic unit in every market.” And Arrow (1959, 43) pointed out even
more strongly that
the Law [of supply and demand] is not on the same logical level as the
hypotheses underlying [aggregate supply and demand as a function
of prices]. It is not explained whose decision it is to change prices in
accordance with [aggregate excess demand]. Each individual participant in the economy is supposed to take prices as given and determine
his choices as to purchase and sales accordingly; there is no one left
over whose job it is to make decisions on price.24
Instead, in a model of local monopolistic and monopsonistic market
power, individuals who act as “market makers” or “dealers” could organize trade, collect the supply of and demand for each commodity in
separate markets, and make it their business to bring them together.
An early attempt to model disequilibrium price dynamics in this way is
Fisher 1972, “On Price Adjustment without an Auctioneer.” Dealers are
given the responsibility for setting prices in their own designated markets. Yet, by assuming they perceive perfectly elastic demand for their
wares, they are effectively reduced to “little auctioneers,” who adjust
prices in the direction of aggregate excess demand, as they are not aware
of their special disequilibrium position.
Exploiting their “local monopoly power,” rational dealers would rather
set purchase and selling prices so as to maximize the modest profit in
the difference between them. Such a well-defined entrepreneurial profit
motive would in fact lead each of the market makers, as observed by
Lange (1944), to purchase and sell equal quantities, so as to avoid excess
demand or supply over time. After all, excess demand at the end of the
market day is a forgone profit opportunity, whereas excess supply leaves
unsold stocks. Hence each dealer clears his or her market out of selfinterest. The study of general disequilibrium thus seems well framed
in the general equilibrium theory of monopolistic competition. A number of early contributors, such as Takashi Negishi (1961b) and Jean-Pascal
Benassy (1976, 1982), indeed initially sketched the contours for such a
24. The text in brackets replaces references to equations.
A Homunculus Fallacy in Economic Theory 207
theory, yet eventually came to focus on the existence of non-Walrasian
equilibrium rather than develop a true disequilibrium theory.25
In a disequilibrium theory of market makers, a further reduction of
presupposed coordination is to allow dealers to have less than complete
and perfect information. Instead, they conjecture perceived demand and
supply curves, base subjectively rational bids and offers on those, and
subsequently update their conjectures over time, using information on
what they were able to purchase and sell at their best-guess prices. The
adjustment process then is one of learning from market experience. This
concept of entrepreneurial market makers has been part of a literary
tradition in Austrian economics.26 In the full disequilibrium model developed in Fisher 1983, price-setting dealers derive their power to adjust
prices individually from their perceptions of transactions constraints,
around which they eventually experiment toward competitive equilibrium.
In a small part of the (mainly rational) learning literature, some more specific attempts have been made to formalize local disequilibrium learning. In Kirman 1975, 1983, and 1995 and in Brousseau and Kirman 1993,
such dynamics is studied in a partial setting. Dealers have a false structural conjecture of demand and also do not know the value of the parameters. They learn using market signals at set prices to update their OLS
estimates of the latter. Simulated price dynamics is quite volatile at first,
but over time converges. Ulrich Witt (1986) and Peter Albin and Duncan
Foley (1992) offer a similar simulation approach. Giorgio Rampa (1989)
models OLS disequilibrium learning and monopolistic price adjustment
in a general equilibrium setting. Hahn (1989) advocates the use of rational Bayesian knowledge updating processes to underpin disequilibrium
theory, and in Schinkel, Tuinstra, and Vermeulen 2002, a model is developed that has these elements and converges to conjectural equilibrium
almost surely.
These developments toward a theory of individual and subjectively rational disequilibrium price dynamics still leave open the question of who
acts as brokers in what commodities. With it come issues of competition
between dealers. Perceived local monopoly power to set prices, reflected
in the structural conjecture of served supply and demand, requires some
25. This literature often uses the term disequilibrium confusingly for non-Walrasian equilibrium allocations, rather than situations outside (non-Walrasian) equilibrium and adjustment. See De Vroey 2002.
26. See, for example, Hayek 1949 and Kirzner 1973.
208 Maarten Pieter Schinkel
foundation in the objective structure of the economy. Hence it is typically assumed that each commodity has only one dealer—which can be
justified by defining commodities by their known dealer as a form of
product differentiation. This imposes a certain fixed order on markets,
neglecting disequilibrium phenomena such as bankruptcy, exit, and
entry. Moreover, it is unclear how a sequence of dispersed purchase and
selling prices, set on the basis of local powers to do so, would converge
over time to unique competitive equilibrium values. Arrow (1959, 47)
suggested that close to equilibrium, individual market power would dissipate. In Fisher 1973, 448, which is “an attempt . . . to provide a sensible
disequilibrium story with a competitive ending,” this idea is modeled by
having monopoly power erode away asymptotically at low enough prices.
Yet a decade of reflection on the topic led Fisher (1983, 50) to conjecture
that such stories are “perhaps something of a fairy tale.”
4. Conclusion
One of the prime open research questions in economics is the precise role
of the workings of markets in establishing equilibrium. The intimate relationship between disequilibrium processes and the relevance of eventual
equilibrium can be understood only from a detailed description of the
specific drivers of the adjustment process. A major obstacle to progress in
the discipline has been that neoclassical economics largely fails to see that
the study of the market process was postponed by Walras, who presupposed order in the form of what developed into the theory of tâtonnement.
Rather than seeking to identify and analyze away elements of this order,
more order was imposed when economics met with the impossibility of
the approach in the form of the SMD result. The obligation to repay this
loan of coordination was scarcely recognized. As a consequence, economic theory builds on a homunculus fallacy. Few economists recognized
the need to reduce the level or presupposed order. The ones who did found
little following in this particular field. Yet elements for constructively
doing away with the homunculus are available and have shown great
promise. Little auctioneers can act in their own private self-interest,
as they understand it from their partial and incomplete picture of the
world. It is not, therefore, that the science is unable to repay the auctioneer loan and consciously postpones the debt further into the future.
Banishing the homunculus should become a major item on the research
agenda of economics. Answers to the question of what makes for market
coordination are most likely to be in “armies of little unorganized market
A Homunculus Fallacy in Economic Theory 209
makers.” Without such a return to the study of competition as a process,
economics’ main teachings remain largely unfounded.
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