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THE FOBMATION OF ECONOMIC MAGNITUDES:
DISEQUILIBRIUM AND STABILITY
Franklin M. Fisher
/I/O,
</33
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
"THE FORMATION OF ECONOMIC MAGNITUDES:
DISEQUILIBRIUM AND STABILITY
Franklin M. Fisher
/I/O,
</33
No. 433
October 1986
M 1.7. UBRARES
APR 2 1 1987
1
DJS£QDJLIBBJUILABD_S3?ABILJTX
Franklin M. Fisher
Massachusetts Institute of Technology
&&st.rac£
The analysis of disequilibrium, and especially, stability is
essential if equilibrium economics is to be
formation
of
a
economic magnitudes understood.
useful tool and the
subject
The
is
a
competi-
tive economy is necessarily driven to equilibrium by the
actions
surveyed, with an eye to the "key question" of whether
of arbitraging agents.
librium
Too often analysis has rested with equi-
modes of thought,
being strongest when considering
the
formulation of plans by individual agents and weakest when analyzing what happens when those plans are frustrated.
sive
treatment
can be found in
iiPBS_sf_Equi.l.i^.r.ium_Espnpmj,C5
Press, 1983)
Fisher,
(Cambridge:
A more exten-
2is^qaiIib.£.i,um_E.QU.nd.a-
Cambridge
University
.
Key words: General equilibrium, disequilibrium, stability
JEL Classification: 020, 030
Franklin M. Fisher
Massachusetts Institute of Technology*
JU_jD±£Sdilc.tj,.on
title of this Conference is "The Formation of
The
Magnitudes."
course
theory
if the papers prepared for it are true to the
Yet,
of modern economic theory,
sense,
real
most of them will,
not concern that subject at all.
which
the
plans and expectations of
mutually compatible.
in a very
economic
Modern
is overwhelmingly a theory of equilibrium.
positions from which there is no incentive to
at
Economic
depart,
economic
analyzes
It
positions
agents'
are
It is almost silent on the question of how
such positions get reached, on how economic magnitudes get formed
if they do not happen already to be in equilibrium.
Equilibrium analysis is an elegant and powerful
viding
mies
pro-
tool,
considerable illumination of the way in which real econooperate.
But the total concentration on
now
equilibrium
characteristic of formal economic models runs the serious risk of
misunderstanding
the basic insights of economics itself.
proposition that competitive industries earn no
Thus,
profits
in
long-run equilibrium is an important (if elementary) theorem.
To
the
take
this to mean that competitive industries
J3.ev.ex
earn profits
it is to lose sight of the fundamental
role
that profits and losses play in the allocation of resources
when
is
not only wrong,
Paper prepared for conference on "The Formation of Economic Magnitudes," Paris, 1987.
*
or technology changes.
demand
equilibria
Pareto-optima
are closely related
competitive
is
basic
a
The policy presecription that (under the conditions of
insight.
the
and
The proposition that
two Welfare Theorems
)
government interference with
a
compe-
titive system is bound to be inefficient requires more than this,
however; it requires the assurance that competitive economies are
close to equilibrium most of the time.
That assurance cannot be
provided by only examining the properties of equilibria.
Nor are such issues restricted to microeconomics.
To take a
leading modern example, the statement that agents will eventually
about
learn
appealing
tions
the
opportunities
and act on systematic profit
assumption.
is
an
The proposition of the rational expecta-
literature that agents always
instantaneously
understand
opportunities thrown up by an immensely complex and changing
economy
is breathtakingly stronger.
That proposition begs
the
question of how agents learn and of the role that arbitrage plays
in the formation of economic magnitudes.
the proposition that,
ple,
under some circumstances,
underemployment equilibria was the major
exist
the
To take an older exam-
Keynesian
toward
literature.
contribution
To show that the economy
such equilibria is a much harder
there can
proposition,
can
of
tend
requiring
analysis of dynamic, disequilibrium behavior.
Indeed,
such
dynamic,
disequilibrium
analysis is
always
required if we are to understand the formation of economic magnitudes.
Certainly, if the economy does not spend most of its time
near equlibrium, disequilibrium analysis is the only useful kind.
Even if equilibrium is the usual
case,
however,
disequilibrium
analysis is indispensable.
provide
tent;
assurance that our equlibrium theories are
the
equilibrium is the usual case,
if
Further,
For one thing, only such analysis can
know
we need to
analysis of the dynamic path that
only
a
consis-
stable system
follows in disequilibrium can tell us to which of several
ble equilibria that system will go.
importance,
derable
This is
analysis
see,
possi-
matter of consi-
not only because multiplicity of equilibria
is the rule rather than the exception,
shall
a
why.
but also because,
of disequilibrium shows that
as
we
dynamic
the
behavior involved often changes the equilibrium that is eventually reached.
There are two fairly common mistakes that must be avoided in
considering such matters.
First, one must not confuse the tauto-
that the economy will move away from positions that are not
logy
equilibria with the much deeper and unproven proposition that the
economy
tion that it spends most of its time near equilibrium)
specific
terms,
arbitrage
the fact that agents will seize
opportunities
opportunities
opportunities
do
on
In more
.
profitable
means that any situation in which
appear is subject to change.
profitable
that
proposi-
always converges to equilibrium (let alone the
It does not
arbitrage opportunities disappear or
not continually arise in the
such
follow
that
new
of
ab-
process
sorbing old ones.
The
avoided
second mistake is the belief that such problems can
by redefinition of terms so that there is no such
as disequilibrium.
prices
because
For example,
be
thing
the non-clearing of markets by
is sometimes said not to be an example of
agents form queues with the length of the
disequilibrium
queue
deter-
mined
the shadow price of time as well as by
by
may
This
markets
be
a
valuable way to think about
to clear,
fail
represented
as
Certainly,
system
To say this,
to say that there is some definite outcome out
only
brium
when
solves
there is a sense in
the equilibrium behavior of a larger
the original one is embedded.
which
happens
How do the queues
disequilibrium behavior of any given
the
prices.
but it reformulates rather than
themselves disappear over time?)
which
what
(What happens to money prices?
that question.
money
can
be
system
in
however,
is
of
equili-
To insist that therefore there is
in the smaller system.
no such thing as disequilibrium is to rob the term
and all equilibrium analysis of meaning.
"equilibrium"
For if "equilibrium" is
to be a useful concept in analyzing a particular system, then one
must
contemplate the possibility of points that are not
bria of that system.
equili-
The fact that such points can be represent-
ed as equilibria in some larger system does not change this.
equilibrium
If
analysis is to be
justified,
question that must first be answered is one of
question
the
crucial
That
stability.
in its most interesting and general form is as follows.
Suppose an economy made up of agents who understand that they are
in
disequilibrium and perceive and act on profit
Does
opportunities.
the action of those agents lead the economy to converge
equilibrium,
and,
if so,
to what sort of equilibrium?
I
to
shall
refer to this as the "key question" of stability analysis.
It is important to note,
competitive
brium
however,
that, while stability of
general equilibrium is perhaps the
question addressed in
a
long literature,
only
disequili-
that
literature
has seldom addressed the key question directly.
recently
agents
as
we
writings on the stability of general equilibrium have
shall see,
only
Rather,
much
endowed agents with
perception.
Instead,
have been supposed to make their plans as though disequi-
librium
and the interaction of those
did not exist,
plans
has
been modeled only as an afterthought at best.
Why should this be?
The answer may be related to the pheno-
of concentration on equilibrium and to the distaste or
menon
least disinterest with which many theorists regard the
stability
Economic analysis is extremely powerful when consi-
literature.
the optimizing behavior of the individual agent.
dering
at
It
is
comfortable with positions in which the plans of those agents are
It must break untrodden ground to describe
mutually compatible.
what happens when this is not so.
This means modelling both the
in which trade takes place when agents plans cannot be
way
pletely
fulfilled and how agents react to frustration.
com-
Neither
aspect can be properly done by considering equilibrium behavior.
2^_2'J±2imment_a^d_J±,s_f:ailu£.e
already indicated,
As
historically
behavior
however,
the study of stability has
been marked by failure to model
as more than an afterthought.
out-of-equilibrium
That
was
particularly
true of the development that characterized the first twenty years
or so of the subject
was P.
It
step
R.
A.
—
the study of tatonnement.
Samuelson (1941) who took the first
in the study of stability.
Hicks
terms
(1939)
Reacting to
a
crucial
suggestion of J.
that "perfect stability" might be
defined
of demand curves that slope down after various prices
in
are
Samuelson pointed out that there could be
allowed to adjust,
study of stability without an explicit dynamic model.
price-adjustment
that
moving
in
demands
,
He assumed
takes place out of equilbrium
the direction indicated by the
no
by
prices
corresponding
excess
assumption that can be written in its general form
an
as:
E^ =
(1)
H
1
where there are
c
prices,
(p)
of
are
Z
i
(p))
commodities,
tions.
(i = 1,
.
.
.
,
subscripted by
c)
p is the vector
i,
the excess demand for commodity
and the H.(.)
p,
are continuous and
i
when
prices
sign-preserving
func-
dot over a variable denotes differentiation with
(A
spect
.
(Z
to time.)
Samuelson proposed the study of
re-
as the only
(1)
out-of-equilibrium adjustment mechanism.
Models of this type are known as "tatonnement" models.
They
assumption
that
suffer
only
from the obvious lack of reality of the
prices
adjust out of equilibrium,
recontracting
ducing)
pro-
(let alone consuming and
Yet that assumption (which goes nicely with the ficti-
Arrow-Debreu world in which all markets open and close
tious
the
.
rather than trading
constantly
with agents
dawn of time) may not be the most troublesome one
poses
of
adjustment
understanding disequilibrium
equations such as
(1)
behavior.
for
Since
are also characteristic of
at
pur-
price
the
later, non-tatonnement literature, it is worth discussing this in
detail.
1.
If
price is zero and excess demand negative, price is
assumed to remain zero.
I generally ignore this complication in
what follows.
.
Whose behavior does equation
re-
the behavior of the individual agents whose
de-
flect
directly
mands
are to be equilibrated.
Indeed,
we now see
In a perfectly competitive economy,
conundrum:
prices
represent?
It cannot
(1)
as given and outside of their control.
prices?
a
central
all agents take
Then who changes
How do sellers know when demand or costs rise that they
can safely raise prices without losing all their customers?
At a
formal level such questions are deep ones.
begs the price-adjustment question to say
only
It
often
done)
whose
job
that
it
(1)
reflects the behavior of
is to adjust prices in such a
markets do not have such specialists.
them
are
endeavors.
such
2
real
that the specialist is rewarded for his
or
her
To understand where and how such price-setting takes
be done by adding
adjust
Most
Those markets that do have
place requires analysis of how markets equilibrate.
done
is
"auctioneer"
an
way.
(as
(1)
as an afterthought,
That cannot
nor is it likely to be
satisfactorily in the tatonnement world where
and there are no consequences to remaining in
only
prices
disequili-
brium.
2.
The auctioneer may have been invented by J.
Schumpeter
lectures at Harvard and was probably introduced into the
literature by Samuelson.
Despite the fact that the construct is
often referred to as the "Walrasian auctioneer," it does not
appear in the work of L. Walras (who did, however, suppose that
prices adjust in the direction indicated by excess demands)
Interestingly, F. Y. Edgeworth wrote (1881, p. 30):
"You might
suppose each dealer to write down his d.§m.§nd
how much of an
article he would take at each price, without attempting to conceal his requirements;
and these data having been furnished to a
sort of market-machine, the pxi.c.£ to be passionlessly evaluated."
I am indebted to P. Newman for this reference.
in
,
that there are no such conseqences provides
fact
The
justification
themselves
for
is
the way in which the behavior of
treated in
tatonnement
enters the dreams of those agents;
never
some
agents
the
Disequilibrium
models.
construct
they
their
demands as though prices are fixed and unchanging and
excess
though their desired transactions will in fact take place.
nothing
as
Since
happens until prices have adjusted to equilibrium (assu-
ming that ever occurs)
,
agents have nothing to gain by being more
sophisticated about what is really happening.
Tatonnement
models,
facets of disequilibrium behavior.
brium
They model the out-of -equili-
interaction of agents in terms of price
adjustment
without any basis for such adjustment mechanism.
such
unsatisfactory
an
agents
to
there
is
basic
little about the two
do
then,
only,
Further, since
not
permit
find their plans frustrated in any meaningful
sense,
adjustment mechanism
does
no analysis of the way in which agents react
to
such
frustration.
Despite these defects,
the analysis of tatonnement was
the
exclusive subject of the first twenty years or so of the stability
one
literature
(roughly 1940-60)
This is understandable
.
recalls that the subject was then in its
because the adjustment process in
perhaps
because,
even
so,
seemed very hard to come by,
(1)
infancy.
when
Perhaps
seems the simplest case and
until the late 1950s major
results
no serious attention seems to
have
been
paid in this period to the underlying defects of the model.
What
is more surprising is the casual view still
countered
sometimes
en-
that stability analysis necessarily means the study of
tatonnement.
Perhaps
partly because of the obvious defects
tatonnement model and partly
the
of the tatonnement effort in I960,
accompanied by
a
collapse
that casual view tends to
be
disdain for the entire subject of stability.
As just indicated,
considerable
because of the total
of
however, the late 1950s seemed
promise for tatonnement results.
time of
a
This was
largely
because of the introduction of Lyapounov's Second Method into the
economics
literature,
rather than because of the attractive na-
ture of the tatonnement model itself.
Samuelson's
Following
tion of whether
of
(1)
was locally stable.
whether
(1)
at which p = 0,
point
brium)
point
tends to converge to a rest
here identical with
and
ques-
Essentially, this is the
the properties of
for
(a
equili-
Walrasian
a
on local properties seemed natural,
approximation
the
(1),
Such con-
if it begins close enough to that rest point.
centration
linear
equation
(which was not voluminous) concentrated on the
literature
question
introduction of
allowed
it
linear
autonomous
differential equations are completely known.
understandable save in historical terms was the
Less
concentration on the relations between local stability of
conditions for Hicksian "perfect stability"
the
as
already
stability
at all.
that,
of
Those conditions
—
functions
—
demand
for
do
with
1947)
and L. Metzler
(1)
on the very
that all goods are gross substitutes
any good goes up when the price of
demand
excess
the
to be equivalent to the local stability of
assumption
and
the alternation in sign
were shown by Samuelson (1941,
strong
(1)
attribute
an
has nothing directly to
principal minors of the Jacobian of
the
(1945)
mentioned,
—
early
any
(excess
other
good
.
increases)
.
.
3
Since
the
particularly
alternation
of the principal minors
interpretable property,
the Samuelson-Metzler
sults are properly be regarded as a lemma rather than a
but
was a long while before any further progress
it
That was done independently by F.
(1958)
not
is
a
re-
theorem,
was
made.
Hahn (1958) and T. Negishi
H.
Each of these authors realized that the economic struc-
.
ture of the problem could be further exploited and each showed
—
Hahn using Walras' Law and Negishi the homogeneity of degree zero
of
excess demand functions
the
assumption
—
itself implied the Hicks conditions on the
minors and hence the local stability of
big development of the late 1950s,
Lyapounov's Second Method.
K.
J.
Arrow and L.
4
principal
(1)
This quite neat contribution was eclipsed,
really
substitutes
gross
that the
the
This was done in
a
Hurwicz (1958) and Arrow,
however,
by the
introduction
of
pair of papers by
H. D. Block,
and
Hurwicz (1959)
Lyapounov's
with
(1)
Second
Method works as
follows.
as an example of a differential equation,
Continuing
suppose that
there exists a function, V(p), which is continuous, bounded
Years later, D. McFadden (1968), writing in the Hicks
3.
Festschrift,
showed that the Hicks conditions imply global stability of (1) on very strong assumptions about relative speeds of
adjustment in different markets.
A.
4.
Lyapounov
Lyapounov's "First Method" for
(1907).
proving stability is the explicit solution of the differential
equations involved,
an alternative never available at the level
of generality of the stability literature.
10
)
.
below, and decreasing through time except at a rest point of
The existence of such a function,
implies that
is Qua§i-s£&bl3
(1)
,
called a "Lyapounov function",
that is, that every limit point
of the time-path of p is a rest point.
in a compact set,
remain
to
points.
unique
in addition,
If,
given
starts.
equilibria.
(Recall
rest
rest points are locally isolated
then
(1)
is
a
that the rest points of
(1)
are
or
glfibjlly
it converges to some rest point no matter
.sickle process;
it
If that path can be shown
then p approaches the set of
initial conditions,
the
(1)
where
Walrasian
5
This powerful tool was used by Arrow,
Hurwicz, and Block to
demonstrate the global stability of tatonnement under
apparently
different
functions.
strong
restrictions on the excess
first such restriction was that of gross
The
completing the early literature.
ize,
a
demand
substitutes,
thus
Unfortunately, as we now real-
both this and nearly every other restriction considered was
special case of the assumption that the Weak Axiom of Revealed
Preference
applies
restriction indeed.
to maxkei demand functions
—
a
very
As a result, Arrow e.t_al.'s conjecture that
tatonnement is .always stable given only those restrictions
as Walras' Law)
strong
(such
that stem from the basic assumptions of microeco-
nomic theory, was
a
bold one indeed.
5.
The limit point, however, generally depends on the initial conditions.
For a more extended discussion as well as
exact statements and proofs,
Note that
see F. M. Fisher (1983)
G.
Debreu has shown that local isolation of equilibria is true
almost everywhere in the appropriate space of economies given
certain differentiability assumptions.
.
11
that conjecture is wrong.
In fact,
provided
a
counter-example
pathological
know
result
similar
(1)
(1960)
economy
is not stable.
Sonnenschein and others,
holds.
Indeed,
so far as
quickly
non-
with
As
now
we
that example
existence of an open set of economies for
the
.
of an exchange
consumers in which
from the work of H.
implies
H. Scarf
anything
which
useful
a
is
known, it appears to be that stability rather than instability of
tatonnement is a special case.
Scarf's counter-example was thus of major historical importance.
Its
true analytical importance today,
realized.
often
however,
is
Scarf did not show that stability analysis was
guaranteed to be unfruitful.
(Indeed,
as we shall see,
a
fruitful development immediately began in the early 1960s.)
ther
Scarf
stability.
not
showed that tj±2nnem,gn£ would not generally lead
very
Rato
This means that the facile proposition that disequi-
librium is cured by fast-enough price adjustment is not generally
true
(although,
stances)
If
of course,
it may be true in
special
circum-
.
price
stability,
adjustment
however,
alone is not sufficient
to
gurantee
then equilibrium economics must rest on the
assumption that quantities also adjust.
While, as we shall see,
Sonnenschein (1972, 1973), Debreu (1974), and R. Mantel
not
(1976) show that the basic assumptions of economic theory do
restrict the excess demand functions except by continuity, homogeneity of degree zero,
and Walras* Law.
Since Scarf's example
and
shows that such restrictions do not imply stability of (1)
since properties such as the signs of the real parts of the
instaeigenvalues of the Jacobian matrix of (1) are continuous,
bility must hold on an open set.
6.
12
such an assumption does indeed lead to more satisfactory stabiliit has a major consequence.
ty results,
When trade takes place
out of equilibrium (and even more when disequilibrium
and
consumption occur)
,
production
the very adjustment process alters
the
equilibrium set.
is easily seen even within the simplest model of
This
exchange.
In
depend
tions
such a model,
pure
the equilibrium prices and alloca-
on the endowments.
If trade takes place
equilibrium, those endowments change.
out
of
Hence, even if the trading
process is globally stable, the equilibrium reached will generally not be one of those corresponding to the initial endowments in
the static sense of the Walras correspondence.
Rather the equi-
librium reached will be path-dependent, dependent on the dynamics
of the process taking place in disequilibrium.
If
such
(ironically
general
effects
led by Scarf himself
(1973))
popular
enterprise
of computing points
of
economy
is
The points computed by such algorithms are the
corresponding statically to the initial endowments of
equilibria
economy.
actually
then the
equilibrium from the underlying data of the
quite misleading.
the
are large,
They are not the equilibria to which the
tends given those endowments.
Hence
such
economy
algorithms
make dangerous predictive (or prescriptive) tools.
More important than this,
analysis
placement
—
comparative statics
the principal tool of equilibrium
—
is called into question.
of equilibrium will not be followed by convergence
the new equilibrium indicated by comparative statics.
will
be followed by a dynamic adjustment process which,
13
Disto
Rather it
if sta-
generally converges to
ble,
parative-statics
results
a
different equilibrium.
are not plentiful in
the foundation for such results,
brium,
While com-
equili-
general
even in partial equili-
brium, has become shaky.
out-of -equilibrium effects may,
Such
of course,
But we have no reason to believe that they are.
tatonnement
means
quantity-adjustment
effects.
ment
that
cannot
we
escape
are negligible
effects
be small.
The failure
by
assuming
relative
of
that
price
to
The doubtful project of tacking anonymous price adjust-
on to an equilibrium model is known to be a failure.
Fur-
ther progress requires more serious attention to what happens out
of equilibrium,
equilibrium
and we see that what happens out of
can have a serious effect on equilibrium itself.
2ji_Txa^i.Dg_Pxsc.ej.sg^.i_Jl3.e_Edgewoxii3_Pxoce5S
The
failure
failure
perhaps,
of
allowed
a
that
equilibrium
equation
stability analysis,
of
beginning
of tatonnement,
more fruitful
development
behavior.
does not imply
however,
and the early 1960s saw
development.
In particular,
look
at
out-of-
remained
the
trade was
now
and some thought
was
while
(1)
supposedly explaining price adjustment,
to take place out of equilibrium,
the
surprisingly,
Not
involved a closer
a
the
The first paper to suggest (by example) that there might
be considerable pay-off in a closer look at the adjustment process appears to have been Hahn (1961)
which considered specialization of (1) instead of restrictions on excess demands as a way
of making progress in tatonnement.
Kagawa and K.
(See also A.
Kuga, 1980.)
7.
14
given
the specification of
to
trading
The
rules.
models were called "non-tatonnement" processes,
is not particularly descriptive,
resulting
but as that name
I
prefer to call them as "trad-
a
modest concession to
ing processes."
processes made only
Trading
in
allowing trade to take place out of equilibrium.
(the original models concerned only pure exchange)
to trade endowments out of equilibrium,
take place until equilibrium was reached.
realism
Households
were permitted
but no consumption could
Indeed,
pre- and
the
post-equilibrium situations were unnaturally separated, for equilibrium
involved
previously
planned
dominance
which
of
markets
opportunities
consumption then allowed but
was perhaps an inevitable
This
over.
exhaustion of trading
an
all present and future goods
beginning of time, but can be considered only
a
given
equilibrium
the Arrow-Debreu model of general
for
already
trade
development,
with
clear
at
the
in
the
first step in the
analysis of the disequilibrium behavior of actual economies.
As already observed,
the price-adjustment equation
retained in trading processes.
adjustment
was
The task then was to specify the
describing changes
in
endowments.
Here
quickly developed one restriction common to all models (in
there
one
equations
(1)
form
or another)
.
That was the assumption that
trade
at
constant prices cannot increase an agent's wealth, since goods of
equal value must be exchanged.
I
shall refer to this as the "No
Swindling" assumption.
That progress might be made by considering trading processes
becomes
apparent when one realizes that the No Swindling assump-
15
implies that any Lyapounov function
alone
tion
that
tatonnement
also
works for trading processes in pure
Essentially
this
is because,
with prices
works
exchange.
constant,
trade
endowments cannot change any household's ordinary demand for
commodity, since wealth will be unaffected.
certainly
change
a
in
in
any
While such trade can
particular household's excess demand for
commodity traded by changing its actual stock,
the
such effects must
Hence
cancel out in pure exchange when summing over households.
trade in endowments does not change aggregate excess demands, and
only move with prices.
demands
those
movement is consistent with
then
move,
it is still
a
such
It follows that if
Lyapounov function when only prices
consistent when trade in
endowments
is
permitted.
This is an interesting result,
sideration
incorporating both some con-
of the underlying theory of the consumer.
stability
that
Surprisingly, it shows
proofs will generally be no harder
processes (in pure exchange) than for tatonnement.
ly,
properties
about out-of-equilibrium behavior and the
trading
for
Unfortunate-
this does not get us very far, since we know that such proofs
are
tion
Further specifica-
usually not available for tatonnement.
of trading processes beyond the No Swindling assumption
is
required if real progress is to be made.
Such specification took the form of two alternative
tions about the way trade takes place.
"Edgeworth
Hahn, (1961)
1962)
process" was introduced by H.
The first of these,
Uzawa (1962)
the second, the "Hahn process"
;
made its first published appearance in
Negishi
(1962)
.
assump-
a
(see also
(named by Negishi,
paper by Hahn
Each of the two processes involves what
16
the
and
turns
out
be a deceptively simple and appealing
assumption
about
The basic assumption of the Edgeworth process is that
trade
to
out-of -equilibrium trade.
place
takes
members
if and only if there exists a set of
agents
whose
can all increase their utilities by trading among
them-
With some complications stem-
selves at the then ruling prices.
from the possibility that initial prices may not permit any
ming
it is easy to see that at least quasi-stability must
such trade,
This is because, for each agent, the utility that would
follow.
be achieved were trade to stop and the endowment then held to
consumed
must be non-decreasing and strictly increasing if
strictly
of such utilities must be non-decreasing and
function)
that
Hence the sum (or any other monotonic
enagages in trade.
agent
be
The negative of the sum can then
increasing out of equilibrium.
be used as a Lyapounov function.
This
is very neat,
but problems emerge when one begins
hard about the basic assumption involved.
think
In
the
to
first
place, it is easy to construct examples in which the only Pareto-
improving
agents.
(other
Indeed,
than
itself.
and
trades
the
are possible involve
only
upper bound on
the number of agents)
large
such
is the number of
numbers
goods are involved,
one.
of
constructions
commodities
Since we wish to deal with models in which all
future
effective
that
that upper bound cannot
present
be
an
Hence the assumption that trade must take place
17
if
such a Pareto- improving possibility exists places
massive
a
o
requirement on the information flow among agents.
A
somewhat
deeper problem lies in the other
Edgeworth-process assumption.
natural
very
agents
ders
place
engaging in it are all made better off.
possibility of moving from trading
the
direction of what
however,
I
of
the
Since trade is voluntary, it seems
assume that trade only takes
to
part
when
the
Once one consi-
processes
in
the
have referred to above as the "key question,"
usefulness of this assumption in the form employed
the
in the Edgeworth process becomes very doubtful.
driven
The "key question" is that of whether the economy is
to
equilibrium
by
the behavior of
arbitraging
taking
agents
of the opportunities thrown up by disequilibrium.
advantage
But
speculating agents can certainly engage in trade not because they
believe
trade
plete.
he
or
that
by
each
but because of the sequence of trades they expect to
com-
An agent who trades apples for bananas in the hope
that
she
their utility will be directly increased
can then make an advantageous trade of
bananas
for
With the
8.
Let there be n agents and c ^ n commodities.
exception of agent n, let agent i hold only commodity i and
desire only commodity i + 1. Let agent n hold only commodity n
and desire only commodity 1.
Then the only Pareto-improving
trade involves all n agents.
The problem is quite similar to
that involved in coalition formation in the theory of the core,
and D.
the
Schmeidler has shown (privately) that,
if c
£ n,
existence of some Pareto-improving trade implies the existence of
such a trade for no more than c agents.
P. Madden (1978) proves
that the existence of a Pareto-improving trade implies the existence of a Pareto-improving bilateral trade, provided that every
agent always has a positive amount of every commodity, but such a
condition cannot be reasonably expected to hold.
(Whether a
weaker condition on agents' holdings might produce a weaker but
still interesting result is an open question.
The construction
of the example above suggests such a possibility.)
18
may
carrots
not care for bananas at all.
agents sell goods for money,
More
realistically,
not because they expect happily
to
consume the money they receive but because they expect to use the
money
worth process,
utility
however,
—
increasing
that agents would gain from each leg of
because
£&££££ to gain can be used
they
extend
to
process to cover multi-part transactions is not
Edgeworth
a
could
Whether the fact that individuals engage
be completed.
trade
is that every individual transaction is
even if trade were to stop so that later legs
transaction
not
The basic assumption of the Edge-
to buy something else.
in
the
known
and seems doubtful.
cannot avoid this problem if one wishes to examine
One
non-naive
serious out-of-equilibrium behavior of agents who have
expectations.
means
that
equilibrium
fact that the economy is not in
The
the
some expected trades may not materialize.
In
turn
this means that agents who expected to gain from such trades will
be disappointed.
As a result,
taken past actions
—
they may very well regret having
actions they would not have taken had
they
realized what was to occur.
This
If
is not restricted to speculative
one considers the extension of the analysis of
cesses
one
phenomenon
a
Edgeworth process.
nically
pro-
consumption,
similar difficulty with the extension
of
the
Both consumption and production involve tech-
irreversible
acts
—
the consumption of goods
transformation of inputs into outputs.
on
trading
to permit out-of-equilibrium production and
encounters
actions.
If those acts are
mistaken expectations about later occurrences
19
—
or
the
taken
either later
prices or the ability to complete later transactions
Lyapounov function depends on agents always
whose
model
then they
This is hard to accomodate
sometimes be regretted.
will
—
in
a
having
non-decreasing utilities.
i^_.Ih <£_flahn_ Px oc eg s
The second of the two important trading processes,
places a much less severe informational requirement
process,
than does the Edgeworth process.
trades
is
kets."
(How
different
if
'
level
It is assumed
of analysis.)
that
"mar-
on
question
markets get organized is a
such
on
In the Hahn process it
supposed that goods are traded in an organized way
buyers
the Hahn
for
a
prospective
and sellers of a given good can find each other and trade
desire to do so
they
—
indeed,
in
versions
some
(Fisher
1972), this is taken to define what is to be meant by a "market."
Naturally, out of equilibrium, it can, and often will happen
prospective
that
buyers and sellers of a given good cannot
complete their planned transactions in that good.
be
unsatisfied
sellers or unsatisfied
buyers.
all
There may thus
principal
The
assumption of the Hahn process is that markets are "orderly,"
the
sense
buyers
one
that,
there are not
af i^£_i£.a.d.e ,
both
unsatisfied
and unsatisfied sellers of the same commodity.
Only
of a given market are agents unable to complete
side
in
on
their
planned transactions.
This assumption can easily be seen to lead in the
of a stability proof.
Trade is supposed to take place instanta-
neously
or
and
look only at post-trade situations.
we
direction
outside of time relative to the rest of the
20
process,
Since markets
are
after
orderly,
for apples,
any agent with unsatisfied excess demand
say, finds that there is aggregate excess demand for
Since
apples.
trade,
(1)
is retained as the price adjustment equation,
the price of apples must be rising.
unsatisfied
Similarly,
any agent
with
excess supply for bananas finds that there is aggre-
gate excess supply for bananas.
Then the price of bananas
be falling, unless that price is already zero.
must
Since anything an
agent wants to buy and cannot buy is becoming more expensive, and
non-free good that an agent wants to sell and cannot sell is
any
becoming cheaper, any agent with either unsatisfied excess demand
or unsatisfied excess supply of non-free goods is becoming
In slightly more formal terms,
off.
—
defined
follows
the agent's £axget utility
as the utility that the agent would get if he or
completed
strictly
all
planned
decreasing
transactions
—
is
if the agent's plans are
non-increasing
frustrated.
a
9
she
and
It
that the sum of such utilities over agents (or any mono-
tonic function of the utilities of individual agents) will
as
worse
Lyapounov function,
decreasing except in equilibrium
serve
when
all agents can complete their planned transactions.
This shows the quasi-stability of the Hahn process.
either assumes or proves boundedness of the prices,
ble to show global stability,
the
strict
If one
it is possi-
since expenditure minimization and
quasi-concavity of indifference curves implies
that
all limit points must be the same.
is
9.
It
With the exception of disposing of free goods.
tiresome to have to constantly repeat this, and I shall not
always do so hereafter.
21
It
is
important to understand the difference
between
Lyapounov functions of the Edgeworth and Hahn processes.
the
In the
Edgeworth process, the utilities that increase out of equilibrium
are the actual utilities that agents would obtain if trade ceased
and
they had to consume their endowments.
the
utilities
utilities
that decrease out of equilibrium are
that agents expect to get by completing
actions at current prices.
In effect,
expectations are not compatible;
be delivered.
can
the
target
their
trans-
out of equilibrium, those
agents jointly expect more than
As the Hahn process goes on,
agents
revise
downward until they do become mutually
expectations
their
In the Hahn process,
com-
patible and equilibrium is reached.
Of course,
will
since the two processes are quite different,
it
sometimes happen in the Hahn process that trade leads to
decrease
a
in the utility that an agent would get if that were his
or her last trade.
This is not a defect,
however.
Indeed, as
can be seen from our earlier discussion of the Edgeworth process,
such a property is desirable,
since we want to focus on ultimate
plans, not myopic desires as the reason for trade.
Moreover, continuing to look ahead toward the "key question"
and more realistic models, the Hahn process has another desirable
feature
that the Edgeqworth process lacks.
Since the Lyapounov
function of the Hahn process involves declining target utilities,
it
should
be fairly easy to accomodate the decline
in
utility
that occurs when an irreversible consumption or production action
is
taken
This turns out to be
and later regretted.
(Fisher 1976a, 1977)
.
22
the
case
Before we can properly get to such matters, however, we must
with
deal
an underlying problem.
Hahn process,
cannot
the
that markets are "orderly" in the sense described,
reasonably maintained without
be
problem
The
The basic assumption of
deeper
consideration.
at issue can be seen by considering
following
the
example.
Suppose that there are at least three
bananas,
croissants.
and
Suppose
that,
commodities,
apples,
at non-zero
current
prices, before trade, apples and bananas are in excess supply and
croissants in excess demand.
Suppose further that some agent, A,
owns only apples and wishes to trade for bananas.
does not wish to sell bananas for apples.
can meet each other,
current prices.
agents
but
Then even though A and
no trade between them will take place at
This means that, post-trade, there can perfectly
well be agents with an unsatisfied excess demand
also
that
B, wishes to sell bananas and buy croissants,
another agent,
B
Suppose
for apples
and
apples.
The
with an unsatisfied excess supply of
apple
market in this example is not "orderly," and
tions
cannot
be ruled out merely by supposing that
such
situa-
agents
can
find each other readily.
problem appears first to have been recognized
This
modern
literature
by
R.
Clower (1965) who pointed out
in
(in
different context) the need to sell before one can purchase.
a
homely
example comes readily to hand.
A
familiar
the
a
But
English
nursery rhyme states:
apologize for using again the same light-hearted example that I have already employed on two previous occasions
(Fisher,
It' is so apt as to be
1976b,
1983, "p.
33).
14;
p.
irresistible.
10.
I
23
Simple Simon met a pieman going to the fair.
x
Said Simple Simon to the pieman,
Let me taste your ware.
Said the pieman to Simple Simon, ^Show me first your penny.
Said Simple Simon to the pieman, * Indeed, I haven't any.*
1
This
is
clear example of a Hahn process economy
a
willing sellers can meet.
buyer
.
and
Indeed, in the rhyme, the prospective
seller of pies meet on their way to
and
"fair")
(the
crisis.
in
are sufficiently well organized that willing buyers
Markets
1
the
marketplace
no trade takes place because
Nevertheless,
buyer has nothing to offer the seller that the seller is
the
willing
to accept.
case of Simple Simon,
The
way
to think about this problem.
element
The
pieman
stability
does not ask Simple Simon for apples or
the
introduction
an
analysis.
bananas
or
and the time has plainly
instead he asks for money,
consider
to
It does so by introducing
far conspicuously lacking from
so
croissants;
come
points up one possible
however,
money
of
stability
into
analysis.
Indeed,
Aside
case.
the
introduction
cannot be long delayed
in
any
from the Simple Simon problem under discussion and
use of money in the intermediate stages of arbitrage
actions,
it.
that
trans-
one cannot get beyond pure exchange without introducing
This is for a reason that, interestingly, does not apply in
equilibrium.
Firms,
profits.
unlike
households,
Suppose that some firm produces
of some commodity, say toothpaste.
toothpaste
are usually assumed to maximize
large excess
supply
Out of equilibrium, even with
in aggregate excess supply,
24
a
the price of
toothpaste
can be positive.
If that price is high enough,
and if there is
no standard medium of exchange in which profits are measured, the
toothpaste producing firm may regard itself as making a
profit,
positive
This means that the
£Y§B_tbo!jgh_it_se!ls_no_toothpagte.
firm's inventory of toothpaste need not be offered for
sale,
the excess supply of toothpaste will have no effect on
that
price.
Only by insisting that profits be measured in
of exchange (and a common unit of account)
medium
a
so
the
common
can we
ensure
that
firms producing commodities other than the exchange
medium
have
an incentive to sell those commodities.
money
This makes
indispensable.
The introduction of money into Hahn process models was begun
by Arrow and Hahn (1971)
.
They assumed that one of the commodi-
ties, "money," plays a special role in that all transactions must
involve it.
get
They then assumed that agents first formulate "tar-
—
excess demands"
excess demands constructed by maximizing
utility functions subject to budget constraints in the usual
—
but
that
demands",
these
constructed
target
excess
wishes
to sell it.
whether
must be distinguished
demand
as follows.
from
for a given commodity,
then
negative
that
Since commodities can be offered
or not the supplier has any money,
excess
"active
If an agent has a
way
for
agent
sale
active excess demand
in such a case is assumed to equal target excess demand.
On the
other hand, positive target excess demands cannot generate offers
to
buy
unless they are backed up by money,
so Arrow
and
Hahn
11.
The device of assuming that the firm distributes toothpaste dividends to its stockholders hardly seems satisfactory.
25
assumed that the agent allocates his or her available money stock
over the goods for which he or she has a positive excess
to the assumption that any good for which the
leads
This
has
positive target excess demand is also one for
a
demand.
agent
which
that
agent has a positive active excess demand, with the active excess
demand never exceeding the target one (agents do not offer to buy
than they really want and always make a positive offer
more
anything
that
they want)
to obey the orderly
assumed
are
unsatisfied
It is active,
.
aggregate
rather than target demands
markets
assumption
excess active demand that is
affect prices according to
With this in hand,
(1)
for
and
assumed
to
.
Arrow and Hahn were able to isolate
Simple
Simon problem by assuming that no agent ever runs out
money.
If this assumption holds,
the
of
then it is easy to see that the
Hahn process stability proof goes through in much the same way as
before.
Prices
change in the direction indicated by unsatisfied
aggregate active demands;
have
the same signs
demands;
same
(post-trade)
as the corresponding
aggregate
finally, unsatisfied individual target demands have the
as the corresponding unsatisfied
signs
demands.
demands
unsatisfied individual active
Hence
target
individual
utilities are still decreasing
active
out
of
equilibrium.
As already indicated,
introduction
12-
of
firms,
the introduction of money permits the
and this was done in
Fisher
(1974).
12
A parallel introduction of firms into the Edgeworth
process was accomplished by F. M. C. B. Saldanha (1982).
^3rl.
26
are assumed to be subject to the orderly
Firms
markets
assump-
tion, but to maximize profits which they ultimately distribute to
their shareholders.
Because
of the orderly markets assumption,
complete
profits
downward.
both because of the direct influence of
phenomenon
is
a
proof follows nicely from it,
a
the
household
The sum of
global
While
stability
employing both profit maximization
the part of firms and expenditure minimization on the part of
households to show that all limit points are the same.
the
orderly
the
Lyapounov function.
now a more complex matter,
of
utilities
on their own transactions and because of
utilities can thus again be used as
boundedness
forecast
Households then find their target
declining fortunes of the firms they own.
on
any firm that cannot
planned transactions must revise its
its
decreasing
market
Shareholders expect to spend those profits.
target-active
excess
demand
distinction
are
Money and
handled
as
before.
This is a pretty story, and one that can even be extended to
permit
out-of-equilibrium production and consumption,
cated above (Fisher,
1976a, 1977).
indi-
as
But the difficulties are all
too apparent.
The
thought.
role
of
money in this model is very
much
an
after-
Agents plan their target excess demands as though they
were in equilibrium.
In so doing,
they take no account of
cash constraint imposed by the institutional structure.
the
Instead,
they allocate their money stocks to their positive excess demands
as though any cash difficulty will necessarily be only temporary,
so that ultimately target transactions will be completed.
27
That naivete is also reflected in the assumption that agents
make
a
tive
target excess demand.
positive offer for every good for which they have
world
Debreu
this
time,
where
So long as we remain in
may not matter.
Arrow-
an
all markets open and close at the
posi-
a
dawn
Once we begin to be serious
of
about
disequilibrium, however, and to permit consumption and production
to
take place before equilibrium is reached,
It
is not reasonable to suppose that agents facing
lot.
liquidity
a
always allocate funds to all demanded commodities.
crisis
of
it matters a
those commodities may not be needed for years,
while
Some
others
may be required for near-term consumption.
And of course the afterthought method of allocating cash
related to the most obvious difficulty.
The Simple Simon problem
has not been solved, but merely well defined.
sary
It is still neces-
to assume that agents never run out of money.
hard to swallow in any case;
is
This may be
it is particularly unpalatable when
agents make their money-allocation plans as though their
planned
sales would always materialize.
In
the same connection,
the time has come to remember
how
awkward the price-adjustment assumptions are in all these models.
We
are not dealing with a case in which agents,
faced with
pending cash shortage when planned sales do not occur,
their prices.
set anonymously,
im-
can lower
Rather, we are still in a world in which price is
and sellers who might benefit from lower prices
28
are just out of luck.
other respects as well the model is less than
In
Money
tory.
13
satisfac-
is assumed to be a commodity entering the
utility
This is required in order to ensure that agents
function.
wish
to hold money in equilibrium, avoiding the "Patinkin problem"
Patinkin,
1949,
equilibrium
in
1950,
this
trading opportunities.
But that problem arises because
1965).
Arrow-Debreu world means
a
cessation
at
previously foreseen prices,
then
motive for holding money would not disappear.
of
of
If equilibrium had the more natural pro-
perty of involving the carrying out of previously planned
actions
(D.
trans-
transactions
the
Yet such a version
equilibrium requires agents to care about the timing of their
transactions.
In several ways,
Hahn
one
that
then, the defects of the more sophisticated
process models point the way toward possible progress.
way or another,
those defects are all related to
the agents in such models
(as
in all the models
the
In
fact
considered
so far) pay very little attention to the fact that the economy is
in
disequilibrium.
go on believing that prices will
They
change and that transactions will be
behavior
and
completed.
phenomena are modeled at best as an
not
Disequilibrium
afterthought.
13.
Some progress can be made here. Fisher (1972) provides
model in which goods are identified by the dealers who sell
them.
In such a model, the orderly markets assumption is essentially trivial, since there is only one agent on the supply side
of
any "market." Since prices are set by suppliers (with buyers
searching for low prices)
they can be adjusted when planned
sales do not occur and cash is low.
But there are plenty of
other difficulties with such a model.
See M. Rothschild (1973).
a
,
29
the difficulties encountered cannot be solved in such a
Plainly,
context.
A
built
we are to address the "key question" of whether
if
full disequilibrium model is required and
must
be
arbi-
traging actions drive the economy to equilibrium.
5-t_.T.ew.§£.ds_.a_Eyll_Di§equilib£ium_Mgdei
So far as
question
I
know,
the only attempt to examine the stability
in the context of a full disequilibrium model in
consumption
and
production
which
equilibrium
take place out of
consciously act on arbitrage opportunities is that of
agents
recent book
(Fisher 1983;
see also Stahl and Fisher
1986)
.
and
my
As
will be seen, that attempt to answer the "key question" cannot be
considered truly successful,
but there is,
I
think,
much to be
learned from it and from its inadequacies.
I
which
begin by considering a problem of only moderate importance
nevertheless exemplifies the need for dropping equilibrium
habits
of thought when thinking about
disequilibrium
problems.
This problem arises when one allows consumption and production to
take place out of equilibrium.
It is common,
correct,
and necessary to regard commodities
consumed or produced at different dates as different
even
if
Debreu
reached,
is
just
they are physically indistinguishable.
world
where nothing ever happens
In the
Arrow-
equilibrium
is
this does not matter; a commodity with a different date
a
different commodity traded on a different market
with its own price.
of
until
commodities
equilibrium,
and
If consumption or production takes place out
however,
then
30
commodity dates take on
a
new
.
Only currently dated commodities can be
significance.
or
produced;
commodities can only
future
be
consumed
traded.
Hence,
disequilibrium consumption or production means allowing
allowing
some commodity dates to be passed before equilibrium is
reached.
Since there can only be trading in current or future commodities,
but
no trading in "pasts," this means that trading in some
com-
modities becomes impossible as the adjustment process unfolds.
To see why this creates a difficulty, consider the following
example.
simplicity,
For
assume that commodities are dated by
At midnight on December 31, 1987, trade in 1987 toothpaste
year.
mean
that
are agents who cannot buy as much 1987 toothpaste as
they
Since
ceases.
there
had planned.
we are out of equilibrium,
this can
Since they must now make do with a different amount
than planned, this can cause a discontinuity in their behavior.
obvious
An
solution
presents
that toothpaste is a durable good
however.
Assume
different
analysis
applies
to
pure
perishable
itself,
somewhat
(a
commodities)
at midnight on December 31, 1987, 1987 and 1988 toothpaste
Then,
are
to this difficulty
perfect substitutes.
Our agent may not be able to buy
the
but this will not create
any
1987 toothpaste he or she planned,
discontinuity, since 1988 toothpaste can be purchased instead.
The
problem cannot be made to go away so
1987 toothpaste is a different commodity from 1988
Since
commodities have different
prices.
paste,
the
prices
do not coincide at midnight on December
two
discontinuity is still
It
mus.t
however.
easily,
is
a
31,
If
1987,
tooththose
then
real possibility.
very tempting to reply to this that the
coincide at that time,
two
prices
because the two commodities are then
31
substitutes.
perfect
Thai
The
that the prices of perfect substitutes must coincide
proposition
an equilibrium proposition.
is
xegigte^
temptation must be
It rests on the
that
argument
arbitrage will erase any difference between the prices.
But that
of arbitrage is what a full stability model is
supposed
working
to be about.
We cannot,
in a disequilibrium framework,
simply
that arbitrage will be successful by the time the crucial
assume
hour arrives.
There is an important sense,
however,
That difficulty stems from the
culty is more apparent than real.
treatment
in which this diffi-
wholly
of the markets for 1987 and 1988 toothpaste as
distinct, with prices set anonymously according to some rule such
as
(1)
In fact, this is unlikely to be the case.
.
Instead, the
same firms that sell 1987 toothpaste are also likely to sell 1988
toothpaste
and to quote prices
for
dealers
Similarly,
both.
specializing in wheat futures are unlikely to deal in futures for
only one date.
But if the same seller
more generally, the
(or,
commodities,
same
dealer)
then
he or she will have an active interest in making sure
quotes prices for both 1987 and 1988
come together at midnight on
those
prices
since
otherwise
arbitrage
the
at
December
dealer's
that
1987,
31,
will
expense
be
possible.
There are three lessons to be learned from all this.
First,
one cannot think about disequilibrium problems using only equili-
brium habits of thought.
in
Certain issues that seem not to matter
equilibrium can matter quite
a
lot out of
it.
Second,
farther one gets into serious disequilibrium analysis,
32
the
the
less
satisfactory
disequilibrium
Third,
the
the assumption of anonymous
is
price
adjustment.
considerations have something to do
with
institutional structure of transactions and the way in which
markets
—
organized
are
subjects on which no
work
been
has
attempted in the disequilibrium context, but which are crucial if
we are ever to gain a satisfactory understanding of the formation
of economic magnitudes.
Such subjects,
plans do not mesh.
get
formulated,
are truly difficult,
for they in-
their
and
It is far easier to consider how those plans
and the analysis of Fisher
producing
length,
some
however,
of what happens when agents interact
analysis
volve
14
a
does this
(1983)
at
which
number of results on the way in
agents plan to take advantage of the arbitrage opportunities they
In the course of so doing, the
see thrown up by changing prices.
positive
cash
assumption
of Arrow and Hahn
less
far
since agents now optimize their planned transactions,
arbitrary,
paying attention to their money stock.
that
becomes
Interestingly, it emerges
reason for trading in the shares of firms
one
anticipated
is
because
dividend streams permit liquidity transfers from one
period to another, and, out of equilibrium, such transfers may be
needed.
Such
agents
come principally
actions
to expect prices to change.
conscious
allowing
arbitraging
from
But allowing agents
of disequilibrium means more than this;
allowing
to
be
it also means
them to realize that their transactions may be
limited
14.
For work on transaction arrangements in general equilibrium, see D. Foley (1970) and Hahn (1971)
.
33
So long as we retain anonymous price adjustment,
in extent.
that such constraints are
we
must
suppose
This
has led to a literature on the analysis of equilibria under
such circumstances
—
absolute.
as
so called "fixed price equilibria."
interesting
More
regarded
disequilibrium
for the study of true
what happens when we allow agents to believe that they can
the constraints they face by making price offers.
example,
sold at a given price is limited.
believes
that
constraint
becomes
case,
a lower
expresses,
an ordinary,
Consider, for
price will bring
seller
If the
more
also
then
the
expected sales as a function of price
and
downward-sloping demand
sales,
curve.
for the usual reason in the analysis of monopoly;
must be given on all units to be sold,
a
this
In
seller will only refrain from offering a lower
the
alter
case of a seller who 'believes that the amount that
the
be
can
is
price
lower price
and marginal revenue will
fall short of marginal cost.
This
there
leads
to a number of
position
constraints
Specifically, the economy can be stuck in
where agents believe they face
and
do
binding
not attempt to get round
them
transaction
with
price
because they believe that it would be unprofitable to
offers
so.
First,
is the distinct possibility in such cases that equilibrium
will be non-Walrasian.
a
problems.
interesting
do
In macroeconomics, this can be regarded as a version of the
original
Keynesian question as to
underemployment
equilibrium.
15.
While such circumstances are sometimes -referred to as
"disequilibrium," they are not properly so-called, since what is
involved is non-Walrasian equilibrium,
rather than dynamic adjustment.
See A. Drazen (1980) for a survey of the literature.
1A
Hahn
shows that it can happen with the
(1978)
agents rational in some sense.
of
Second,
beliefs
the crucial question
whether an equilibrium is Walrasian or non-Walrasian
the
question
whether perceived monopoly power
of
analyzing equilibria;
agents
nature
(1983)
In this regard,
.
(assuming
perceptions
whether
ways after equilibrium is reached) will the
the
not
or
Only where
monopoly power remain (and change over
of
that
there is a relation between
shows,
constraints are actually binding therein.
liquidity
in
it is interesting
the equilibrium and the question of
of
certain
reached)
^.s
Fisher
as
vanishes
it pretty clearly depends on the experien-
encounter on the way to equilibrium
some equilibrium
that,
becomes
This is not a question that can be answered by only
equilibrium.
ces
the
of
time
in
equilibrium
be non-Walrasian and cash remain a problem.
Whether
some
or not a given equilibrium is
clarification
Walrasian,
of the role of money is
however,
We
achieved.
saw
above that the equilibria of trading processes (or of tatonnement
models,
that matter) were merely an exhaustion
for
opportunities.
a full model,
In
such as the one under discusrather, equili-
transactions do not cease in equilibrium;
sion,
trading
of
brium involves the carrying out of previously made optimal
planned
involving
transactions
at correctly
foreseen
plans
prices.
This means that the transactions demand for money does not disappear in equilibrium.
bearing
asset
(so that there is no explanation for
holding of non-interest-bearing money)
hold
that
asset
interest-
While money in this model is an
,
this explains why agents
rather than others bearing the
35
equilibrium
same
rate
of
even though money itself enters neither
interest in equilibrium,
utility or production functions.
iu_DyD3mics_aDd_stabiiity_in_3_Fuii_Model
All this is very interesting,
when
happens
frustrated.
but it says little about what
agents interact out of equilibrium and
plans
What can be said about such interactions and
the "key question" of whether they lead to stability?
is here,
are
about
Alas,
it
as already indicated, that the analysis under discussion
produces less than satisfactory answers.
We
price-adjustment
mous
equation
left over
(1)
such price adjustment take place?
tatonnement
from
Individual price adjustment is essential.
days.
anony-
have already seen that one cannot retain the old
does
But how
The answer suggested above is
that prices are set optimally depending on perceived monopoly (or
monopsony)
power.
take us very far.
How
do
That is all well and good,
but it does
not
How do such perceptions get formed and change?
institutions arise determining which agents
make
price
offers and which choose among offers?
Out of equilibrium, where
offers and acceptances will not match,
how does partial matching
take place?
On these crucial questions,
little guidance.
ments
strong
Rather,
Fisher (1983) offers relatively
price movements, like all other movevague
in the model are assumed to be restricted by a
restriction
understand
called "No Favorable
Surprise"
(NFS)
that restriction and the motivation for it,
.
but
To
requires
us to step back for a moment and consider the purpose of stabili-
ty analysis.
36
economies
Real
discovery
The
shocks.
subject to a succession
are
of new
products,
new
exogenous
of
processes,
new
sources of raw materials, new demands, and new ways of organizing
production are,
as emphasized by J.
Schumpeter
(1911)
ving forces of economic development and growth.
the dri-
,
It is unreason-
to suppose that such Schumpeterian shocks are all
able
and can be incorporated as part of equilibrium.
foreseen
Rather, equili-
brium analysis, if it is useful at all, is so because the economy
adjusts to such shocks,
rapidly
approaching a
equilibrium
new
long before the next shock occurs.
The
of stability analysis,
role
question
is to analyze
of whether such adjustment in fact takes
analyzing
means
then,
the part of the Schumpeterian
This
place.
model
the
occurring
after the initial innovation, when imitators enter and act on the
profit
opportunities
question"
can
be
they see.
What
I
interpreted as the question of
action
does in fact lead the system to absorb
terian
shock.
analysis
called
have
Evidently,
then,
the
a
the
"key
whether
such
Schumpe-
given
first task of
stability
fur-
is to answer this question on the assumption that
ther Schumpeterian shocks do not occur.
There is more to it than this,
however.
In a full
model,
where agents form their own expectations, there is the possibility
that agents will perceive Schumpeterian opportunities that do
not exist.
If such agents have the resources with which to back
their perceptions,
entrepreneur
equilibrium will at least be postponed.
who believes that he or she can profitably build
better mousetrap and who has the money to invest will affect
37
The
a
the
.
economy
even
if the world does not in fact beat a path
to
the
Stability implies that such occasions disappear, at least
door.
asymptotically,
no stability proof in a complete model
and
can
succeed without either proving or assuming that this happens.
The basic first step in an adequate analysis of stability as
a
full attack on the "key question," therefore,
one
is the weak
showing that arbitrage leads to equilibrium if no new unfore-
of
seen opportunities arise.
able
never
Surprise."
This is the assumption of "No
More precisely,
NFS assumes that
surprised by the unforeseen appearance of
opportunities
causing
them
to deviate from
plan
formed
In other words,
Useful new opportunities (technological
must
are
favorable
new,
now optimal is assumed to have been feasible
time ago.
example)
agents
previously
optimal plans if those plans are still feasible.
any
Favor-
be foreseen at least a short time
short
a
change,
for
agents
before
actually change plans so as to act on them.
It is not hard to see that,
a
special
case,
declining
well
NFS implies that agents
out of equilibrium.
in a foreseen way
technological
expected
as in the Hahn process which is
1
target utilities
While agents can be doing
(including taking advantage
progress)
,
any
of
are
quite
foreseen
what
abrupt departures from
nust mean declines in utility (if they matter at
was
all)
With
this in hand,
low,
although the details are technically complex and require
a
global stability proof can be made to fola
number of non-primitive assumptions on the dynamics involved.
The
problem with this is that NFS itself is not
assumption,
either.
a
primitive
It is all very well to argue as above that
one must exclude further exogenous Schumpeterian shocks in exami-
38
stability.
ning
It
is far stronger to rule out the
favorable
opportunities that may suddenly arise in the course of adjustment
to an existing shock.
this difficulty arises precisely because we have
Evidently,
no
model of how agents interact in reacting to
good
brium.
This
endogenous
causes
us to be unable to
describe
disequiliexactly
surprises do or do not arise and makes NFS
how
somewhat
a
unsatisfactory assumption.
Like earlier models,
only partially successful.
then, the analysis of Fisher
(1983)
is
It is strongest when dealing with the
plans of individual agents or with equilibrium.
It is weak when
considering
cannot
fulfilled
it
how
those plans interact when they
While
and how agents then change their expectations.
succeeds in doing away with anonymous
price
be
all
adjustment,
it
We still
tells us very little about how prices are in fact set.
have much to learn about the formation of economic magnitudes.
To learn how economic magnitudes are formed requires serious
modelling
of disequilibrium.
resources
are allocated,
how
ganized,
they play,
things,
If we are ever to
understand
how consumption and production are or-
prices come to be what they are and the role
we must examine disequilibrium behavior.
this
means
how
examining the ways in which
that
Among other
change
agents
The
16.
There is at least one other problem with NFS.
agents in the model being described have point expectations and
often
economists
no subjective uncertainty.
(They are all
wrong but never uncertain.)
It is an open question as to whether
there exists a version of NFS that is both palatable and strong
enough to produce a similar stability result when subjective
uncertainty is permitted.
—
39
their
expectations when their plans are frustrated.
such questions cannot be begged by using equilibrium
particular,
the
Obviously,
tools.
assumption of rational expectations can tell us
nothing at all about how disequilibrium works.)
We cannot simply
examine positions in which economic magnitudes happen to be
that there is no tendency to change.
of
(In
To understand the workings
the "Invisible Hand" it is not enough to understand what
world looks like when the "Invisible Hand" has nothing to do.
40
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^
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