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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
THE NEU KEYNE5IAN WICROFOUNDAT IDN5
Julio Rotemberg
Working Paper *tl925-87
August 1987
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
THE NEU KEYNE5IAN fllCROFOUNDAT I0N5
Jul io Rotemberg
Working Paper «19E5-87
August 1987
The New Keyneslan Mlcrofoundatlons
Julio
Rotemberg
Revised April 1987
Sloan School of Management and NBER.
I would like to thank Olivier
Blanchard, Stephen Cecchetti, Stanley Fischer, Greg Mankiw, Caterina Nelson
and Lawrence Summers for helpful comments and suggestions. Stephen Cecchetti
also made his data available.
M.I.T. LIBRARIES
NOV
1
2 10P7
RECEIVED
THE NEW KEYNESIAN MICROFOUNDATIONS
Abstract
This paper surveys some recent efforts
at
deriving the standard
Keynesian effects of money on output from models
maximize their welfare.
in
which individual agents
While other models with continua of equilibria are
considered, most attention
is
spent on model with costs of changing prices.
Models of the latter type also turn out to have multiple equilibria because,
when
a firm increases its price,
to raise their
and
own.
These
infinite horizon models.
its
creates an incentive for
its
competitors
multiplicities are discussed in both two period
The
multiplicities affect both the qualitative
features of the equilibria and their welfare properties.
1
also analyze the
extent to which small costs of changing prices can generate large (or costly
from a welfare viewpoint) business cycles.
individual prices
is
of existing models.
used
Aggregate data and data on
to discuss the empirical
strengths and weaknesses
^
-3-
I
Introduction
The central
Idea of Keynesian economics
The contrast with
stimulate aggregate activity.
when an increase
in the
is
money supply
is
demand
that increases in
classical models
considered.
is
In classical models with
textbook-style demand curves for money balances, an unexpected
all
increase in the
money simply
clearest
raises aU nominal prices^.
once and for
According
to
Keynes and his followers prices (or wages) respond slowly and the resulting
increase in real money balances raises output.
This paper surveys some recent efforts at deriving this effect of money
on output using models
in
which individual agents maximize their welfare.
The models provide microfoundations
in that
they start from these optimizing
agents and construct equilibria In which no individual agent wants to change
what she
is
doing.
Two types
explicitly or implicitly that,
of
changing
its price.
of models are considered.
for each individual firm,
there
The
is
first
assumes
some cost
This assumption, which may appear somewhat ad hoc
,
has the advantage of being consistent with the rather long spells for which
In the second category are models with
individual prices remain constant.
continua of equilibria.
In these models,
economy from one equilibrium
return to
Its
normal level
nonexistent In the second.
characteristic.
is
money
to another.
weak
WhUe
in the first
The two types
affects output
by moving the
the pressure for output to
category of models
of models also share
it
is
another
Several of the multiple equilibrium models lay considerable
stress on departures from the Walrasian model which are also important in the
literature on costly price adjustment.
I
am thus surveying here only
a subset of the models
whose authors have
-4-
adopted the "Keynesian"
Because
label.
of space considerations,
1
only
include models In which output depends on nominal variables such as money.
These provide the starkest contrast with
classical models.
It
is
worth
mentioning however that the label "Keynesian" has been affixed also to models
in
which preexisting distortions magnify the effect of government spending on
The mechanisms incorporated
output^.
in
those models may well also magnify
the effects of money on output considered here.
WhUe my emphasis
output,
it
is
on models
in
worth emphasizing that,
Important as well.
demand (due
is
accomodated by
an effect of money on
price are rigid, other variables are
pessimism about the future) are not
Instead, they directly
the prices of these goods.
falls in
is
with rigid prices faUs in investment
In particular,
to animal spirits or
if
which there
reduce the output of these sectors and aggregate output. Similar reasoning
applies to changes in government spending.
The prototype model
of the first type
Walrasian paradigm in three ways.
necessary for
is,
it
is
hard
First,
which
I
consider deviates from the
certain agents set prices.
to think of a Walrasian auctioneer,
which keeps prices rigid.
This
is
whatever that
Usually the agents that set prices are viewed
as monopolistic competitors.
Second, since the emphasis
variable must matter.
demand
for money.
This
is
is
on nominal rigidities some nominal
accomplished by postulating a textbook -style
When only these two deviations are operative,
unanticipated, once and for aU increases in nominal aggregate demand, which
are usually modelled as increases in money do not affect the real allocation
of resources.
The third and
critical ingredient in the
some reason for prices to be rigid.
(1977),
Rotemberg (1982a, b, 1983)
,
In Barro (1972),
prototype model
is
Sheshinski and Weiss
Mankiw (1985), Parkin (1986) and BaU and
Romer (1986b) there exists an
explicit cost of
changing prices whUe
Blanchard (1983,1985), Akerlof and YeUen (1985), Calvo (1983), Caplln and
Spulber (1986) and BaU and Romer (1986a) restrict directly the frequency of
price adjustment.
Given this
list of
ingredients, one might ask in aU seriousness what
new about the current generation
of
is
The major difference
Keynesian models.
between the current and previous generations (Fischer (1976), Taylor (1980a))
is
an emphasis on the behavior of product markets^.
This advantage
important theoretical advantage.
is
This emphasis has one
that
it
is
possible to be
quite precise about what a monopolistic seller of a good would do
This
prices are costly to change.
In those models
rigidity.
is
it
Is
in
if,
say,
contrast of standard models of wage
difficult to
model simultaneously the
presence of wage rigidity and the behavior of firms and workers in the
presence of the rigidity.
In particular,
firms are able to hire as
truly rigid,
it
is
hard
much labor
to see
why,
if
wages are
as they desire at the rigid
wages.
This theoretical advantage also has an empirical counterpart.
(1977)
and
Hall (1980)
in individuals'
have pointed out the observation
wages does not prove the existence
from wage rigidity.
The reason
for this
is
of infrequent
of allocative
in Section II,
observed rigidity
allocation.
of
it
is
much more
difficult to
changes
consequences
that rigid individual
at least consistent with efficient determination of the level of
As discussed
As Barro
wages are
employment.
argue that the
consumer goods prices has no effect on resource
In that Section
I,
also discuss aggregate evidence for the
existence of price rigidities.
A second advantage
models
is
that
is
that they require only
sometimes claimed for the new Keynesian
smaU price
rigidities to
produce large
-6-
fluctuations in
(1985)
insight
GNP.
This point
and Parkin (1986) and
is
is
will
due
to Akerlof
be referred to as
that the profit function of any agent
optimal price lead to only second order losses.
In Section III,
I
who
tiie
PAYM
The
Insight.
sets prices
is
Hence smaU deviations from the
horizontal at that agent's optimum price.
large output swings.
and Yellen (1985), Mankiw
Yet they are consistent
witli
discuss somewhat more generally the
applications of this insight to macroeconomic problems.
The paper then goes on
to present in Section IV a static
model of
monopolistic competition which forms the basis for the later discussion of
price rigidity.
its
This model
is
classical in that,
without price rigidities,
unique equilibrium has monetary shocks affecting prices alone.
Section V, a once and for aU change in the
money stock
is
In
analyzed in a
simple two period variant of the static model to which costs of changing
prices have been added.
fall
In this model monetary expansions, at least
if
they
While some Issues which arise in
within a certain range, affect output.
models with more periods are masked by the two period assumption, this model
has several interesting features including a multiplicity of equilibria.
particular, for a range of monetary shocks both changed and
In
unchanged prices
can be consistent with equilibrium.
The welfare properties
monetary shocks
also In Ball
costly,
is
explored
of equilibrium price rigidity in
The question which
in Section VI.
and Romer (1986b, 1987)
is,
response to
is
addressed
granted that changing prices
do prices respond too much or too
little
to
monetary shocks.
is
These
welfare conclusions prove to be ambiguous precisely because of the
multiplicity of equilibria.
This multiplicity
apparent difficulty inherent
is
in anaylizing the
and multiple periods. These are covered
also one reason for the
models with infinite horizons
In Section VII.
-7-
Sectlon VIII focuses on models In which the multiplicity of equilibria
is,
by
itself,
taken to be Keynesian.
thought of as being due
Here, the different equilibria can be
to differences In the beliefs individuals
about the future or about the current behavior of others.
equilibrium that
chosen
is
is
a function of expectations,
depending on animal
can be though as
In these models,
which include
(1982), Weitzman (1982),
can have
Since the
these equilibria
spirits.
Stiglitz
(1979,1984,1985), Diamond
Woglom (1982), Bryant (1983), Geanakoplos and
Polemacharkis (1986), Roberts (1986) and Woodford (1986), money affects
Gconomlc activity
Some
if
switches the economy from one equilibrium to another.
of these models exhibit recognizable price rigidity while other do not.
In any event they
which
first
it
is
all
avoid any explicit cost of changing prices.
more important here than
type
is
why
in the
my
issue
discussion of the models of the
the particular Keynesian sequence of equilibria
Section VI concludes with
An
is
chosen.
personal assessment of the new Keynesian
microfoundations and of promising directions of future research.
II
The
factual
background
The most discussed evidence
for the existence of nominal rigidities of
GNP
with past values of the money
any kind
is
supply.
Since the work of Sims (1972), this correlation has been studied in
the correlation of current
the context of relatively unconstrained vector autoregressions.
hypothesis that this correlation
to
is
The
absent from US data (or that money
fails
Granger cause output) can be rejected using some specifications whUe
can be accepted using others.
it
Eichenbaum and Singleton (1986) and Bernanke
(1986) are two recent examples of opposite results.
Leaving aside
statistical significance,
increases in
if
money are
correlated with subsequent Increases in output because of nominal rigidities
they should also be correlated with gradual increases
fact the slow response of prices
which
is at
in prices.
the center of the
It is
in
much more
structured empirical analysis of Rotemberg (1982a) as well as of the evidence
on nominal rigidities presented in Gordon (1983).
responses of the price level and output
to a
1
thus report on the
monetary innovation within
The vector
vector autoregression very similar to Bernanke (198G)'s.
variables that
the
of
consider consists of the logarithms of military spending,
I
money supply, GNP, the
implicit price deflator for
US treasury
rate of return on
bUls^.
It
GNP, and the nominal
also includes constants
deterministic time trends. This autoregression
is
and
estimated with quarterly
data from the second quarter of 1953 to the third quarter of 1986.
gives the responses of
the
a
money supply.
money output and prices
Table
1
one percent innovation
in
As can be seen from the table output rises gradually
before falling back to
its
long run position (this return
while prices rise gradually.
This second fact
nominal rigidities as the first.
not depend very
to a
US
is
is
oscillatory)
just as consistent with
Interestingly the short term dynamics do
much on whether the system
is
estimated in first differences
or not.
While the correlations between
money and output have been subject
extensive empirical analysis, their Interpretation
because money
is at least to
is
to
somewhat problematic
some degree endogenous.
On
the one hand, King
and Plosser (1983) note that the private sector may create more money when
its
demand
is
expected
to rise.
This suggests a positive correlation
unrelated to price rigidity.
On
between money and ouput
consistent with nominal rigidities
is
the other hand, the absence of correlation
if
the Federal
-9-
Reserve
using money purposefully to stabilize output (See Mankiw (1986a)).
is
Neither of these stories accounts for the gradual increase
follows increases in
A
is
prices which
in
money.
related set of correlations which
less subject to this endogeneity
is
given by the relationship between tax reforms and aggregate activity.
Poterba, Rotemberg and Summers (1986) note that
rigidities increases in indirect taxes
in
the absence of nominal
accompanied by reductions
in direct
taxes of the same magnitude should affect neither prices nor output.
can be seen as follows.
final
This
Suppose the government Increases sales taxes on
goods and reduces income taxes leaving government revenue unaffected.
Since the burden of taxes
by the side
of the
is
the same and since these two taxes differ only
market on which money
is
collected, output should be
With an unchanged demand for money, prices should be unaffected
unaffected.
This means that with flexible wages and prices, pre-tax wages must
as well.
wages are unchanged) and pre-tax prices must
fall
(so that after tax nominal
fall
as well (so prices inclusive of tax are unaffected).
rigidities,
pre-tax prices or wages
balances and output.
will
With nominal
not faU thus reducing real
Using both US and
Summers find that these switches do Indeed
UK
data, Poterba,
raise prices
money
Rotemberg and
and lower output.
While this evidence supports the existence of some nominal rigidities
says
little
about whether wages or prices are more rigid.
it
This extremely
important question appears intrinsically difficult to answer because the
ratio of
wages
means that
it
to prices exhibits
appears possible
very
little
correlation with
GNP^.
This
to believe that only prices are subject to
nominal rigidities whereas insurance or efficiency wage considerations keep
real
to
wages
stable.
Alternatively one
nominal rigidities whereas pricing
may
is
believe that only wages are subject
given by a constant markup over
10-
wages.
One notable attempt
is
To
gauge the relative rigidity of prices and wages
He studies how prices respond
Blanchard (1986b).
and viceversa.
to
to innovations in
wages
identify these two innovations he restricts the
contemporaneous response of each variable
Under these
to the other.
identifying assumptions prices appear more rigid as their response to wages
is
slower than the response of wages to prices.
in prices
If rigidities
and wages are
a central determinant of
GNP,
then, other things equal, countries with more movements in prices and wages
Thus the absence
ought to have less output fluctuations.
of
any evidence
that countries with high inflation rates have more stable levels of output
might be viewed as discomfitting to nominal rigidities.
Yet, as Mankiw
discusses below these countries exhibit smaUer responses of output to
Thus the
nominal shocks.
instability in their
GNP
is
perhaps due
to the
existence of larger nominal disturbances.
At the micro
level,
it
is
apparent to those with eyesight that
individual prices and wages stay constant for long periods of time.
In the
US, hourly wages are normally changed yearly even when there are no explicit
The
contracts.
price of candy bars at the corner grocery store also changes
very rarely.
The significance
by noting
(1977),
of the individual
wage data has been widely questioned
that most employment relations are relatively long -term (See Barro
HaU
(1980)).
Thus, a particular paycheck need not represent the
payment for the services actually rendered the month before;
as that month's installment on what
is
These installments could be relatively
it
can be viewed
a rather long stream of payments.
inflexible with
hours worked or even on individual consumption.
no effect on either
For this to be true there
.
-11-
must
some mechanism which ensures that
of course be
additional hour today, he receives not just the current
amount of future payments which
also a different
is
if
one worker works one
wage per hour but
appropriate given his
current marginal utUity of leisure.
I
now turn
to data
on product price rigidity.
US
(1935) based his assertion that prices in the
industry price indices.
These indices move
if
BLS
are "administered" are
little,
remained unchanged from June 1929 to May 1937.
spurious
The data on which Means
the index for tin
This rigidity would be
quotes given to BLS employees move less than quotes given to
Yet using data gathered by Stigler and Kindahl (1970) on
genuine buyers.
actual transactions prices Carlton (1986) concludes that price rigidity
is
pervasive
However, Carlton himself appears unsure
of this price rigidity.
goods sold
The
Many
to firms.
Stigler
installment payments.
and Kindahl data are for intermediate
of these transactions are also part of a
Thus they
continuing relation.
of the aUocative significance
too can be viewed,
In other words,
there
at least in part,
as
may again be mechanisms
that
ensure that when a firm today buys more of some good the stream of payments
from the buyer
well.
to the seller is affected not
One mechanism capable
Carlton mentions
is
of
only today but
in
the future as
ensuring an efficient allocation which
rationing, buyers
may simply be unable
to
buy more
at the
posted price.
We can only be sure that the
allocation
if
rigidity of a price affects resource
two conditions are met.
at this price.
First transactions
must be carried out
Second there must be nothing that prevents an individual from
buying one unit more (or
less) of the
current price for the good.
good and thereby having to pay only the
Without rethinking the entire fabric of
-12-
economics we must concede that prices of goods sold
fulfill
in stores to Individuals
both requirements.
So the evidence of Cecchetti (1986) that the newstand price of magazines
is
very rigid (Reader's Digest changed
1950 and 1980)
is
simply inconsistent with the absence of aUocative effects.
We can now be sure
of
newstand price six times between
its
that at least some monopolisticaUy competitive producers
goods have meaningfully rigid prices.
of focusing on such
This
product price rigidity.
is
one of the main advantages
Yet, once one accepts that there
are some goods in which price rigidity plays some aUocative role,
observed
difficult to maintain that the price rigidity
long term relationships
One remarkable
is
fact
totally
in the
it
is
context of more
devoid of such a role.
about the rigidity of Individual prices
is
that
prices of monopolies tend to stay constant for longer periods of time than do
This fact, which has some
those of duopolies or other tight oligopolies.
bearing on the theories
I
will
survey below was originally uncovered by
Stigler (1947) in his attack on the kinked
demand theory
of oligopoly.
finding has been confirmed by several subsequent studies.
These are surveyed
Unlike Reader's Digest, the newstand prices
in
Rotemberg and Saloner (1986).
of
Time and Newsweek each changed nine times between 1950 and 1980.
Ill
Objective Functions are Flat at the
In this Section
I
The
Top
discuss somewhat broadly the advantage conferred on
Keynesian economics of the
PAYM
insight that price setters have only second
order costs of being away from their optimal price.
Taken
as a broad
statement about the fact that small deviations from optimal actions can have
macroeconomic consequences
It
offers a great
many
possibilities.
-13-
For instance, consider a Robinson Crusoe economy
work
to eat.
There
Is
between working and not working a
have only a second order effect on
Now suppose we
Crusoe
follow Akerlof
little
work
utility.
and Yellen (1985) and consider "nearmost
to at
A straightforward near-
second order losses relative to rational strategies.
randomize a
strictly indifferent
Small changes in
more.
bit
is
These strategies are defined as leading
rational" strategies.
rational model of
which Crusoe must
an optimal amount of work that solves the food-leisure
Yet, at this optimum point,
choice of Crusoe.
in
macro fluctuations would have Robinson Crusoe simply
little bit
over the amount of effort he expends'.
would have the considerable advantage of simplicity.
Such
a
model
This model could also
explain the comovements of other variables with GNP; nothing prevents
Crusoe's randomization from being a
One objection
to this
use of
little
PAYM
is
that in the Crusoe model
of
second order.
insight
the welfare cost of the economic fluctuations
It
systematic."
bit
Is
Instead,
might be argued that in the presence of monopoly or other distortion, the
costs to the Individual
while,
who leaves
his price
unchanged can be
of
simultaneously, the cost to society from the price rigidity
first order.
Below
I
quarrel with this view;
second order
may be
of
appears invalid whenever
it
output moves both up and down Instead of moving only down.
So the
PAYM
Insight does not,
by
itself,
justify rigid prices.
It
does
offer some relief from the notion that models with price rigidity are ipso
facto implausible because keeping prices flexible
only partial.
The insight
cheap.
is
So
why
firms In the world opting to keep their prices fixed
Perhaps this
Is
is
also justifies keeping output fixed in response to
changes that make output changes profitable.
vary.
This relief
a coincidence.
More
likely,
are the near-rational
whUe
their quantities
one needs nontrivial
:
14-
costs from making prices flexible.
Before closing this section
richness that the
PAYM
is
is
worth speculating on the additional
insight would give more traditional dynamic models.
In such models, the effects of temporary increases In government spending
depend on the marginal propensity
is
essentially Indifferent as to
consume.
Yet, an optimizing individual
when he spends an
additional dollar of
This means that the marginal propensity to consume can be any
income.
number
to
(positive or negative),
and individuals would
still
finite
only suffer second
order losses from their lack of perfect optimization.
IV
A
Static Model with
In this section
I
Monopoly
consider a simple static general equilibrium model.
This model borrows heavily from Rotemberg (1982b), Mankiw (1985), Blanchard
and Kiyotaki (1985) and BaU and Romer (1986b).
at
t
The representative consumer
has a utility function given by":
Ut
J
[(l/J)I(JCit)0]P/S/3
=
-
(1)
Lt,
1=1
where there are J goods,
while L^
is
labor supplied at
guarantee concavity.
t.
C}^^
is
the consumption of good
The parameter
Consumers maximize
at
t
3
i
at time
must be smaller than one
=
Et
Z
p^-tU^.
In equation (2),
p
(2)
is
to
the expected present discounted
value of U^ which can be written as
Vt
t
a discount factor while E^ takes expectations
-15-
known
condltional on information
at
In the simplest version of the model
t.
opportunities for Intertemporal trade are limited so maximizing (2)
Throughout,
equivalent to maximizing (1).
I
is
impose a cash-in-advance
constraint which requires that
Z
PitCit < Mt.
(3)
i
where
M|-
the level of
Is
The next question
at
t.
to
assume that money
and nonlabor income
analysis so that
that there
is
is
Is
how money
is
acquired.
the only asset and that
at t^^.
applies
it
money balances and P^
In principle,
it
is
the price of good
is
1
The simplest approach
money
at
t
is
equal to labor
is
possible to extend the
when there are other assets
Suppose
as well.
an asset whose nominal rate of return from
t
to
t+ 1
is
i^.
Then, the usual intertemporal budget constraint would require that
M^/Rx
I
=
R^
=
TT
At
+
IW^L^/R^
(4)
.
T>t
T>t
(1 +
ij)
(5)
0<j<T
where W^
is
the nominal
wage
at
t.
Obviously, when (5)
is
the
appropriate constraint, the path of interest rates must adjust for (3) to
hold.
Since (3) holds, one can obtain the
subject to (3).
demand
for goods
by maximizing
This gives:
Cit = (Pit/Pt)-^(Mt/Pt)/J
where r equals 1/(1-9) and
(6)
(1)
16-
Pt = [I (Pit)l-^]1/(1-^),
1
so that Ft Is a price index for period
functions
lilce
t.
Constant elasticity demand
or the very slight generalization in which real money
(6),
balances are raised to a power as weU, are a virtual constant in this
literature.
If,
in addition,
it
Is
assumed that no saving takes place, one
can obtain a static labor supply schedule, which
is
given by:
Lt = (Wt/Pt)l/1-P
(7)
which means that labor supply
function
is
concave
in
upwards sloping as long as the
is
utility
consumption.
Firms are assumed to be monopolistic competitors who maximize the
expected present discounted value of profits.
These firms are assumed
to
take the wage as given and to have access to a linear technology so that
Qit = Lit,
where
Q^
(8)
is
output of good
i
at
t
whUe
input into good
L}t is labor
i
at t.
In the absence of price rigidities the firm's problem
is
thus the usual
monopoly problem with constant marginal cost W^ and constant
demand.
For the monopolists problem to be well defined, this elasticity r
must exceed one, so that
Wt/9.
elasticity of
9
must be between zero and one.
Under the assumption that the labor market
can be obtained from (7) and (6).
clears,
Prices then equal
equilibrium wages
Using these wages, the optimal price from
the point of the view of a single firm, P*t
is
approximately 1^:
17-
P*t = Pt(Mt/Pt)l'^/9
When
real
(9)
firms charge this optimal price, equilibrium aggregate output,
all
Q^/(^'p).
money balances and employment equal
Under perfect competition, which obtains here
by two firms competing
Gmployment
one, output
So,
one.
is
in
if
each good
Bertrand fashion, the real wage
since
9
Is
less than one
is
and 1/(1-3)
supplied
is
one and
greater than
is
The
lower under monopoly than under perfect competition.
is
tendency for monopoly
to raise price translates in
general equilibrium into
low real wages which discourage labor supply.
IV An Increase In the Money Supply
The
in a
Two-Period Model
simplest dynamic model in which the effects of increases in
the presence of rigid prices can be studied has two periods.
period money
is
given by some
In the second period,
absence of
rigidities,
Mq and
is
prices would rise
by k%, output and
to
remain at
money equal
money Increases unexpectedly by
In
In the first
expected
k%.
to
In the
real balances
Suppose however that changing prices
would be unaffected.
(1985),
value
Prices are therefore given by (9) with
this level forever.
Mq.
initial
money
is
costly.
Mankiw
Akerlof and Yellen (1985) and Blanchard and Klyotaki (1986) compute
the size of this cost which leaves firms indifferent between maintaining the
first
period price and raising their price.
The way
this computation
and Klyotaki (1986)
compute the gain
is
to
is
Mankiw
(1985) and Blanchard
assume that aU firms hold their price fixed and
to a single firm
this gain f(k) where,
carried out in
for small k,
from optimally changing
f(k)
is
its
proportional to k^.
price.
to
Denote
For costs of
18-
changing prices equal
As discussed
Rotemberg and Saloner (1986)
This
raises its price.
substitutes for good
all
not changing prices
This can be seen as follows.
unique.
j
in
to f(k),
will raise
this equilibrium is not
Suppose that the firm which
demand
of firms
good
sells
producing
With the demand curves given by (6), the demand for
j.
other firms increases as long as the elasticity of demand,
r,
exceeds
This additional demand provides an additional incentive to raise
one.
Thus,
prices.
price,
it
costs of changing prices equal f(k) and one firm raises its
if
becomes optimal for
all
the others to change their price.
would of course also make
collective price increase
original firm to raise its price.
all
the
an equilibrium.
is
the firms raise their price.
There
bigger than some
would not change
price even
costs larger than f*(k)
is
optimal for the
thus also equilibrium
in
which
Of course, for costs of changing prices
sufficiently big (i.e.
its
is
it
Such a
if
critical level f'''(k))
a single firm
aU other firms changed theirs.
Only for
not changing prices the unique equilibrium.
For
costs of changing prices between f(k) and f*(k) there are two additional
equilibria.
In one of these, aU the firms
change their price.
In the
other, a fraction a between zero and one of the firms change their price.
This fraction a
is
this fraction is
changing
increasing
Its
in the cost of
changing prices.
Given that
price, firms are indifferent between changing
their prices or not.
StUl,
for some level of costs which, for k small,
is
this point,
worth raising the question
is
changes costly.
changing prices.
proportional to
the unique equilibrium and, given (6), output rises.
k^, price fixity
it
is
of
what precisely makes price
There are undoubtely some small administrative costs
These are sometimes referred
more than the printing
of
At
to as
of
"menu" costs although
menus must be Involved since the newstand price
of
-19-
magazlnes
which
is
is
printed with the rest of the magazine,
Another possible cost,
.
stressed by Okunl2 (1981, p. 141-53) and Rotemberg (1982b),
the
is
cost of customer dissatisfaction with firms whose pricing appears erratic^^'.
and
Ideally such customer dissatisfaction would be modelled explicitly
much remains
to
be done on
this.
For the moment imagine that any change
At least to some
price costs goodwill which affects future purchases.
extent, the loss in goodwUl by one's competitor
even possible that the
reduced
if
a gain to oneself.
is
others are changing their price as well.
the multiplicity of equilibria mentioned above,
equilibria in which
all
It
changing one's own price
loss in goodwill from
since
in
is
is
This would exacerbate
it
would mean
when k
firms change their prices exist even
is
quite
small.
The increased output produced when money
work more.
It
is
additional effort.
real
wage adjusts
static
In the simple model outlined above, W^
to
make workers
willing to
In the case in
is
work more.
which there
in the real
is
wage can be
is
generally more
alternative approach
They postulate
is
With utility
we know that the equilibrium nominal wage
discounted at the nominal interest rate
is
adopted
independent of time.
in
Blanchard and Kiyotaki (1986).
that workers each possess unique attributes so that they too
act as monopolistic competitors
utility
For the case of
compute but, conceptually, no new problems emerge.
strictly linear in labor supply,
An
flexible so the
an intertemporal budget
constraint as in (4), the required change in the real wage
difficult to
when they
set their
wage.
Then
their loss in
from keeping their wages constant and agreeing to work more
response
workers
important to discuss the mechanism that brings forth this
budget constraints, the required change
obtained from (7).
rises requires that
to increases in
M
can also be suitably bounded.
in
Both of these
-20-
approaches have the very un-Keyneslan implication that
in
recessions workers
are close to indifferent between working and not working.
Suppose then that one believes that intertemporal substitution of
leisure cannot explain the
movements
in
employment 1'*.
not believe that the constancy of goods' prices
But,
the classical model.
is
The paper by Akerlof and Yellen
unnecessary and that
is
the only departure from
is
one then required to believe that there are
nominal wage rigidities as weD?
suggests that this
One can then obviously
is
it
(1985)
sufficient for there to be a
"real" imperfection in the labor market.
Akerlof and YeUen (1985) postulate an "efficiency" wage which employers
pay
to increase
worker diligence.
In their model,
increasing In the wage they receive.
depends only on the responsiveness
effort
by workers
is
This implies that the optimal real wage
of effort to the real
wage^^.
It is
Independent of employment and can easily be above the marginal rate of
substitution between consumption and leisure.
results from reductions in the
money supply
The decline
in the
in
output which
presence of rigid prices
then leaves the real wage unaffected, while reducing labor demand and
increasing unemployment.
V Are
Macroeconomic Fluctuations Excessive?
In this Section
supply.
I
Suppose, as
in equal quantities.
Lt^/P
-
Lt-
:
Welfare Issues
discuss the welfare effects of changes in the money
is
true in any equilibrium that
Then using
(8),
all
goods are supplied
one can write individual
utility as:
(10)
-21-
Since the level of output supplied by monopolistic competitors
lower
is
than one (the competitive level), the derivative of the representative
with respect to employment
utility (10)
Expansions
equilibrium.
Then, since
aggregate fluctuations
money supply
A
is
a
utility is
concave
in
sometimes high and other
is
consumption the existence of
reduces welfare.
Itself also
As Mankiw
popular accounts of business
Moreover, suppose that output
fluctuations.
the
output are good, contractions are bad.
this accords well with
(1985) points out,
times low.
in
positive at the monopolistic
is
Stabilizing output using
good idea.
different question
is
always change their prices
whether stabilizing output by forcing firms
is
a good idea.
to
This question of whether there
is
excessive price rigidity (or excessive output variability) given the costs of
changing prices
is
addressed
and Romer (1986b, 1987)
in Ball
.
The answer
is
not obvious because the losses from the fluctuations in output are of second
order!",
I
same order as the cost of changing prices.
^j^g
now present
(1986b, 1987)
Likely to
.
a simplified version of the
Consider k% changes
be positive or negative.
in the
If
arguments
in Ball
money supply which are equally
prices are unchanged, employment
changes by k% as well so the second order effects on
utility are
(B-l)LBk2/2
Since utility
is
linear in leisure,
to the fluctuations.
this can
if
all
to:
Now consider
Here,
I
be interpreted as the
the costs of changing prices
compute the costs
that the unique equilibrium has constant prices.
even
equal
(11)
leisure cost of the fluctuations.
which lead
and Romer
f'''(k)
which ensure
These costs are such that
firms but one change their price optimally,
i.e.
by k%, the
•22-
remaining firm would prefer to keep
its
This cost
is
thus equal
having output differ from the optimal output by rk% at the
to the cost from
equilibrium levels of real wages and real
easUy computed
price fixed.
money balances.
This cost
is
to be:
(r-l)QPk2/2
in
At the equilibrium real wage this equals:
nominal terms.
(r-l)Q3k2/2
(12)
Equation (12) gives the costs to a firm from changing
units of leisure.
its
prices while (11) gives the costs to individuals from price rigidity.
Price rigidity
is
thus excessive,
costs of changing prices
I(l-B)/[J(r-l)]
where
is
I
>
if
(13)
1
the number of individuals.
rigidity excessive because utility
when output
of
demand,
fluctuates.
r,
Similarly,
is
of at least
of 3
renders price
a high value for the perceived elasticity
let
output fluctuate a great deal
Such large fluctuations are costly
so a high value of r reduces price rigidity.
demand
A low value
very concave and individuals lose much
means that firms must
alone keep their prices fixed.
elasticity of
more than the
in that individuals lose
If
I
if
to firms,
equals J and firms face an
two the ratio in (13)
is
less than one.
Prices move too much.
Ball
they
and Romer (198Gb, 1987) also conclude that ratios
of the
form of
-23-
(13) are not vinambiguously greater than one.
It
analyzed the equilibria with least rigidity since
necessary
of f*(k) Is
Romer (1986b)
likely.
to
In Ball
worth noting that
I
have
have assumed that a cost
I
keep prices constant.
If
instead, as in Ball and
excess rigidity becomes more
a cost of only f(k) is required,
As noted
is
and Romer (1987) the welfare properties of the
model depend on the choice of equilibrium.
This dependence might be even more severe
changing prices represents mainly a loss
having
all
if
all
firms change theirs as well.
firms change their prices could be
individual costs of changing prices.
one
felt
the cost of
Then
customer goodwill.
any single firm could be much larger
in goodwill to
alone than
in
if
if
it
changes
In other words,
much lower than
its
the loss
prices
the cost from
the
sum
of
In this case equilibria with rigid
prices would tend to be more inefficient than equilibria with more flexible
prices.
As we
will see in
the next section, once dynamics are explicitly
recognized the choice of equilibrium determines not only welfare but also the
qualitative features of the model.
it
is
worth noting that the expression (11)
for the welfare cost of fluctuations
is
valid both
Before closing this section,
One interesting feature
competition.
fluctuations
is
of (11)
Is
under monopoly and
that the cost of k%
bigger under competition (when L
Because the relevant part of the
utility function
is
one) than under monopoly.
has constant relative risk
aversion, individuals are willing to give up a certain fraction of their
consumption
to eliminate
k% fluctuations.
represents more consumption when output
Such a constant fraction
is
high, as under competition.
VI Dynamic Models of Costly Price Adjustment:
i)
Ss rules
.
-24-
The two period model obviously
In the presence of costs of changing prices the
economies with rigid prices.
price that
inherited from the past
is
capture an important feature of
fails to
is
not necessariliy the price that was
optimal just before the latest change in the
money supply.
This has the
important consequence that when prices start far out of line, even a smaD
change
in the
money supply can
To take
change prices.
get firms over the brink and induce them to
this into account,
money supply evolves over
a
model
is
needed
in
which the
time and firms adopt optimal dynamic strategies.
For the case of fixed costs of changing prices, a general model of this type
Moreover the multiplicity
has yet to be developed.
plagues even the simple model of section IV makes
will
One case
be badly behaved^'.
of equilibria that
it
for which equilibria
Rotemberg (1983) and Parkin (198G))
is
such a model
likely that
have been studied
(in
the case of constant rate of monetary
growth
Sheshinski and Weiss (1977) consider a firm for
in the
absence of costs of changing prices
They prove
will follow
an Ss pricing policy.
The price
to S times P*.
At this point the price
rate, the time
i.e.
it
constant rate.
is
is
Each price change leads to a price equal
then kept constant until
changed again.
Since
P'^'^
it
equals
grows
Now suppose
happens
that the
grow
to
is
fixed,
is
money supply grows
at the rate g.
Then
a firm with a
price constant for a period of length
by gT every
time
demand function
desired price growing at the rate g.
it
changes
its
price.
sP''',
and that the price
at the rate g
thus choose to keep
its
P'''.
constant as weU.
its
price
times
at a constant
given by (6) would see
its
s
takes for a constant price to decrease from SP* to
the time during which the price
level also
at a
the optimal price
presence of fixed costs of changing prices, the firm
in the
that,
grows
P'''^
whom
It
would
T and change
Rotemberg (1983) assumes
•25-
demand functions and
that there are a continuum of firms with such
that they
He
start off uniformly distributed over the time of their last price change.
shows that
in this case,
level (defined as the
firms) does indeed
there
unique equilibrium
a
is
unweighted geometric average
grow
of the prices of different
The reason
at the rate g.
in wiiich the price
for this
that over
is
Interval of length t, a fraction x/T of firms change their prices
by
that prices rise on average
any
by gT so
Thus aggregate output does not vary over
gt.
time.
In this equilibrium the distribution of the ratio of actual prices to
P*t
is
uniform with boundaries S and
As Caplin and Spulber (1986) have
s.
emphasized, the distribution of real prices
is
(which
fact permits a different interpretation
time -invariant as well.
I
will
This
refer to as
interpretation B) of the constancy of the rate of growth of the price level.
In an interval of length
t,
rises
P'"'
by
rg.
This means that a fraction
Tg/(S-s) of firms find their price out of line and adjust their price by (Ss)
.
Thus the average price
It is
worth noting that
rises
as in Sheshinski and Weiss (1977) or
if
Rotemberg (1983) the Ss rule
by xg^°
is
due
changing prices, an
to fixed costs of
increase in the rate of inflation increases the size of individual price
changes.
More generally, the only case for which
Ss rule
optimal
Is
is
it
Is
known
the case of a constant rate of increase of
Nonetheless, Caplin and Spulber (1986) assume that S and
is
is
that,
once again, the costs
to firms
small in a wide range of circumstances.
Still,
P'''.
s
are fixed
One defense
independently of the stochastic nature of the economy.
approach
that a constant
from fixing these variables
it
is
difficult to see
exactly what form of "near-rationality" leads to a constant Ss rule^^.
implication of constant Ss rules
is
for this
that price changes are
all
One
of equal size
26-
when measured
percentage terms.
In
This obviously rules out the possibility
that the prices of some products sometimes
Is
many products.
counterfactual for
shows that
in
the
US
This
rise.
Nonetheless Cechettl's (1986) study
the average percent change of individual magazines
prices in the more inflationary 1970's
On
average for the 1960's.
Israeli noodles,
and other times
fall
is
not appreciably different from the
the other hand,
study of the prices
in their
Sheshinski, Tischler and Weiss (1981) report price increases
which are on average more than twice as high
more inflationary period
in the
1974-1978 than in the period 1965-1973.
The
implications of a constant Ss rule together with what appears like a
technical assumption that P* have a monotone continuous sample path are
Suppose that firms start with their prices
nothing short of startling.
Assume that
uniformly distributed over the interval [SP*,sP*].
over some interval
t
by
Then
v.
rises
by v over an
B given above.
interval,
there
rises,
a fraction v/(S-s) of firms adjust their
price by (S-s) so that the price level rises by v.
of the interpretation
P'''
It
means
This
that,
if
an equilibrium
is
just a rewording
is
money supply
the
which the price level
in
does as well even though individual prices are rigid.
The requirement
sample paths be monotone and continuous
to
is
distribution of prices remains uniform after
necessary
all
changes
monetary "shock".
By
a shock,
which money goes up very
in the interim,
fast.
I
mean
If it
a
ensure that the
in the
What the Caplin and Spulber theory obviously misses
is
very short period
happens so
that
fast that
money supply.
the effect of a
of time
during
no prices adjust
the adjustment of prices after the monetary shock leaves a
distribution of prices with an atom at SP'^;
different possibility
is
that while the
it
is
no longer uniform.
money supply
fast some firms are adjusting their prices as well.
is
A
temporarily growing
These firms,
if
they are
27-
ought
ratlonal
to anticipate that prices will
They should thus Increase
near future.
and thus abandon the Ss rule.
Another way
nonneutralities
of seeing
to
is
is
how optimal
their
which P*
is
growing
expected
own prices by more than
price adjustment rules create
at the rate g
that,
to a
steady state in
and firms are following the optimal Ss
without any jump
lower level
to prevail forever.
initially in a
is
in
the rate of growth of P*
P''',
This lower rate of growth
g'.
is
then
Firms must therefore revise their optimal Ss
rule according to the formulae in Sheshinski and Weiss.
have a smaller band of prices, a higher value,
It
is
now optimal
to
for the low relative price
s',
which triggers a price change and a lower value,
set
(S-s)
consider the partial equilibrium story of Tsiddon
He then assumes
unexpectedly shifts
relatively fast in the
likely to reintroduce nonneutralities.
Tsiddon assumes that the economy
(1987).
rule.
This
grow
for the price that
S',
is
when prices are changed.
The question
between S and
Is
how
the firms whose prices are between s and
should respond.
S'
Clearly those
low a price, i.e those between sP* and
s'P'^,
who
choose to
let their
adjust their price
price be eroded
by
or
find themselves with too
are beyond the price that
triggers a change; they should raise their price to S'P*.
find themselves with too high a price, i.e.
s'
Instead, those
who
those between S'P* and SP*, may
Even
inflation.
downward the downward adjustment
if
they choose to
(S'-S)
is
much
smaller
than the upwards adjustment (S'-s) so that the price index rises on the
instant in which the rate of growth of P* falls.
this to
mean that
which contribute
because P*
is
policies of disinflation
to recessions.
It
is
tempting to interpret
promote upward revisions
This interpretation
not being determined in equilibrium.
disinflationary episodes are likely to be accompanied
is
in prices
somewhat premature
In particular,
by increases
in the
demand
for
the rate of
money.
Suppose the disinflation
money growth.
Is
attempted by simply reducing
Then P* would jump down
as soon as
money growth
slows down, thereby reducing the incentive for prices to rise^^.
The great insight
of Tsiddon's
paper
is
that the optimal change of Ss
rules that accompanies changes in monetary policy has, itself, aggregate
consequences which are missed when the Ss rule
spite of this,
is
assumed
the paper by Caplin and Spulber (1986)
is
to
be constant.
In
valuable for
stressing that the pervasive rigidity of Individual prices does not
automatically Imply that monetary injections raise output.
Another way of making
this point is the following.
changing prices very small changes
very large price changes.
the firm
is
in the
external environment can trigger
This occurs because at the instant of price change
almost Indifferent between maintaining
while longer or incurring the cost of price change
different price.
Is
With fixed costs of
its
current price for a
now and moving
This Indifference can easily be broken.
to a quite
This means that
it
possible to Imagine distributions of prices such that a small increase in
the
money supply makes many firms Increase
increase in the
money supply triggers
their price a lot so that an
a recessional.
The message from
line of thinking Is that the distribution of prices Is all important
deciding whether an Increase in the money supply
expansionary22.
in popular
II)
This
is
is
this
when
contractionary or
not the sort of variable that finds a natural home
Keynesian discussions.
Staggering
The equilibrium with constant
inflation considered in
Rotemberg (1982)
has both a constant Ss rule and intervals of constant length between price
-29-
Indeed, Just as with constant Ss rules, keeping the Interval
changes.
between price changes constant
Yet there
constant rate^S.
Romer (1986a),
Ball
is
Is
generally optimal only
when
P'''
grows
at a
(Blanchard (1983,1986a), Ball and
a literature
and Cecchetti (1986), Parkin (1986)) which assumes that
prices are set for intervals of constant length.
spawned under the influence
This literature probably
of the earlier literature on rigid labor
markets
(Fischer (1976), Taylor (1980)) in which contracts of constant length have
descriptive appeal.
For prices, the notion that the interval between price changes
constant
is
clearly counterf actual.
There
is
is
much anecdotal evidence and
some hard evidence such as Cechetti's that price changes are more frequent
when
inflation
high^'*.
is
Thus Reader's Digest changed
both January 1974 and January 1975, while
it
kept
its
its
newstand price
in
price constant between
September 1957 and January 1967.
It
is
worth pointing out that the assumption of a constant interval
between price changes makes the degree of price rigidity
estimate with aggregate data.
One
possibility (Taylor (1980b))
a certain length for this interval before estimation.
knowledge
of the discount rate
of prices,
there
procedure
of Christiano (1985)
is
to
impose
In this case,
used by firms completely determines the path
nothing else to estimate.
is
difficult to
Alternatively, one can use the
who estimates the model repeatedly,
letting
the period for which prices are fixed be different multiples of the sampling
interval.
If
Comparison of these different estimates
in addition to
is
of course difficult.
maintaining the assumption of constant intervals one
imposes the condition that the number of firms that change their price
interval of length
t
is
constant.
I.e.
in
that firms are uniformly distributed
over the the time since they last changed their prices, some interesting
any
.
-30-
dynamic responses of output
particular,
under
money emerge (See Blanchard
to
In
(1983)).
Blanchard shows that the
this "staggering" assumption,
length of time over which a particular once and for
all
Increase In money
affects output can exceed the length of time for which individual prices are
fixed
One question that has emerged
in this
work
is,
assuming firms maintain
constant the intervals for which their prices are fixed,
changes be staggered or
will
change their prices
will firms
will their
price
same time
at the
i.e
This question has been asked both of models of
they be synchronized^^.
labor contracts (Fethke and Policano (1984), Matsukawa (1985)) and of price
setters (Parkin (1986),
their specifics, there
Ball
While the results differ in
tendency for staggered and synchronized
a
is
and Romer (1986a)).
equilibria to coexist.
This coexistence can be seen most easily for the case of constant money
growth whose staggered equilibrium
now consider synchronized
is
equilibria.
discussed
previous section.
in the
We already saw
in Section
other firms raise their prices at a point in time the demand for
VI that
all
I
if
other
firms rises. This increase in demand, in turn, raises the incentive to raise
prices.
This means that
if
all
other firms are changing their prices
together very often, each individual firm will want to do so as well.
this equilibrium the only reason a firm
do
so.
changes
The
firm thus has no desire to change
what brings about
is
its
its
price
is
because others
price between the price
This lack of desire to deviate from the equilibrium
of others.
equilibria
changes
its
existence.
Moreover the logic
of these
such that there are several of these equilibria.
by the length
At
of time
particular that there
during which
is
all
prices are constant^^.
no reason for synchronized equilibria
is
synchronized
These differ
This means
to
be
in
.
31-
periodlc.
The key difference between synchronized and staggered
in
equilibria
is
that
the former both the price level and output jump around discontinuously
Such jumps would presumably be reported on by
This lacks descriptive appeal.
newspapers.
StlU,
in
between price changes
both of these equilibria, as long as the interval
is
constant, monetary changes generally affect output.
In the staggered setting they do so because only some firms
change prices.
In synchronized equilibria they do so because, most of the time, aU prices
are constant.
The authors mentioned above have
tried to derive conditions
One possible
either the staggered or the synchronized equilibria disappear.
criticism of the staggered equilibrium
brings back the uniform distribution
a
is
if
that
it
it
is
unstable.
ever disturbed.
is
myriad modifications of the model which ensure
the presence of idiosyncratic shocks (BaU and
under which
Nothing
Yet, there are
These include
stability.
Romer (1986a)),
small
differences in the Ss policies of different firms (Caplin and Spulber
(1986)), as well as the randomization which
is
optimal to foU speculators
(Benabou (1986a)).
There are several ways
The
first is to
(1986a)).
of ruling out perfectly synchronized equilibria.
assume that there are firm specific shocks (BaU and Romer
Yet, even in the presence of such shocks there can be differing
degrees of bunching after a monetary shock.
The second
is
to
assume the
government would rapidly reduce the money supply
if
increase together (Parkin (1986)).
assume that when another
firm raises its price the
is
demand
Tlie third
for one's
is
to
own product
aU prices were
actually falls.
impossible with the cash-in-advance constraint used here.
Blanchard (1987) proves
it
to
be possible
if
to
However,
the elasticity of a firm's
This
-32-
demand with respect
to real
Ball
Finally,
firm's price.
money balances exceeds that with respect
and Cecchetti (1986) argue that firms want
learn about their optimal price from their competitors price.
wait until others have changed their price.
lead to a classic
war
of attrition^'.
to
They may thus
In continuous time this would
Moreover, unless learning about prices
charged by other takes time, price changes would stUl occurr
iii)
to the
in spurts.
Quadratic Costs of Changing Prices
The
difficulties with the fixed costs of
changing prices model
in a
dynamic setting are akin to those of investment models with fixed costs of
investment.
If
anything they are more severe because of the induced
multiplicity of equilibria.
literature
is
to
The standard
solution in the investment
The
pretend that the costs of investment are convex.
justification for this,
that
it
Is
easier to absorb
new capacity
into the
firm at a slow rate, flies in the face of the lumpiness of actual investment
projects.
The reason such models survive professional scrutiny
is
that
whatever the weakness of the assumption one can actually solve them and
obtain aggregate investment equations In a form suitable for estimation.
A
similar reasoning might apply to costs of
changing prices.
one could in principle argue that the cost of Increasing prices
of upset customers
is
Here too
the cost
and that customers might be more than proportionately
upset with larger price changes^".
that individual price adjustment
is
Again one would have
lumpy.
to confront the fact
Here this observation
is
more
damaging, because the main reason for taking models of costly price
adjustment seriously
is
the fact that individual prices seem sticky.
In a series of papers (Rotemberg (1982a, 1982b))
I
have nonetheless
-33-
pursued the Implications
of quadratic costs of
further justifications for their use after
changing prices.
draw out
I
These models start from the maximization
demand given by
(6)
and the technology
As argued above,
it
Et
^ p^
1
in the
*
upper case
the cost of changing prices
then possible to take a quadratic
is
where
o
and
6
Rotemberg (1982a) then
letters
Is
(13)
lower case letters are the logarithms
at t,
high.
[(l-a)(5-l)/6]
*
path of prices
absence of costs of
c(pjt+j-pit+j-i)2]
where E^ takes expectations
Pit = °Plt-l
to a
minimizes:
[(Pit+j-P*itH)^
of the respective
their implications.
This leads
(8).
approximation of from the firm's profits around P*.
postulates that firm
give some
of firm profits subject to the
P* (given by (9)) which the firm would charge
changing prices.
I
are related to
and
parameter which
c is a
The
solution to this problem
I
(1/6)J p*t+j
p
and
bigger than one.
c;
is
high
if
is:
(14)
the former
is
smaller than one
This solution has a natural
while the latter
is
interpretation.
Because the costs of increasing price are convex, firms opt
to
change their prices slowly.
and
P*'s.
Because
it
Prices are a weighted average of past prices
wUl also be costly
to
change prices
in the future,
future P*'s are taken into account as well.
Aggregation
of (14) accross firms,
which
is
trivial
recognized, gives rise to an equation analogous to (14)
price level
is
a
once symmetry
in
is
which the current
weighted average of the past price level and present and
future levels of the money supply.
This dependence of current prices on the
.
34-
future
is,
of course,
common
to all
models
in
which rational firms have rigid
prices
The main advantage
of this quadratic
equations that can easily be estimated.
approach
is
that
leads to
It
Rotemberg (1982b) applies
aggregate US data while GiovannJni and Rotemberg (198G) apply
it
to
it
simultaneously to German prices and the dollar/DM exchange rate.
The model
tracks fairly well the behavior of prices and exchange rates^".
The obvious
implication of this model
is
money supply translate themselves rather slowly
raise output.
sudden increases
that
in the
into price increases,
so they
This brings back the issue of how such a model, even when only
applied to aggregate data, can be consistent with the sharp and sporadic
price Increases observed in micro data.
The obvious answer
to this is that
models of this type capture the existence of some firms who delay their price
changes relative
One model
version of (14)
to the
underlying fundamentals.
of delay
whose equilibrium looks
is
presented
in
exogenously given probability
This probability
time period^^.
Calvo does not allow
Its
it
to
He assumes that firms have an
Calvo (1983).
n of
is
identical to the aggregate
changing their price
in
any particular
presumably chosen optimally as weU but
vary over time.
An
optimizing firm
who changes
price and minimizes (13) with c set equal to zero will thus charge a
price Z^ which
is
a weighted
sum
of current
and expected future
P''''s:
Zt = (l-(l-n)p){I [(l-TT)p]J p"<t.j]
The future
P*'s are less important the higher
rate at which the future
is
discounted.
Is
ti
The logarithm
and the higher the
of the price level is
then a weighted average of the logarithm of the past price level (with weight
-35-
(l-it))
Pt
and
=
(with weight
z
(l-i')Pt-l
which
Is
'
it):
Tr(l-(l-iT)p){Z [(l-TT)p]J p*t.j}
indistinguishable from the aggregate version of (1^)^^
.
Thus
the estimates in Rotemberg (1982)'s favorite specification imply that in the
the postwar
US about
8 percent of prices are adjusted
time between price adjustments
is
about
3 years.
every quarter; the mean
Instead, the estimates of
Giovanninl and Rotemberg (1986) imply that between 1974 and 1982 the average
time between price adjustments in
Germany was
of only about 12
months.
This probabilistic interpretation of an equation such as (14) has both
The Calvo model has the advantage
strengths and weaknesses.
that Individual
price changes are large while the price level adjusts sluggishly.
observation that price changes are more common
is
periods of high inflation
inconsistent with a constant probability of changing prices.
also falls to explain
A
is
in
why
Yet, the
The model
price changes are stochastic.
partial equilibrium reason for randomizing the timing of price
He considers demand functions for goods that
given in Benabou (1986a).
Firms for
are storable.
changes
whom
the date of price change
is
known wUl then be
subject to speculative attacks; individual wUl hoard their goods just before
the price rises.
There
is
then no pure strategy equilibrium to the game
between price setters with constant costs
The
solution
A
is
is
for the price
change
to
of
changing prices and speculators.
occur at a random date.
different reason for delay and possibly even for somewhat
random delay
that there are both costs to gathering information and costs of changing
prices.
By
costs of gathering information
I
have
and Saloner (1986), that the firm does not know
in
its
mind, as do Rotemberg
optimal price without
-36-
spending resources.
only these costs are present, prices should change
If
often since firms would charge their best guess of the optimal price.
Suppose however that these costs coexist with costs
of
changing prices.
Then
firms will keep prices constant for some time, occasionally investigate the
Suppose then that the money
optimal price and only then change prices.
supply rises by a known amount.
their optimal price
Not
firms will respond
all
and some firms wUl react only with delay.
would obviouly become somewhat stochastic
is
observed randomly.
It
Is
if
by investigating
This delay
information of varying quality
worth stressing, however, that
at this point
we
lack even partial equilibrium models in which costs of gathering information
and
of price adjustment are important.
VII Multiple Equilibria
As we have seen, small costs
equilibria.
of
Yet, at least in the two period model and for a specified range
monetary growth,
rigidity
is
the equilibria feature price rigidity, and this price
all
responsible for the Keynesian outcomes.
a literature In
which the multiplicity
Keynesian economics
teams and
in
is
In this section
of equilibria can,
The connection between
viewed as Keynesian.
in
changing prices generate multiple
of
by
itself,
I
review
be
multiple equilibria and
clearly articulated in Bryant (1983)'s model of effort
The connection
Woodford (1986).
is
apparent once one
recognizes that the equilibria differ by the (correct) beliefs agents have
about their environment.
The great strength
possibility that
These
beliefs can be
of these models
employment can
fall
below
adverse shift in technology or tastes.
is
thought of as animal spirits.
that they illustrate the
full
employment without any
At least some of these models find
37-
The
two other features of Keynesian thinking more difficult to accomodate.
first is that large fluctuations in
output are accompanied by long periods
which individual prices are rigid.
In these models,
predictably.
The second
changes
for
is
money
in
must switch the economy from one equilibrium
money
that
to
affects output
have an effect they
They must thus
another.
to
affect agents beliefs about their environment in prespecified ways.
way
problem
of posing this
is
that one can only
output once a particular equilibrium
little
is
in
know how money
Another
will affect
Yet the models provide
selected.
guidance for this selection.
Somewhat arbitrarily,
three strands.
The
first
I
divide this literature on multiple equilibria in
strand (which
is
embodied
in
Stiglitz
and
(1979,
1984)
and Woglom (1982))
is
closely connected to price rigidity
of Sections IV- VI.
It
starts from partial equilibrium models with multiple
equilibria.
Then,
a
change
unchanged nominal prices.
in the
to the
models
money supply can be consistent with
The second strand considers
fairly classical
models but modifies the institutions of price setting, wage setting, hiring
of labor
and purchasing
equilibria.
(1982),
of commodities
Models of this type include those of Diamond (1982), Weitzman
Cooper and John (1985) and Roberts (1986).
on the overlapping generations model.
this
and thereby achieves multiple
The third strand focuses
As Kehoe and Levine (1985) demonstrate
model can posess a great many equilibria.
These have been given
Keynesian interpretations by Geanakoplos and Polemarchakis (1986) and
Woodford (1986).
i)
I
consider these ideas
in
turn.
Partial Equilibrium Multiplicities
Consider an oligopoly whose member-firms
live forever
and produce
a
-38-
homogeneous good subject
usual Bertrand one of charging marginal cost.
with higher prices.
These occur, as
knows that any undercutting
a price
war
not too
many
in
in
is
the
Yet there are also equilibria
Friedman (1971) because each firm
agreed upon price
of the implicitly
which price reverts to marginal cost.
firms,
One equilibrium
to constant marginal costs.
Indeed,
will lead to
there are
if
any price between the monopoly price and marginal cost
constitutes such an equilibrium.
Thus, as
Stiglitz
(1984), notes there
exists in particular an equilibrium in which nominal prices stay constant
over some period of time.
This equilibrium
the oligopolists except insofar
it
is
not particularly desirable to
Rotemberg and
facilitates coordination.
Saloner (1986b) argue that when a collusive equilibrium of this type
maintained through price leadership
for
all
(i.e.
firms) then the rigidity of prices
oligopoly.
The advantage
exploiting the follower
to relative shifts in
by
is
is
letting one firm pick the price
actually useful to the
of rigidity is that
by varying the price
it
prevents the leader from
to its
own advantage
in
response
demand.
Similar multiplicities arise in Stiglltz's (1979,1985) model of search.
He considers
equilibria in which aU firms charge the same price.
one firm decides to charge a different price.
its
A
firm that chooses to lower
price attracts very few customers because search
attracts only those people with very low search costs
all
its
price
it
costly.
is
who are
search repeatedly in order to find the one cheap store)
instead to raise
Suppose
.
If
(Indeed
it
willing to
the firm chooses
wiU lose many more customers since they are
sure that they can obtain a lower price by going to one additional store.
Thus the demand curve facing an individual
charged by
all
the other firms.
firms has a kink at the price
This tends to make this price optimal.
Hence there are multiple equilibria and
it
is
possible (and perhaps even
39-
natural) to keep nominal prices
It
worth briefly drawing the contrast between
is
costs of changing prices,
upset customers"^^.
implies that
firms.
unchanged even when the money supply rises^^
it
Is
when these are viewed
particularly
The two are obviously
costly to charge a price different from that of other
that in the search model
is
prices even
If
single firm would benefit,
stabilizes its
Two
it
is
i.e.
The key difference between the
worth matching other firms'
an environment with very volatile prices, a
in
it
would please
its
customers,
it
if
own.
observations deserve to be made about the multiplicities
The
such a change
believe prices will change,
The second
fundamental changes.
among firms
with price rigidity.
in
these
these models are as consistent with excessively
first is that
rigid as with excessively volatile prices.
competition
this is
Instead, the models with costs
these are extremely volatile.
changing prices assume that
models.
as the cost of
In the equilibria in which others keep their prices constant,
two models
and
related since the search model
the same as making prices costly to change.
of
this search story
to
is
In these models,
will
if
take place even
people
if
nothing
that these stories rely critically on
generate the multiplicities which are associated
Thus they are hard
to reconcile with the
evidence that
monopolies keep their prices more rigid than oligopolies.
ii)
Multiplicities
In this section,
in
due
I
to
non-Walrasian Institutions
svirvey models which
both goods and labor markets.
In these models the institutional
as well as the timing of production,
explicitly.
abandon the Walrasian auctioneer
Diamond (1982) presents
framework
pricing and exchange are modelled
a search
model
in
which opportunities
to
These opportunities differ
produce arrive randomly.
needed
to obtain
one unit of output.
amount
in the
of effort
Having produced, individuals must then
search for a trading partner, i.e. another person who has also produced.
when they trade the
Only
fruits of their production with one another can they
In this model there are different equilibria corresponding to
consume.
different effort levels individuals are wUling to incur.
others are
If
wUling to incur much effort, there are many trading opportunities (search
much
for trading partners will be short) and expending
worthwhile.
is
One interpretation
that individuals
work
little
because, even though measured real wages are
Another interpretation
will
wages
is
a
is
be difficult to
lack of a mechanism
it
difficult to
purchase useful
This lacks descriptive power for Western countries.
goods and services.
it
that firms are not employing workers because they
sell
Under
the output.
this interpretation the
whereby the unemployed workers might be able
Is
considered
in the related
are not time consuming.
It
and purchasing decisions.
output
is
sold^''.
in
framework only
differs from that
Initially,
Workers then offer their labor.
finally,
down
model of Roberts (198G).
This model deviates less from the Arrow-Debreu framework
wages.
to bid
drawback.
Such a mechanism
of pricing
becomes
for the equilibria with low levels of output
high, individuals fear that they will find
fear
effort
that transactions
in the
sequence
firms announce prices and
Next, firms decide who to hire and,
Even when he restricts himself
to equilibria in
which prices and wages equal their Walrasian levels, output can be anywhere
between zero and the Walrasian
model
is
level.
What
is
most remarkable about this
that equilibria with low output have true involuntary unemployment;
workers who do not work envy those who do.
understood as follows.
As
in the
These equilibria can be
second interpretation of the Diamond model.
-41-
other firms hire few workers, few Individuals
if
own product and therefore one's demand
such low expected demand
The key question
there
its
model
price will attract a great
wage wUl
its
in the
is
why,
if
there are unemployed workers,
After
to fall.
all,
a firm
who
many customers, while one who lowers
A
firm
given a theoretically very ingenious
is
who contemplates deviating by lowering
"threatened" with a drastic change in the equilibrium
is
to
stUl be offering appealing positions to the otherwise
answer by Roberts.
and wage
The natural response
few workers oneself.
This rather old question
unemployed.
be low.
will
no pressure for wages and prices
is
lowers
to hire
Is
be able to afford one's
will
if
its
it
price
does
so.
As
I
mentioned,
in
Roberts' model there
constant returns to scale technology, the
If
even leaving out one
any firm lowers
one with
also an equilibrium with full
Moreover, since several firms produce any given good with a
emplojmient.
feasible
Is
full
its
full
of the firms.
employment equilibrium
Thus Roberts
(1986) assumes that
wage then the equilibrium immediately
employment where
this particular firm
is
shifts to the
inactive.
unemployment) and keeping the same prices and wages as
all
necessary that,
if
a firm
non-Walrasian model
producing good
j
lowers
its
it
all
the other firms.
Several features of this construction deserve to be noted.
in a
This leaves
wage (and thereby eliminationg
firms indifferent between lowering their
support the Walrasian equilibrium
is
is
First,
to
obviously
wages below the
Walrasian level, those employed by the firm be employable (at Walrasian
wages)
In
another firm producing good
j.
Roberts, however, requires one
order of magnitude more information and coordination.
j
lowers
as well.
its
wage firms producing goods other than
j
When
a firm producing
must react dramatically
Second, the unemployment equilibria are not robust
to the
-42-
Such a firm would prefer
Introduction of a single civic-minded firm^^.
eliminate
unemployment
if
it
could do so without affecting profits.
model, this can be achieved by lowering wages and prices.
are a
little off
the mark, there
with low output.
may be other ways
The model should be seen
Walrasian auctioneer
equilibria are unique
if
In the
These criticisms
of supporting equilibria
Once the
as an important warning.
abandoned care must be taken
is
to
to
ensure that
one seeks to perform standard comparative statics.
This warning seems particularly pertinent for the models surveyed in Section
IV which lack auctioneers in both goods and labor markets*'".
Ill
Multiplicities in the
Overlapping Generation Model
The standard overlapping generations models
the other models considered in this survey.
a Walrasian auctioneer
and dynamics are
Kehoe and Levlne (1985) have shown,
live for
if
of
differs considerably from
In particular,
prices are set by
paramount importance.
there are several goods (or
more than two periods), the model can have continua
foresight equilibria aU of which converge to a steady state.
multiplicity can be thought of as follows.
Walrasian auctioneer
who
StUl,
as
agents
if
of perfect
This
In each period, there
is
a
clears current markets for goods and labor.
If
agents have different expectations about prices tomorrow, the prices that
clear markets today will differ as well.
There are multiple equilibria
because different prices today are supported by different (correct) beliefs
about prices in the future.
It
is
thus natural to index these equilibria by
the beliefs about the future that they require.
Geanakoplos and Polemarchakis (1986) consider a model whose
multiplicities can
be indexed by two numbers
.
They
associate one
number with
-43-
Gxpected future output and the other with the current nominal wage.
these numbers are picked outside the model.
If
supply leaves these two variables unaffected,
it
effects.
One great advantage
model
of their
is
an increase
.
money
in the
has the usual Keynesian
that
is
it
analysis using the standard IS-LM graphical apparatus.
model, prices are not rigid per se
Both
amenable to
Note that In this
Nominal wages stay constant when the
money supply changes because expectations
of future variables,
future wages, have changed In just the right way.
including
For this story of price
rigidity to be convincing, an intuitive justification for this response of
expectations about the future
will
have
be provided.
to
VIII Conclusions
In these conclusions,
I
give
weaknesses
of the recent crop of
noting that
I
views about the strengths and
Keynesian microfoundations.
must start by
I
view the existence of multiple equilibria as a weakness
economic model.
First,
difficult to reject.
many things can happen
if
Indeed whether
it
is
when there are
multiple equilibria
to reject
in
any
much more
the models are
even possible
an open question.
like those in Section VII is
importantly,
my own
models
Secondly, and perhaps more
it
is
impossible to
know how
the economy wUl react to any particular government policy.
Therefore
All three
view the models surveyed
in the last section as incomplete.
types of models suggest literally that any level of output
equilibrium.
locally
I
My hope
is
unique equilibria
that
in
ways wiU be found
these models.
to rule out all
For Instance,
in
is
but a set of
the case of
supergames the equilibrium with the highest profits for the oligopoly,
least
when the
firms are symmetric, appears natural.
If
an
this locally
at
unique
-44-
GNP
set of equilibria turns out to involve expansions in
response
in
to
increases in the money supply, the models would obviously provide more solid
Keynesian microfoundations.
Unfortunately this criticism also applies at least to some extent to
models
in
which there are costs of changing prices.
the obvious purpose of these models
The reason, as
equilibria.
showed,
I
is
is
true even though
unique Keynesian
to provide
is
This
that any increase in prices
firms creates an additional incentive to raise one's
own
price.
tend to be equilibria with varying degrees of price rigidity.
by other
There thus
Moreover these
equilibria can be qualitatively quite different; in some the price level
evolves smoothly, in others
dramatically,
is
it
subject to large jumps.
Perhaps most
whenever prices are different from optimal prices there exists
the possibility that prices will change simply because they are expected to
change.
Here too
Yet, there
is
it
would be good
to
know how
perhaps another way
to select equilibria.
Suppose
of thinking of these models.
the evolution of money can be characterized by a stationary stochastic
process.
Then an equilibrium can be thought
of as a stochastic process for
prices which dictates the prices to every conceivable eventuality.
mentioned above, there are many such equilibria.
multiplicity,
the model would
microfoundations
If
still
As
In spite of this
provide rather strong Keynesian
every such equilibrium exhibited positive correlation
between monetary surprises and output.
This would
question of how to empirically validate the model.
still
leave open the
Tests would have to be
designed that examine only the features which are common accros equilibria.
Even
this is not
enough.
There must
also be some equilibrium
which
consistent with both the aggregate price data (prices respond slowly to
money) and the individual price data
(inflation
makes price changes larger
is
-45-
As
and more frequent).
clear from the discussion in Section VII,
is
no
While some of the existing
existing model satisfies these dual requirements.
models can account for some features of the aggregate data, they do not
explain the Individual data.
The task proposed
in
the previous paragraphs
are two grounds for feeling
It
will ultimately
daunting.
is
The
be completed.
Yet, there
first is
the pervasive microeconomlc evidence that firms perceive price changes as
costly.
In particular,
by
the fact uncovered
Stigler that prices of
monopolies are more rigid than prices of duopolies
is,
Rotemberg and
as
Saloner (1986) show, an almost natural consequence of fixed costs of changing
prices.
This
most easily seen when a decrease
is
reason for a single firm
undercut
its
in
an oligopoly
in cost
to lower its prices is its desire to
competitors and take customers from them.
to lower prices
This
which monopolists obviously don't perceive.
equilibrium with rigid prices
is
more easUy disturbed
Oligopolists are more likely to change prices
when
for optimism
is
is
an incentive
So the
an oligopoly.
in
costs change or, as
Rotemberg and Saloner (198G) show, even when there
The second reason
Then, one
occurs.
aggregate inflation.
is
that the papers
I
have surveyed
in
sections V-VII, while not the final word, have clarified greatly which
Thus
features of price rigidity lead to Keynesian effects and which do not.
we have learned from Caplln and Spulber (198G) and Tsiddon (1986)
that
it
Is
the fact that firms will optimally change both the lowest relative price they
are wUiing to tolerate and the relative price they set
their price which
is
responsible for monp'
.
when they change
y nonneutralitles.
Similarly the
staggering literature teaches us one Important form the muiiiplic1tio<5 of the
static
model take when firms are embedded
in a
dynamic context.
It
also
shows how these multiplicities can be consistent with having each equilibrium
.
-46-
be subject to monetary noneutralitles.
Finally the models of
Rotemberg and
Calvo show how aggregate dynamics may be easier to understand and estimate
when
Individual decisions involve some stochastic elements
-47-
FOOTNOTES
effect from increases in money balances on
operate
through
the effect of open-market operations on
real activity which
balances
money
accross
families.
See Grossman and Weiss
the distribution of
1
Note that
I
am Ignoring the
(1983), Rotemberg (1984), Fusselman and Grossman (1986) and Romer (1986) for
an analysis of these effects. Here I am implicitely treating changes in
money as being proportionately equal accross families.
In the Treatise on Money Keynes says: "neither economists nor bankers have
in their minds as to the casual process through which a
reduction in the quantity of money leads eventually to a new equilibrium with
a lower level of money-earnings and of prices" (v. 1 p. 272, emphasis added).
In the General Theory p. 173 this mechanism is outlined in recognizable IS-LM
2
been quite clear
terms.
3
Models of this type Include those of Hart (1982) Startz (1984, 1986) and
,
Mankiw (1986b).
4
This emphasis Itself is not altogether novel.
(1980), Gordon (1981) and Okun (1981).
See Means (1935),
McCaUum
This list also gives the ordering of the variables.
Only lagged
variables (four lags of each variable) enter in the equation that explains
current military spending and so on.
5
6
See Geary and Kennan (1982).
Suppose Robinson Crusoe's utility function is Cobb-Douglas over
consumption and leisure with an exponent on consumption equal to 1/3.
Suppose that there are 24 hours of leisure per period and that there is a
linear technology that converts hours of work into consumption.
Then optimal
labor supply is 8 hours.
Raising labor supply by 10% lowers utility by .2%.
7
8
Near rationality can justify also the polar opposite of excessive
movements in output. It is for instance near rational for Robinson Crusoe
to
maintain constant his leisure in response to small variation in his
productivity.
9
all
The model can thus be interpreted as either having a single consumer or
variables can be interpreted on a per capita basis.
10
This approach creates some delicate issues of timing.
First the money
supply is announced. Then, nominal wages are set to clear the labor market.
This is followed by an opportunity for firms to set (or change) their prices.
Banks then must extend credit to workers and equity-holders. This credit is
in the form of money which is spent on goods.
At the end of the period the
firms then given the money to the banks in the name of the workers and
capitalists thereby canceling their debts.
11
This approximation
is
exact whenever, as in the flexible price
.
-48-
equillbrlum, firms
all
charge the same price.
12
Okun's analysis differs from that in the text because he feel that
customers are upset only if firms change prices in response to demand changes
while they accept changes based on movements in costs.
Whichever of these costs is deemed important, it is obviously minimized
prices are quoted in the unit of the means of payment.
McCallum (198G)
also argues that fixing prices in different units (i.e. in terms of an index
13
when
of prices) provides only small benefits.
14
See Mankiw, Rotemberg and Summers (1985), Eichenbaum, Hansen and
Singleton (1985) for aggregate evidence on this sort of intertemporal
substitution.
15
For a general discussion on the strengths and weaknesses of efficiency
wage models see Katz (1986) and
Stiglitz
(198G).
16
To first order, the gain from an expansion equals the size of the
expansion times the marginal utility of employment. Thus if contractions are
as likely as expansions of the same size the first order effects of both
cancel
17
Indeed, Gertner (1986) shows that In a simple dynamic model with fixed
costs of changing prices the multiplicity of equilibria makes it possible to
support the collusive outcome in an oligopoly. Deviations from this
equilibrium are deterred with the credible the threat of moving to another
equilibrium.
18
This is the same interpretation as above once
with constant Inflation (S-s) equals gT.
it
is
recognized that,
19
One possibility is that, where it for costs of changing prices alone,
firms would keep their prices fixed for even longer intervals and thus have
even bigger price changes whenever they choose to change their price. The
firms might then be forced into a constant S,s rule if customers found
nominal increases of more than (S-s) percent intolerable.
See Dornbusch and Fischer (1986) for evidence that the major episodes of
accompanied by great surges in money demand. That these
increases in money demand are generally not fully accomodated by expanded
money supply can be seen from the high interest rates which tend to accompany
20
disinflation are
disinflations.
21
It is actually quite easy to construct fuUy worked out examples in
which monetary expansions reduce output In these models. Suppose the economy
starts in a boom.
Now consider a sudden increase in the money supply after
which money will be constant. This tends to make all firms adjust their
price to the new long run optimal level.
This brings output back to its
normal level.
22
This result is reminiscent of the importance of the cross sectional
distribution of money balances in general equilibrium models in which money
-49-
See
held because there Is a fixed costs of converting bonds into money.
Grossman and Weiss (1983), Rotemberg (1984), Fusselman and Grossman (1986),
Romer (1986).
Is
possible to have i.l.d. demand shocks as well (as in Parkin
Conversely if
only
if price must be set before demand is observed.
(1986))
there is any stochastic element to demand that is observed before prices are
for some realizations of demand,
set it will be generally optimal, at least
to incurr the cost and change price.
23
It
is
Additional evidence against the hypothesis that the interval between
24
price changes is constant is provided by Lieberman and Zilberfarb (1985) and
Sheshisnkl, Tlschler and Weiss (1985).
25
This synchronization
26
See BaU and Romer (1987).
27
28
is
called
bunching by Parkin (1986).
See Fudenberg and Tlrole (1986) and the refernces cited therein.
As Cecchettl points out this may be responsible for the fact that the
magazine price changes does not rise appreciably in the 1970's.
size of
29
It is
dynamics;
when required to fit all aggregate output
demand equation given by aggregating (6) is too simple.
statistically rejected
the
30
Calvo's model is In continuous time but the basic structure
as the discrete time model presented below.
is
the same
This argument may imply that other solutions to quadratic optimization
problems (such as those for investment, labor demand or inventory
accumulation) are also intimately linked to the solution of problems with
31
random delays.
32
The macroeconomic multiplicities that result from the story in Stiglitz
(1979) can be found In Woglom (1982).
33
The model of Benabou (1986b) has both search costs and costs of changing
prices although here these are best interpreted as adminlstative costs.
With
both these costs and positive inflation he shows that there exists an
equilibrium in which prices are dispersed even when the corresponding static
model has as Its unique equilibrium all firms charging the monopoly price.
34
This describes timing in the second of Robert's models.
In his first
model workers must simultaneously announce their offers of labor and puchases
of goods.
As a result individuals refuse to purchase from low-priced firms
if they fear that these will be unable to attract the necessary workers.
35
Joe Kennedy's Citizens Energy Corporation
is
ruled out.
The uniqueness of the model fleshed out in Section IV is due
presence of a Walraslan auctioneer who clears the labor market.
36
to the
50-
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Instability,
-55-
Table 1
Monetary Innovation
Vector Autoregresslon
Responses
a)
System
in
Levels
Money
Response
Quarter
of
1
1
2
3
4
to a
GNP
Deflator
In a
1813
/I
w83
Date Due
MtT LieRARIES
3
TDflD D04
TEA 33b
;'i^Aj