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MONOPOLISTIC COMPETITION, AGGREGATE DEMAND
EXTERNALITIES AND REAL EFFECTS OF NOMINAL MONEY
Olivier
J.
Blanchard
Nobuhiro Kiyotaki
.__
Mojjonhoj-
108!
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
4
1986
MONOPOLISTIC COMPETITION, AGGREGATE DEMAND
EXTERNALITIES AND REAL EFFECTS OF NOMINAL MONEY
Olivier
J.
Blanchard
Nobuhiro Kiyotaki
No.
401
November 1985
Monopolistic competition, aggregate demand externalities and
effects of nominal money
real
Olivier
J.
Blanchard and Nobuhiro Kiyotaki
November 19B5
*
MIT and University of Wisconsin-Madison. We thank Andy Abel, Rudi Dornbusch,
Hall, Jeff Sachs, Larry Summers and Marty Weitzman ior useful discussions.
Bob
ABSTRACT
A
long standing issue in macroeconomics it that of
competition to fluctuations in output.
monopolistic competition and the role
output.
We first
show that monopol
1
st
the relation of
this paper we examine the relation between
In
of
aggregate demand
cal
1
y
that
is
small
in
the determination of
competitive economies exhibit an
aggregate demand externality. Me then show that, because
menu costs,
imperfect
of
this externality,
small
costs of changing prices may lead to large effects of
aggregate demand on output and on welfare.
A
long standing issue in macroeconomi ci ii thit of
competition to fluctuations in output.
monopolistic competition and the role
output.
We first
show that monopol
aggregate demand externality.
menu costs,
that
is
small
i
st
We then
cost of
the relation of
imperfect
this paper we examine the relation between
In
of
aggregate demand in the determination
cal
1
of
competitive economies exhibit an
y
because of this externality,
show that,
changing prices may lead to large effects
small
of
aggregate demand on output and on welfare.
The paper
organized as follows.
is
Section
I
builds
a
simple general equilibrium
model, with monopolistic competition in both labor and goods markets,
nominal
money
|
it
then characterizes the equilibrium.
Section
II
and with
characterizes the
inefficiency associated with monopolistic competition and shows the inefficiency to
be due to an
in
aggregate demand externality.
nominal money,
order,
costs
of
Section III studies the effects of changes
when money is the numeraire,
changing prices.
It
and when
there are small,
shows that changes in nominal
first order effects on output and welfare,
second
money may have
shows the close relation between this
and
result and the results obtained in Section II.
Section
I.
We want
to construct
market but small
of
A
model
monopolistic competition
of
a
model
in
which each price setter is large in its own
with respect to the economy.
monopolistic competition.
The most convenient assumption
The simplest model
of
is
that
monopolistic competition, for our
i
purposes, would be one
of
households using labor to produce differentiated goods.
However, because we want to focus later on both wage and price decisions, and want
the model
to be easily comparable to the standard
with both households and firms,
model
labor and goods markets are monopol
i
st
macroeconomi
1
y
competitive.
which is an imperfect substitute for other products
model, we construct
Each firm sells
product
a
each household sells
|
a
type of
The assumption of
labor which is an imperfect substitute for other types.
monopolistic competition in both sets
of
transparence rather than for realism.
Although we choose to interpret suppliers
labor as individual
unions or syndicates
markets is made for symmetry and
of
households, an alternative interpretation is to think of them as
(as
in
Hart
(1982)).
The second choice follows from the need to avoid Say's law,
the supply of
a
Both
labor and goods markets.
and with separate
cal
c
goods produced by the monopol i sti cal
1
or
the result that
competitive firms automatically
y
generates its own demand. To avoid this, we must allow agents to have the choice
between consumption
model,
of
these goods and something else.
the choice is between consumption and savings.
competition,
for example),
the choice is between produced goods and
or
between produced goods and leisure
In
In
a
the standard macroeconomi
other models of monopolistic
non produced good
(Starts
19BS).
assume that the choice is between buying goods and holding money.
and most crudely achieved by having real
agents.
Thus,
c
Here,
(Hart,
we
1
982
shall
This is most simply
money balances in the utility function of
money plays the role of the non produced good and provides services 12
A Clower constraint would lead to similar results. Developing an
explicitly intertemporal model just to justify why money is positively valued
does not seem worth the additional complexity here.
There are however differences between money and a non produced good,
^hich arise from the fact that real, not nominal money balances enter utility
we shall point out differences as we go along.
.
firm
Money is alio the numeraire, to that
terms of money
will
play essentially no role
this will
;
and workers quote prices and wages in
this and the next section,
in
but
become important in Section III
The third choice is to make assumptions about utility and technology which lead
to demand
and pricing relations which are as close to traditional
so as to allow an
easy comparison with standard macroeconomi
c
ones as possible,
models.
This however
sometimes requires strong restrictions on utility and technology, which we shall
indicate as we go along.
The model
3
The economy is composed of
firms,
m
each producing
imperfect substitute for the other goods, and
short,
each of them owning
other types.
As
a
result,
a
n
a
specific good which is an
consumer- workers, households for
labor which is an imperfect substitute for the
type of
each firm has some monopoly power when
and each worker has some monopoly power when he sets his wage*.
it
sets its price,
We now describe the
problem faced by each firm and each household.
Fi_rms_
are indexed by
Y,
=
i
=
[ N,j ~~c~
(
j
The model
,
=
l,...,m.
cr-1
n
(1)
i
cr
)
"F^l
Each firm
i
has the following technology
1_
a
l
can De viewed as an extension of the Di xi t-St i gl i tz (1977)
monopolistic competition to macroeconomics.
Since in equilibrium each labor supplier sells some of his labor to all
firms, it is again more appropriate to think of labor suppliers as craft
unions rather than individual workers. However since we want to analyze labor
supply and consumption decisions simultaneously, we shall continue to refer to
iabor suppliers as "consumer-workers" or "households".
model
of
:
Yi
denotes the output of firm
used in the production of output
j
«=
i.
i.
entering symmetrically 5
j
denotes the quantity
There are
The production function
l,...,n.
Ni
is
a
n
CES production function,
parameter
is
a
equal
to the
the elasticity of
marginal
for short
follows-.
what
in
ourselves to the case where
or
substitution
demand for each type of
of
j
indexed
with all
j,
inputs
.
to the elasticity of
elasticity
labor of type
different types of labor,
The two parameters characterising the technology are « and
equal
of
of
inputs in production
a.
|
The parameter
it
will
alio be the
labor with respect to the relative wage.
inverse of the degree of returns to scale
o-l
|
a
is
an
The
will
cost with respect to output -elasticity of marginal
To guarantee the existence of
is
c
be
cost
equilibrium, we limit
strictly greater than unity and where
equal
to
a
is
i
are given by
greater than unity.
Each period,
(2)
Pi
the firm maximises profits.
V,
=
P,Y,
denotes the nominal
associated with labor type
function
(1).
It
output price of firm
j.
The firm maximises
takes as given nominal
i.
(2)
Wj
denotes the nominal wage
subject to the production
wages and the prices of the other outputs.
a
below as
result
of
utility maximisation by households. We assume that the number
firms is large enough that taking other prices as given is equivalent to taking the
price level
It
downward sloping demand schedule for its product, which will be derived
also faces
a
profits for firm
Nominal
as
given.
We take the numDer of firms as given. The issue of
ixed costs of production can therefore be left aside.
whether there are
of
Houieholdi are indexed by
j,
j
supplies labor
derives utility fro« leisure, consumption and real money balances.
It
{unction is given by
(3)
Uj
«
(Cj)
where
Cj
>=
(
1-K
=
6
.,
(
d,
e
6-i
I
_1_
i-e
E P«
1_
m
i
is
"1
consumption index -basket- which gives the effect
a
goods on utility.
household
a
Cj
is
CEB function of
utility symmetrically.
1-6
)
the consumption of
j.
|
the Cij's.
is
6
good with respect to its relative price.
is
All
types
of
the elasticity of
parameter between zero and one.
Nominal
price index associated with Cj.
We
substitution between
demand for each type
To guarantee existence of
shall
real
an
money balances on utility.
equilibrium,
labor supplied by household
is
assumed to be equal
j.
p-1
to or
is
V
is
a
money balances &re deflated by the nominal
refer to
P
as
the price level.
The third term in utility gives the disutility from work.
p
by
restricted to be greater than unity.
The second term gives the effect of
;
i
of
consumption goods enter
also be the elasticity of
will
it
denotes the consumption of good
Cij
The parameter
consumption goods in utility
of
Its utility
l
m
«
The first term,
j.
Nj
e-i
E Ci
i
P
type
P
(Mj'/P)
in
and
of
i
*
6
Household
»l,...,n.
j
the elasticity of
greater than unity 67
Nj
marginal
is
the amount of
disutility
.
"
The assumption that utility is homogeneous of degree one in consumption
and real money balances, as well as additively separable in consumption and
'eal money balances on the one hand and leisure on the other is made to
eliminate income effects on labor supply. Under these assumptions, competitive
labor supply would just be a function of the real wage, using the price index
lefined in the text. It also implies that utility is linear in income
this
acilitates welfare evaluations.
For reasons which will be clear below, we shall exclude the case where
i
of
labor
Households maximise utility subject to
prices and other wages as given.
a
budget constraint.
Again we assume that
is
n
other wages as given is equivalent to taking the nominal
faces
downward demand schedule
a
result
o-f
maximisation by
pro-fit
its type
'for
o-f
C,
+
j
denotes the initial
going to household
T
alto
which will be derived as the
is
Mj
'
«=
Wj
Nj
+
hj
endowment
o-f
money.
+
E V,
i-1
given by
i
V«j
j
is
the share
by
the equilibrium is given in the appendix.
o-f
o-f
pro-fits
o-f
-firm
i
-for
goods and labor and by
The relation between real
expenditures, which we shall
(5)
=
Y
Y
£
(
(M/P)
K
E
j=l
E
i-1
are equal
call
aggregate demand
-for
Cu
pair
o-f
short,
)/P and
P
£
(d/m) E
1-6
Pi
_1_
>
1-e
i»l
-for
to unity,
goods and labor are given by
i
a_
price and wage rules
aggregate consumption
where
m
Pi
The demand -functions
p
a
money balances and real
m
n
(6)
The equilibrium can
relation between real money balances and aggregate demand,
a
pair of demand -functions
and
It
he equilibrium
be characterised
a
as given.
j.
The derivation
Doth
wage level
m
E Pi
i-1
Mj
large enough that taking
The budget constraint
-firms.
m
(4)
labor,
Each household takes
is
given by
:
:
-e
C
(7)
(P. /P)
(M/P)
Kc
Nj
(8)
(M/P)
Kn
where the wage index
n
=
W
(9)
(l_
n
(W.,/W)
given by
is
W
1-ff
E Wj
J«l
j
«=[
(11)
(Wj/W)
=[
(M/P)
)K~
(P/W)
(M/P)
r
The letters K,
Kc
,
K„,
KP
,
)
l
,
.
.
.
,m
.
,m
(l/(l+e(«f-l)
1
(1/ (l+tr(p-l)
on
actual
money gives equation
its nominal
elasticity (-6).
index,
labor is
function
with elasticity
the
firms and households,
money
a
linear
in
equilibrium, desired money
good relative to aggregate demand
is
a
function
of
price to the nominal price index, the price level, with
The demand for
a
the parameters of
(5).
labor by firms is
depends on the demand for goods and thus on real
type of
l,...,n
money balances and consumption expenditures.
The demand for each type of
the ratio of
of
=
starting with the relation between real
Aggregating over households and using the fact that,
equal
)
First order conditions for households imply
balances and aggregate demand.
relation between desired real
)
j
]
K„ are constants which depend
interpret these equations,
)
i-i,. ..,(n
technology and the utility function as well as the number
We
)
]
o(p-l)
1
.
:
(w/P)
cr/ (cr-
.
1-ff
<e/ (e-i) )K P
(
,
J_
)
or-
(p,/p)
l
i
The price and wage rules are given by
(io)
B
-a
o
»
i
(-a).
of
the ratio of
a
derived demand for labor
money balances.
its nominal
;
it
The demand for each
wage to the nominal
wage
We now consider
the pr i ce rul
e
Given the price level, each firm is
.
with non increasing returns to scale and decides about
P,/P.
increase in the real wage
An
its real
a
monopolist
-or relative- price
shifts the marginal cost curve upward,
(W/P)
leading to an increase in the relative price.
increase in real
An
shifts the demand curve for each product upward
;
if
money balances
the firm operates under
strictly
decreasing returns, the marginal cost curve is upward sloping and the relative price
increases.
the firm operates under
If
constant returns,
the shift
in
aggregate demand
has no effect on its relative price.
We
finally consider the wage rule
utility maximisation problem
their wealth,
homogenous
wealth,
think of households as solving their
They first Bolve for the allocation of
two steps.
including labor income, between consumption of the different products
money balances.
and real
in
We can
.
After this step,
the assumption that utility is linearly
consumption and real money balances implies that utility is linear in
in
thus linear
in
labor income.
supply and the nominal wage.
The next step is to solve for the level
Given that utility is linear in labor income,
of
labor
we can
think of households as monopolists maximising the surplus from supplying labor.
Formally,
in
if
denotes the constant marginal utility
u
the second step
The real
(Wj/W) (W/P).
as well
as
a
Nj
=
Kn(M/P)
wage relevant for worker
j
is Wj/P,
Nj
The demand for
real
real
wealth, households solve
:
P
u<Wj/P)
max
of
labor of
money balances
(M/P)
type
j
is
a
-U
(Wj/W)
which we can write as the product
function of the relative wage
(Wj/W)
An
increase in the aggregate real wage
thus to decrease its relative wage
labor supply,
balances leads,
Mage.
If
p
is
(W/P)
if
is
p
(Wj/W).
An
j
H
the marginal
disutility
workers supply more labor at the same relative wage,
in
of
increase its
to
increase in real money
strictly greater than unity, to an increase
to unity,
equal
leads household
the relative
in
labor is constant,
response to an increase
in
aggregate demand.
Symmetric equilibrium
Equilibrium and symmetry, both across
all
•firms
relative prices and all relative wages must be equal to unity.
for all
i
and Wj
=
for
W
all
j,
and substituting
implies that
and across households,
in
equations
(10)
Thus,
and
using
(11)
Pi
gives
=
:
r-i
(12)
(P/W)
=
(6/(0-1))
(13)
(W/P)
=
(cr/
KP
(M/P)
K„
(M/P)
b(P-1)
Equation
(12),
(o—l>
)
which is obtained from the individual
price rules and the
requirement that all prices be the same gives the price wage ratio
function of real money balances.
If
(P/W)
as
a
firms operate under strictly decreasing returns,
the price wage ratio is an increasing function of
the level
money balances.
consistent with firms' behavior
a
Equi val ent
decreasing function
of
1
y
,
real
the real
wage
(W/P)
money balances.
We shall
of
output,
thus of real
refer to equation
(12)
as
"aggregate price rule".
Equation
(13),
which is obtained from the individual
requirement that all wages be the same aives the real waae
wage rules and the
(W/P)
as
a
function
of
is
the
P
FIGURE
1.
THE MONOPOLI ST1CALLY COMPETITIVE EQUILIBRIUM.
tcgf^/p)
wi
ty
V
(
z.
-tea
**e
(m/?)+
i~u\t
Lo»ii-AMh)
10
real
money balance*.
If
it
p
strictly greater than unity, that if
increasing marginal disutility
of
work,
an
increase
in
leads to an increase in the derived demand for labor,
real
wage.
The real
•function of
real
wage consistent with households'
money balances.
We shall
real
if
workers have
money balances, which
requires an increase in the
behavior is an increasing
refer to equation
(13)
as
the
"aggregate
wage rule".
Equilibrium values
(W/P)
of
and
(M/P)
are obtained from equations
The equilibrium value of
output follows from
graphically
As
vertical
in
Figure
1.
axis and log(MVP)
horizontal axis.
I
f
a
and
(12)
(or
p
and
(13)
are
(5).
log
(12)
we measure
linear,
logY as the two are linearly related)
are both strictly greater than unity,
equilibrium determines the real wage and real money balances.
level
of
Given real
log(W/P)
on
the
the
the aggregate wage
Given nominal
The
money,
it
money balances, we obtain the equilibrium
1
looks very much like the characterization of equilibrium under per-fect
competition, with an upward labor supply curve and
is
on
aggregate demand and output.
Figure
What
(13).
The equilibrium is characterised
rule is upward sloping while the aggregate price rule is downward sloping.
determines the price level.
and
therefore the effect
we now turn.
of
a
downward sloping labor demand.
monopolistic competition
?
This is the issue to which
i
11
Section
Inefficiency and externalities
2.
Comparing monopolistic competition and perfect competition
To characterize
the inefficiency associated with monopolistic competition,
first compare the equilibrium to the competitive equilibrium.
we
The competitive
equilibrium is derived under the same assumptions about tastes, technology and the
number of firms and households, but assuming that each firm
its price
(wage)
as given
when deciding about its output
(labor).
The competitive equilibrium is very similar to the monopol
one.
The demand functions for goods and labor are still
(B).
The price and wage rules are identical
the absence of 6/(0-1)
rules
(the constant
in
terms
1
st
,
K„
,
Kp
,
KM
and
to equations
K
cal
1
y
competitive
given by equations
and
(10)
(11),
the price rules and the absence of o7(o— 1)
Kc
takes
(each household)
in
(7)
and
except for
the wage
are the same in both equilibria).
(The
derivation is left to the reader). The explanation is simple. The term 6/(0-1)
is
excess of price over marginal
firms
in
the goods market
cost.
;
if
cost,
reflecting the degree
of
monopoly power
of
the
firms act competitively, price is instead equal to marginal
The same explanation applies to households.
Again,
to be the
symmetry requires
same
terms 6/(0-1)
;
in
in
equilibrium all nominal prices and all nominal wages
this gives equations identical
to
(12)
the aggregate price rule and o7(cr-l)
in
and
(13),
but without the
the aggregate wage rule.
The
price wage ratio consistent with firms' behavior is lower in the competitive case by
6/(6-1)
at
any level
of
real
money balances
(output);
the real
household's behavior is lower in the competitive case by
wage consistent with
cr/((j-l)
at
any level
of
real
)
FIGURE
2.
MONOPOLISTICALLY COMPETITIVE AND COMPETITIVE EQUILIBRIA,
ioo, (\*j/f)
( t A^err
}
°$f<r/u-
^>j>f^
)
)
fyyf* eo$(M/p)
+
co»*~t
i
i
12
money balances.
The monopol
i
cal
*t
price rulet are drawn in Figure
A
gives the monopol
i
sti cal
The equilibrium level
equilibrium
j
1
1
competitive and competitive aggregate wage and
y
Point
2.
gives the competitive equilibrium, point
A'
competitive equilibrium.
y
money balances
real
of
the price level
higher.
is
is
lower in the monopolistic
Employment and output are lower.
What
happens to the real wage is ambiguous and depends on the degrees of monopoly power in
H,
the goods and the labor markets.
for
example,
there is monopolistic competition
in
the goods market but perfect competition
is
unambiguously lower under monopolistic competition.
Denoting by
the ratio of
R
equilibrium to output
in
the labor market,
output in the monopol i at cal
the competitive equilibrium,
in
is
R
1
wage
then the real
competitive
y
given by
i
1
r
=
{
_£-j_
_e-j.
is
an
<
increasing function
of
cr
the competitive equilibrium.
or the
R
is
is
R
small
labor markets can have
a
:
an
The higher the elasticity of
and 6.
substitution between goods or between types
both close to unity,
1
e
tr
R
cxp-i
)
of
labor,
the closer
increasing function
of
the economy to
is
and p.
o
the existence of monopoly power
in
If
a
and
p
are
either the goods
large effect on equilibrium output.
Aggregate demand externalities
Under monopolistic competition,
low.
We have shown
output of monopol
i
sti cal
1
y
produced goods is too
above that this follows from the existence of monopoly power in
price and wage setting.
An
alternative way
from an aggregate demand externality.
of
thinking about
it
is
that it follows
y
i
.
13
The argument
each price
price
it
and
follows
:
in
the monopol
i
st
cal
1
competitive
y
equilibrium,
setter has, given other prices, no incentive to decrease its own
(wage)
(wage)
as
increase its output
decrease their prices simultaneously
aggregate demand.
(labor).
i
Suppose however that all
this increases real
money balances and
The increase in output reduces the initial
distortion
underproduction and underemployment and increases social welfare
We now make the argument
of
63
By the definition of
more precise.
price setters
.
a
monopol
i
st
i
cal
1
competitive equilibrium, no firm has an incentive to decrease its price, and no
worker has an incentive to decrease its wage, given other prices and wages.
now
a
proportional
all
i
and
1
j,
decrease
all
in
which leaves all
wages and all prices,
(dPi/Pi)
«(dW,/Wj)
Consider
<
,
for
relative prices unchanged but decreases the price
evel
Consider first the change in the real
output and employment,
the real
value of firms' '.
5
At
a
value of each firm is unchanged.
price level however increases real
given level
The decrease in the
money balances and aggregate demand.
shifts outward the demand curve faced by each firm and increases profit
in
demand at
Thus,
a
the real
This in turn
:
an
increase
given relative price increases profit as price exceeds marginal
value of each firm increases.
An alternative way of stating the argument is as follows
If starting
from the monopol sti cal y competitive equilibrium, a firm decreased its price,
this would lead to a small decrease in the price level and thus to a small
increase in aggregate demand. While the other firms and households would
benefit from this increase in aggregate demand, the original firm cannot
capture these benefits and thus has no incentive to decrease its price. We
have chosen to present the argument in the text to facilitate comparison with
the argument of Section III.
What happens to the real value of firms is obviously of no direct
relevance for welfare. This step is however required to characterize what
happens to the utility of households below.
:
l
of
1
cost.
i
14
Consider then the effect
utility of each household.
of
a
proportional reduction
Consider household
j.
of
pricei and wages on the
We have seen that,
once the
household has chosen the allocation of his wealth between real money balances and
consumption, we can write its utility asi
P
Uj
where
the
u(I.i/P)
<=
th
household.
j
Nj
the constant marginal
is
u
-
utility
[p
Utility
utility-
<Wj/P)Nj
-
we have seen
j
Hi
the sum of
is
aggregate demand.
real
Using the budget constraint,
Thus,
wealth and
I,
we can express
the total
is
utility as
wealth
o-f
:
m
p
«
Uj
of
+
]
u
E V,j/P
i-1
three terms.
+
(Mj/P)
u
The second
is
profit income -in terms
increase
that each firm's profit goes up after an
this term increases.
surplus from supplying labor.
At
a
of
in
The first term is the household's
given level of employment, Nj,
change in wages and prices leaves this term unchanged.
the proportional
But the increase in aggregate
demand and the implied derived increase in employment implies that this term
increases
:
at
a
given real
wage,
an
outward shift in the demand for labor increases
utility as the real wage initially exceeds the marginal utility
term is the real
level.
10
Thus,
of
leisure.
value of the money stock, which increases with the fall
utility unambiguously increases
10
.
Note that, if we were performing the same experiment in the neighborood
not of the monopol i st cal 1 y competitive but of the competitive equilibrium,
the first two terms would be equal to zero. The third one would however still
oe present. This is one of the implications of our use of real money as the
non produced good. If real money enters utility, then the competitive
equilibrium 15 not a Pareto optimum, as a small decrease in the price level
increases welfare. This inefficiency of the competitive equilibrium disappears
if money is replaced by a non produced good, while the aggregate deamand
externality under monopolistic competition remains valid (see Kiyotaki 19B4).
in
The third
the price
1
15
The notion of
It
an
aggregate demand externality
has been formalised in various recent papers)
surface relatively little in common,
an
is
idea in macroeconomics.
old
although these papers have on the
they share the following properties
i
increase in one agent's activity increases the activity level and welfare
general
a
increase in activity,
may be welfare improving
11
.
if
Diamond
it
(
can be engineered,
9B2
builds
)
by
of
others
j
taxation or other means,
macroeconomi
a
an
c
where trade
model
takes place through search and shows that increased search by one trader has
externalities as
trade.
Starts
it
increases the probability for other traders to find
(1964)
builds
a
macroeconomi
observe effort by individual workers.
c
model
profitable
which firms can not directly
in
This leads to
a
payment scheme which has the
a
implication that the optimal amount effort for each worker depends on the level
effort put in by other workers.
In
both cases,
a
small
of
increase in activity is
welfare improving.
Identifying the inefficiency associated with monopolistic competition as an
aggregate demand externality does not however imply that movements
in
demand affect output.
12
(12)
and
(13)
Consider for example changes in nominal
are homogeneous of
degree zero in
P,
W
and
fl
,
money
nominal
aggregate
.
As equations
money is
obviously neutral, affecting all nominal prices and wages proportionately and leaving
output and employment unchanged
11
12
best
13
13
.
Thus something else is needed to obtain real
similar point is made by Cooper and
As we have not specified how money is
to think of them as helicopter drops.
A
John
[1985].
introduced in this economy,
it
is
Here, and in the next section, instead of focusing on the effects of
aggregate demand on output in general, we focus for convenience on the more
narrow question of whether changes in nominal money have real effects. The
•esults here and in the next section would apply eoually to non monetary pure
aggregate demand shifts, i.e. shifts which leave labor supply unchanged at a
mven real wage, where the real wage is defined as the wage in terms of the
:onsumption basket. If we modify the utility function to be
16
effects of nominal money.
We examine
the effects of
costs of price letting in the
next section.
1-*
*
Uj
»
(C.i
)
(
(Hj/P)+e)
p
-
Hi
P
«
Then shifts in t will shift the demand for goods given real money balances,
while leaving labor supply unchanged at a given real wage and are therefore
pure aggregate demand shocks. By contrast, shifts in V are not pure aggregate
deamnd shocks.
17
Section
3.
Menu costs and real
We now introduce small
effects
of
nominal
money
costs of setting prices, small
There are
"menu" coBts.
obviously costs to changing prices, which range from the cost
of
changing tags and
printing new catalogs to gathering the information needed to choose the new prices,
informing new customers
these costs,
of
these prices and so on.
which cannot be very large,
This section shows that they may.
activity
in
important macroeconomi
is
c
whether
effects.
menu costs may imply large movements in
response to demand, and may have large welfare effects'*.
The first part of
nominal
Small
can have
The question however
money,
the section formalizes the argument for small
changes in
and shows the close relation between the aggregate demand externality
argument of the previous section and the argument presented in this section.
second part considers larger changes in nominal
money,
The
and focuses on the effects of
structural parameters on the ratio of output and welfare effects to menu costs.
14
We are not the first to make this point. Mankiw (19B5) has pointed out
under imperfect competition, private and social costs of price setting could differ
substantially, leaving open the possibility of large welfare effects of demand changes.
Akerlof and Yellen (19B5a, 19B5b) have emphasized the potential welfare effects of near
rationality under imperfect competition. Decision makers are said to be "near rational" if
they react to changes in the environment only if not reacting would entail a first order
loss. As Akerlof and Yellen point out however, near rationality can be described as full
rationality subject to second order costs of taking decisions, so that their analysis is
directly relevant to this section. Dur contribution is to point out the relation to the
aggregate demand externality emphasized in the last section, and because our model is more
explicitly based on utility and profit maximisation, to give a more detailed welfare
analysis.
that,
le
The effects of
small
changes
by considering
We start
money
nominal
in
the effects of
small
*
change
nominal
in
At
dM,
The argument proceeds
starting from the equilibrium described in the first section.
as follows
money,
i
nominal
the initial
change in aggregate demand,
thus to
a
thu6
a
change
in
nominal
in
money leads to
change in the demand facing each firm,
the change in output
demand is satisfied,
demand for labor,
prices and wages, the change
implies in turn
If
change in the derived
a
the demand facing each worker.
UnlesB firms
Unless
operate under constant returns, each firm wants to change its relative price.
workers have constant marginal utility of
relative wage.
leisure,
its relative price
is
of
second order
who does not adjust his relative wage.
the argument
is
effects on welfare
j
coincidence is not accidental and we return to
first.
:
Vi
over
=
Pi
Let
Vi
Vi (P,
:
be
Vi*
=
a
direct application
the value of
,P,W,M)
.
money.
prices
The second part of
money balances has first order
Let
V,*
Vi*(P,W,M).
firm
be
i.
and of
The argument has very much the same structure
the aggregate demand externality argument of
is
worker
show that the effect on welfare is indeed first order,
we
the same sign as the change in money.
The first part
a
The implication is that nominal
that the change in real
to show
the utility of
Thus second order menu costs may prevent firms
wages do not adjust to the change in nominal
and nominal
firm which does not adjust
a
the same is true of
;
and workers from adjusting prices and wages.
as
each worker wants to change his
show however that the loss in value to
We
a
V«
is
of
a
the previous section
it
;
this
below.
the envelope theorem.
function of
the maximised value of
Pi
firm
as
i,
The envelope theorem then says that
well
Consider firms
as
of
P,
W
and
after maximisation
:
M
FIGURE
to*
3.
AGGREGATE DEMAND EXTERNALITIES AND MENU COSTS
(P/m)
V
p/m )
K>
&>$(?/*')
t**f%Y \ouiS.
-
oua*~)
h>f)(v-/M>)
e°$(t>jM)
VC*) ^vo^'f
.
b^-CPJh)
i
i
19
dV.Vdtl
To
8V./SM
-
first order,
a
same whether or not
it
+
(8V,/8Pi) (dPi/dH)
the effect of
a
4V./4M
change in
the value of
the firm is the
adjusts its price optimally in response to the change
Exactly the same argument applies to the utility
menu costs
on
M
of
the household.
H,
second order
Thus,
larger than the second order loss in utility or in value)
(but
in
will
prevent each firm from changing its price given other prices and wages and each
worker from changing its wage given other prices and wages.
all
nominal
implies
a
implication is that
prices and wages remain unchanged and that the increase in nominal money
proportional
increase
What remains to be shown
in
real
money balances.
that the change in real
is
first order effects on welfare.
aggregate demand and employment, raises
from supplying labor.
stical
1
y
Thus,
it
money balances has positive
However, as we have already shown in the previous
section, the increase in real money balances,
monopol
The
f
associated with the increase
rms prof
'
increases welfare
i
in
ts and
the households'
the neighborood of
in
surpluses
the
competitive equilibrium.
The relation between aggregate demand externalities and the argument of
section is illustrated using the diagram in Figure
Figure
function
of
3
plots the price rule
the price level.
(10)
.
giving the price chosen by firm
The logarithm of
while the logarithm of the price of the
3 ,=
th
i
this
the price level
is
on
i
as
a
the vertical
firm is on the horizontal
one
\
axis
both are
The reason why the argument below is only an illustration is that it only looks at
taking the real wage as given
it is thus only a partial equilibrium argument. The
argument would be a general equilibrium one if we were looking at an economy composed of
louseholds, each producing a differentiated good.
firms,
;
20
measured as ratios to nominal money.
The price rule is drawn tor
(assumed to be set at its monopol
(W/P)
as
log(P«/M)
a
linear function of
firm
(Pi/M)
of
and
(P/M)
The symmetric monopol
lfc
.
intersection
i
sti cal
log(P/M).
price rule has slope greater than one.
combinations
i
1
1
y
of
profit for the
real
competitive equilibrium is given by the
the price rule and the 45 degree line,
of
monopoly power, the
iioprofit loci, giving
We also draw
which yield the same level
sti cal
wage
competitive value) and gives
y
the presence of
In
given real
a
point
E.
Point
A
gives the
highest real profit point on the 45 degree line.
The aggregate demand externality argument can
Consider
a
wage constant.
degree line.
However,
in
proportional
small
decrease
of
price s,
The equilibrium moves from point
the absence of
set of
move from point
E
prices,
to
a
real
this movement back to
lfc
point like
E'
along the 45
a
point like point E'.
E,
so that
small
increase in nominal
money
.
At
money balances would increase and the economy would
the presence of menu costs however,
real
a
E.
But,
find in its interest to increase its price until
hi gher
to
money and the real
coordination, no firm has an incentive to reduce prices
The menu cost argument considers instead
In
keeping nominal
The profit of each firm rises with the increase in aggregate demand.
away from the equilibrium point
the initial
E
then be stated as follows.
absent menu costs,
each firm would
the economy had returned to point
these menu costs,
if
the economy remains at E'
large enough, can prevent
and all
firms end up with
profits.
The figure assumes decreasing returns to scale. Note also that, as firms take the
level as given when choosing their own price, isoprofit loci are horizontal along
the price rule.
rice
E.
21
similar argument, although slightly More complicated, holds
A
shall
not present
It
The presence of
s pecific
r
aggregate demand externality does not depend on the nature
an
We
ole played by mon ey in this section.
produced good, and on the nature of the numeraire.
on money being
wages.
here.
it
also important to note the
is
•for
The results of
of
the
this section depend
That money iB the numeraire
the non produced good and the numeraire.
implies that, given menu costs, unchanged prices and wages mean unchanged nominal
prices and wages.
That money is the non produced good implies that as the government
can vary the amount of
adjust,
nominal
change the amount
money,
real
of
can,
it
prices and wages do not
nominal
if
money balances, the real
quantity
of
the non
produced good.
The effects
If
we want
o-f
larger changes in nominal
to examine
changes in money.
larger changes,
For
its proof
for
money, we can no
larger changes in nominal
the effects of
longer use the result derived above,
money
relies on the assumption of small
the private opportunity costs of
not adjusting
prices in response to the change in money -private costs, for short- are no longer
negligible and depend on the parameters
dependence
as on
the model.
We now investigate this
.
The private costs faced by
well
of
a
firm depends on the size of the demand shifts as
the two parameters a and
order in response to
a
change
in
6.
aggregate demand, thus roughly proportional to the
square of the change in aggregate demand.
private opportunity cost to
a
these costs are of second
As we have seen,
More precisely,
firm expressed as
associated with not adjusting its price
in
a
define L(A
proportion
response to
a
of
change
|
a, 8)
initial
of
100A'/,
to be the
revenues,
in
aggregate
)
22
other firms and households keep their prices and wages unchanged.
demand, when all
simple computation, we get
by
Then,
Kb
{[ (ot-i> 2
«,e>
i
where o(A 2
is
)
i
<e-n ]/[2(i+e(o-n
i.e the closer
the smaller the private cost.
In
costs of not adjusting prices are equal
monopolist to
a
multiplicative Bhift
and
c.
opportunity cost to
proportion
initial
of
response to
a
the optimal
as
a
is
equal
<e-l)/e«] L(
where
If
p
(
is
©-
1
If
v
is
if
in
100A7.
(1+A)
-1
close to unity,
very large,
j
p,(r)
6
L
in
demand
the higher the elasticity of
|
not adjusting prices.
The two important parameters for
the same way as above,
the private
a
i.e if
of
:
,
share
of
wage income in GNP.
the elasticity of
private costs
disutility
if
a
aggregate demand, when all other firms and
/6b is the initial
marginal
of
consumption), associated with not adjusting the wage in
labor is close to unity,
limit,
response
Thus private costs are an increasing function
households keep their prices and wages unchanged, is given by
[
then private
to one,
worker, measured in terms of consumption and expressed as
change of
a
returns are the returns to
to zero
we define the function
If
)
if
Exactly the same analysis applies to workers.
p
o(A 2
the limit,
the higher the private costs of
with respect to price,
them are
+
to constant
They are also an increasing function of
a.
a2
isoelastic demand under constant marginal
in
cost is to leave the price unchanged.
of
]>
third order.
of
The closer « is to one,
scale,
>
labor
the marginal
disutility
of
not adjusting wages are small
is
constant, private costs ire equal
;
labor types are close substitutes, private costs of
adjusting wages are high.
in
of
the
to zero,
not
23
Table la gives the size of menu costs at
proportion
a
of
the firm's revenues
(GNP produced by the firm)
which trt just sufficient to prevent
its price in response to
change in demand
(in
a
terms of consumption)
as
a
proportion
Ta ble
lb
firm from adjusting
gives the size
initial consumption
menu costs
(GNP consumed by the
worker from adjusting his wage.
a
(a)
(b)
Loss in utility (in terms of consumption)
to a worker from not adjusting wages (as
a
proportion of initial consumption)*
Mi/Mo -
Loss in value to a firm from not
adjusting prices (as a proportion
of initial revenues)
=
M,/Mo
al
theta
pha
1.1
1.05
5
1.1
2
1.0
1.3
*
:
5
5
=
6
5
|
the initial
Thus,
a
beta
1. 10
.013
1.4
.001
.00B
.004
.031
1.4
.000
.018
.000
.071
1.2
1.6
.
20
=
003V.
1.
level
1.05
1. 10
5
.066V.
.265
2
.027
.105
si
gma
20
.025
.112
5
5
.
Ill
.418
100
.451
.
1
of
nominal
money,
Mi
the
level
after the change.
given the unit elasticity of aggregate demand with respect to real
balances and the assumption that all
other prices have not changed,
changes in demand to the firm.
less than
.017.
of
money
table la gives
the private costs associated with not changing prices in the face of
The main conclusion is that very small
5V.
and
10'/.
menu costs
,say
revenues, may be sufficient to prevent adjustment of prices.
Results are qualitatively similar for workers.
not
of
Changes in aggregate demand and menu costs
1
"
is
of
which are just sufficient to prevent
worker)
Mo
Table
|
a
changing the effects of changes of
+57.
and
Table
+10'/.
lb
in
gives the private costs of
the demand for final
goods.
It
24
assumes that
and
of
5.5"/.
at
values
to
for p«1.6 and
i
consumption,
so that
between 1.2 and 1.6.
p
costs are again very small
negligible
1.1,
approximately. We expect
117.
O'f
equal
is
a
as
|
117.
a
p
For
changes in the derived demand
p
values of
is
change
in
demand,
they reach
at
looks
lb
required menu
of
.457.
least from the point of
between private costs and welfare effects
in
the change in nominal
dependence is
that table
so
close to unity,
p
output,
,
i.e.
employment and real
change in nominal money at given prices and wages.
size of
a
initial
number which is no longer negligible.
a
resulting from the changes
a
than
increases however, required menu costs become non
The more relevant comparison however,
welfare,
to be higher
labor are
•for
view
the change in utility
money which are implied by
Welfare effects depend on the
money as well as on the parameters
a,
6
p,
complex one and we shall not analyze it here in detail.
a
numerical examples.
It
and
money,
57.
and
107.
and different
cr
Table
gives the required menu costs and welfare effects
with two different changes in nominal
O'f
|
2
the
gives
associated
values of the
structural parameters.
For each of
of
menu costs,
the two changes in money,
expressed as
prices and wages
;
a
proportion
of
the first column gives the minimum value
GNP,
which prevents adjustment of nominal
this value is the sum of menu costs required to prevent firms from
adjusting their prices and workers from adjusting their wages,
prices.
at
given other wages and
The second column gives the welfare effects of an increase in nominal
unchanged prices and wages, expressed
proportion
of
GNP.
in
terms of consumption,
The third gives the ratio of
again as
a
welfare effects to menu costs.
money
25
Table
2
weHirt effects
Menu costs and
Mi/Mo
beta
alpha
1.05
«=
M,/Mo
Welfare Ratio
Effects
Menu
Costs
Menu
Costs
»
1.10
Welfare Ratio
effects
<e-cr»5)
1.
1.2
1.4
1.6
1
1.2
03'/.
1.797.
.077.
1.B37.
60
26
.11'/.
1.917.
.04
V.
1.B27.
.087.
.
1.2
1.4
1.6
.
137.
.
037.
117.
3.547.
32
.287.
3.607.
13
17
.467.
3.727.
B
.157.
3.
57%
24
1.B77.
45
24
.337.
11
9B7.
15
3.677.
3.83'/
1
.
.
.
537.
7
(6»-cr«=10)
1.
1.2
1.4
1.6
1
1.2
7.
31
.117.
1.667.
17
1.027.
17
.237.
1.937.
6
097.
1.117.
12
.367.
2.057.
6
.047.
.997.
25
.167.
1.B77.
12
.077.
1.077.
16
.297.
2.017.
7
.117,
1.277.
12
.447.
2.247.
5
.
1.2
1.4
1.6
.94
.067.
Welfare effects turn out not to be much affected by the specific values of the
parameters, at least for the range
of
values we consider in the table.
Thus,
the
ratio of welfare effects to menu cost has the same qualitative behavior as that
the ratio of
cr
output movements to menu costs.
close to unity,
from 60
for
and
It
is
largest for values of
decreases as these parameters increase.
low values of
a,
p,
©
and
cr
to 5 for
In
high values of
a,
p,
the table,
it
of
and
varies
these parameters.
Demand determination of output
We have until
now assumed that
increases in real
money balances at constant
prices and wages led to increases in output and employment.
the effects of
small
changes
in
money,
When we were analyzing
this assumption was clearly warranted
;
in
the
FIGURE
A.
DEMAND DETERMINATION OF OUTPUT.
-toa (u//p)
^Ovtp^fc'feW'
U>Aj
U»w
7^1"t
&>$ V
(=
Coa
(m/ ? ) t
h-cp vvtc.
U*.>ta~l
).
26
monopol
initial
i
stical
1
competitive equilibrium, as price exceeds marginal cost,
y
always be willing to satisfy
firms Mill
The same is true of workers
price.
disutility
of
their type of
Even
the case.
if
of
wage initially exceeds the marginal
as the real
increase
small
a
in
demand for
they have the option of either
firms do not adjust their price,
cost exceeds price.
we
increase in demand at the existing
When we consider larger changes in money, this may no longer be
accomodating or rationing demand
theory,
small
willingly accomodate
labor, workers will
labor.
:
a
|
they will
resort to the second option
marginal
From standard monopoly
The same analysis applies to workers.
know that firms and workers will
if
accomodate relative increases in demand
(
1
<e/(e-n>«-i
and
(o7 (cr-1
)
)
p-1
This raises the question of whether,
respectively
assuming menu costs to be large enough, an
increase in demand can increase output all the way to its competitive level.
answer is provided in Figure
4.
Figure
4
replicates Figure
price and wage rules under competitive and monopol
is
the monopolistic competitive equilibrium,
monopol
i
sti cal
1
y
satisfy demand, at
that
is
point
B.
they reach the competitive locus.
rather than supply.
demand.
H
given price wage ratio,
a
The shaded area
shaded area
is
.the
sti cal
1
and draws the aggregate
2
competitive conditions.
y
competitive one.
competitive price rule, price exceeds marginal
will
until
A'
l
By
a
the set
is
F
the set of
It
In
of
real
cost
marginal
our case,
A
Along the
;
thus firms
cost equals price,
firms will
supply up to
output-real wage at which firms will ration
similar argument, workers will
supply up to point B'.
The
wage combinations where workers do not satisfy labor
The figure makes it clear that an
output and employment.
until
The
increase in nominal
also makes clear that,
no matter
how
money will
increase
large menu costs are,
i
27
it
impossible, unless the competitive and monopol sti cal
is
i
are equal,
1
y
competitive real wages
the competitive equilibrium through an increase in nominal
to attain
money.
What happens therefore as demand increases depends on both menu costs and supply
constraints.
If
menu costs are large,
If
menu costs are small,
a
supply constraints will come into effect first.
more likely case,
prices and wages adjust before supply
constraints come into effect.
Conclusi pn
The results of
Keynesian models
:
this paper are tantal
i
z
ngl
cIobb to those
y
under monopolistic competition,
of
traditional
output is too low,
because
of
an
aggregate demand externality. This externality, together with small menu costs,
implies that movements in demand can affect output and welfare.
increases
in
money can increase both output and welfare.
nominal
In
In
particular,
fact,
believe these results to be important to the understanding of macroeconomi
fluctuations,
it
is
also clear that there is still
justify Keynesian results.
The scope for small
effects in our model
respect to the real
individual
Let us mention some of
a
while we
c
long way to go for this model
the main
to
issues.
menu costs to lead to large output, employment and welfare
depends critically on the elasticity
wage being large enough
labor supply suggests however
a
(on
small
(p-1)
of
labor supply with
being small).
elasticity.
Evidence
on
Thus the "menu cost"
approach runs into the same problem as the imperfect information approach to output
fluctuations
to demand
if
:
neither can easily generate large fluctuations in output in response
the real
wage elasticity of
labor supply is low.
As
in
the
imperfect
information case, the theory may be rescued by the distinction between temporary and
26
permanent changes in demand.
supply than individuals.
possibility
is
that unions have
a
Hatter labor
More likely, the assumption that labor markets operate as
(competitive or monopol
Bpot markets
abandoned
An other
i
sti cal
1
competitive)
y
may have to be
17
.
The analysis of
this paper is purely static.
issues in extending the model
the presence of
menu costs.
to
If
decisions, with fixed lengths
There are substantial
look at the dynamic effects of
demand on output,
menu costs lead to staggered nominal
of
time between decisions,
conceptual
the model
in
price and wage
delivers,
depending on the particular staggering structure, the same qualitative results as
recent macroeconomi
(1979)
c
and Blanchard
models with staggering,
(19B3)
(see Blanchard
such as those by Akerlof
(19B5)
for
however menu costs lead price and wage setters to use
random periods of time between decisions,
response to
a
level,
and
a
large amount,
little effect of real
price structure
(see Caplin
a
(
1
(S,s)
9B5)
,
a
If
policies, which imply
few prices may be readjusted
implying
money on output,
and Spul ber
more detailed argument).
the results may be quite different
change in aggregate demand, only
may however be readjusted by
a
Taylor
(1969),
in
|
\
they
large change in the price
apart form the distortions on the
and Blanchard and Fischer
(39B5)
for
further discussion).
17
This is the direction taken by Akerlof and Yellen (19B5b) who formalize the goods
market as monopol i sti cal 1 y competitive and the labor market using the "efficiency wage"
hypothesi s.
Append!
x
This appendix derives the market equilibrium conditions
functions
each type of
of
to
(11)
The first derives the demand
the text and proceeds in three steps.
in
cjiven
(5)
labor and each type of product by solving part of
firms and households.
the maximization problems of
These functions hold
whether or not prices and wages are set by workers and firms at their profit
or
utility maximizing level.
The second derives price rules from firms'
profit maximization and wage rules from workers'
utility maximization.
The
third characterises market equilibrium.
Demands for product and labor types
1.
In order to maximize profit, each firm minimizes its production cost
given level of output and wages
a)
for
a
t
n
min
E Wj
N.
subject to
j
(
Nu
E
j«l
N tJ
cr
u-l
cTlcr-l
n
T1?)
-U
(Wj/W)
E Wj
N,
cr
=(n
j
>
Yi
j-1
Solving this minimisation problem gives
Ni
1_
«
i
a
Y,
1
and
j
=
,
=
(n
1-a)
n
where
=
W
(
(1/n)
The demand for
=
where
=
-cr
J_
)
type
(a2)
1-cr
j
therefore given by
is
:
s
j
=
(Wj/W)
m
n
N/n
<a3)
1
N
=.
(E E Wj
i
N
(al)
Y,
-cr
E N
1
1
E Wj
j= l
labor of
m
Nj
W
l
can be
Nu)/W
(n
1-cr)
E Y
i
j
a
m
1
=
=
4
l
interpreted as the aggregate labor index
In order to maximize utility, each household chooses the optimum
b)
composition of consumption and money holdings for a given level of total
wealth Ij and product prices
:
(a4)
e-i
«
A,
max
EC (i
(
l-v
e*
(Mj'/P)
>e-l
«
HI
subject to
E Pi
i
=
C»
Mj
+
j
«=
'
Ij
l
Solving this maximization problem gives
Cu
-e
(Pi/P)
-
i
(a5)
Ij/Pm)
(if
and
Aj
(a6)
(*7)
I.i/P
u
1-9
where
(d/a)
=
P
E P.
i-1
can be interpreted as the marginal
p
The demand for product of
n
-e
Y
and
1-e
)
t
=
Cm
E
J
=
=
is
i
(If
utility
m
e-1)
o-f
laB)
(1-K
real
wealth
therefore given by
1
(a9)
(Y/m)
(P. /P)
l
m
n
where
type
u
1-lf
*
1
1
*
Y
n
C»j>/P
E Pi
(E
(X/P)
=
i
j
(alO)
E Ij
3*1
denotes real aggregate consumption expenditures o-f households and will
to as "aggregate demand".
Note that la5)
(at), (a9) and (alO) imply the following rel ation
between aggregate demand and aggregate desired real money balances
Y
be referred
,
1
(*/(!-*)
2.
where
M'/P
)
H"
(all)
E H'j
j-i
=
Price and waoe rules
a) Taking as given wages and the price level, each firm chooses its
price and output so as to maximize profit
1
n
Vi
=
Pi
Yi
-
E Wj
j-l
(al2)
N.j
subject to the cost function (al) and the demand function for its
product (a9). Solving the above maximization problem gives
:
or-
1
Pi
=
<e/(0-l))n
a
1-ff
Yi
1
W,
=
[
(
(
G/
(
&-
1
)
)
n
1-tr
equivalently
l-«
1
Pi/P
or
m
ot-1
)
(W/P)
(Y
(al3)
1
)]
(l+e<«-l)
(al4)
.
implies that thi price it equal
Equation (all)
Marginal cost.
to 6/($-l)
timet the
Taking as given prices and other wages, each household chooses its
Mage and labor supply so as to maximize utility. Using (a6)
b)
i
P
Uj
u
«=
(al5)
Nj
-
,/P
I
subject to the demand for its type
constraint
of
labor
(a3)
and the budget
i
=
Ij
Nj
Wj
+
Vu
E
laUl
Mj
+
i
Solving this maximization problem gives
i
P-1
u
Wj/P
(ff/(ir-l))p
«=
Nj
equivalently
or
,
P-1
1-P
Wj/W
to
cr
/
=
[
(
(cr/
(tr-1)
)
MP/WMN
(p/u)n
(a!7)
1
)]
Equation lalB) implies that the real wage, in terms
cr—
times the marginal disutility of labor.
1
<
(alB)
(l + ff(p-D)
of
utility,
equal
is
)
Market equilibrium
3.
In equilibrium, desired real money balances must be equal to actual
balances. Thus M
M'. Replacing in (all) gives
Y
=
(K/U-V)
)
This is equation
(al9)
,
we get
(al9)
M/P
=
[(n
1
-ex
ex
-or)
U/(l-X)
)
m
If
[n
(a9)
and
E
(
=
(P,/P)
ex
)
(M/P)
<a20)
l
:
1
N
(a4),
choose the same -not necessarily optimal- price, this
-firms
all
-tx6
(T)
3
i
reduces to
from equations
Then,
:
1
N
the text.
in
(5)
1-cr
1
m
-ex
ex
U/d-H
)
ex
]
(M/P)
(a21)
Substituting equation (al9) into (a9) gives the demand function for
product i, equation (7) in the text. Substituting equation (a21) into
equation (a3) gives the demand function for labor of type j, equation (B) in
the text. Note that as we have not used the price and wage rules to derive
these demand functions, they hold even when prices or wages are not set
optimal 1 y
Substituting equation (a 19-) into (al4) gives the price rule for firm i,
equation (10) in the text. Substituting (al9) into (alB) gives the wage rule
for worker j, equation (11) in the text.
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353-374
1969)
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of
inflation", QJE B3-3
(Auguit
I
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i
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3-24
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:
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B
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i
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a
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IIIIIIIII
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,
1060
M*
47fi
.
:\
t
:
s-
Date Due
13**
BAY03W90
JAN.
4
-Q a