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Digitized by the Internet Archive
in
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http://www.archive.org/details/wagepricespiralOOblan
DEC
working paper
department
of economics
THE WAGE PRICE SPIRAL
Olivier
No.
400
J.
Blanchard
November 1985
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
4
1986
THE WAGE PRICE SPIRAL
Olivier
No.
400
J.
Blanchard
November 1985
DEC3
THE WAGE PRICE SPIRAL'
Olivier
J.
Blanchard
November 19B5
This a much revised version of "Inflexible Relative Prices and
Price Level Inertia." I thank Andrew Abel, Rudiger Dornbusch,
William Nordhaus, Jeffrey Sachs and Larry Bummers for discussions,
Comments by John Sutton and an anonymous referee have lead to
substantial changes.
thank the N5F for financial support.
*
I
Abstract
This paper rehabilitates the old wage price spiral.
It
shows that,
lUer
an
increase in aggregate demand, the process of adjustment of nominal prices and nominal
wages results
•from
attempts by workers to maintain or increase their real wage and by
firms to maintain or increase their markups of prices over wages.
price and wage setting,
staggering
of
price and wage decisions,
inflexible real
of
price level
output.
the process of
adjustment would be instantaneous
the adjustment takes time.
wages and markups *re to shifts in demand,
inertia,
the longer
Under continuous
;
under
The more
the higher
is
the degree
lasting are the effects of aggregate demand on
For
dynamics.
increase in aggregate demand,
An
employment
,
would start
"wage price spiral
the
long time,
i
"
it
was
a
element
central
of
macroeconomi
was argued, would increase output and
leading firms to desire higher prices and workers higher wages;
a
c
wage price spiral, which would end only
this "demand pull"
and when
if
this
inflation decreased real money balances sufficiently to return the economy to steady
could start from
desire from workers to increase their real
state.
Or
the spiral
wages,
or
from firms to increase their profit margins,
a
sides to maintain the same wage and price in the face of
these would also start
through the effect
of
a
wage price spiral,
centerstage.
With rational
there could not be
a
-prices above wages).
adverse supply shock
an
lead to "cost push"
inflation on real money balances,
With the advent of rational
from the attempts by both
or
lead to
or
simultaneous increase
The effect of
dynamics 2
.
left
an
in
all
real
wages and all markups
(of
increase in aggregate demand was to increase
in
order to decrease
The same reasoning applied to supply
comeback,
or
the adjustment was instantaneous.
this paper is that the wage price spiral
more precisely that wage price spiral
any economy in which not
make this point,
Gone were the wage price
.
The proposition of
in
1
workers and firms had to understand that either real wages or profit margins
:
both had to decrease;
spiral
recession
a
expectations, workers and firms had to understand that
money balances and leave output unchanged.
shocks.
inflation, and
expectations, the wage price spiral
nominal wages and prices simultaneously and instantaneously,
real
j
all
should make
a
dynamics 6re likely to be present
price and wage decisions are taken simultaneously.
the paper builds
a
model
which is based on two main assumptions.
first is monopolistic competition in the goods and labor markets
;
To
The
monopolistic
competition gives the simplest acceptable price setting environment to examine such
issues.
The second is staggering of
price and wage decisions.
These two assumptions
together generate dynamics very similar to those described above
this model
.
More precisely,
in
:
Price level dynamics are indeed the result of attempts by workers to maintain
(or
increase or decrease as the case may be)
(or
increase or decrease)
their markups.
their real
wage and by (iris to maintain
Furthermore, there is
a
direct relation
between the inflexibility of real wages and markups to shifts in demand and the
degree of price level
inertia.
The smaller the effect of
shifts in the demand for
goods on the markup, and the smaller the effect of shifts in the demand for labor on
the real
the more slowly will
wage,
the nominal
price level
adjust to offset
aggregate demand disturbances.
As the nominal
price level
adjusts slowly to its equilibrium value, changes in
nominal money have long lasting effects on real
money and aggregate demand.
movements in aggregate demand are not too large,
aggregate demand determines output
in
a
If
sense to be made precise later,
suppliers willingly accomodate the increased
:
demand for goods and labor.
Finally,
there is,
movements.
as
the economy is predominantly affected by aggregate demand shocks,
if
first approximation,
a
In
no relation
between output and real wage
response for example to an increase
in
nominal money,
temporarily increases before returning back to its equilibrium level
output
|
during this
adjustment process, the real wage is neither systematically lower nor higher but
simply oscillates around its equilibrium value.
The paper
the absence of
dynamic effects
is
organised as follows.
staggering.
of
changes
suggests extensions.
Section
in
II
nominal
Section
3
characterises the equilibrium
in
introduces staggering and characterises the
money.
Section III presents conclusions and
I.
Price Setting Hodel
later staggering of price decisions,
we must have
a
model
which price decisions are not taken by an auctioneer but by economic agents.
As we
If
in
ft
we
are to introduce
want to focus on the real
we need
wage,
a
with
model
labor and goods markets.
We want
agents to choose prices and wages, but no single agent to choose either the aggregate
price or wage level
;
the simplest assumption
imperfect substitutes, and many types
substitutes.
we choose
Thus,
model
a
of
is
labor,
to have many
all
of
goods,
all
of
them
them also imperfect
with monopolistic competition
in
the goods and
the labor markets.
1)
The Price and Waoe Rules
I
have derived elsewhere the equilibrium of an economy with monopolistic
competition
in
starting from utility and profit
the labor and the goods markets,
maximisation tBlanchard and Kiyotaki,
1
9B5 3
.
I
shall
start here directly from the
demand functions and the equilibrium price and wage rules
they are sufficiently
;
simple and intuitive that little is lost by not reporting the details of
the
deri vat i on.
There are
good
i
labor,
m
firms,
has nominal
indexed by
each producing
price Pi.
j
=
l,...,n
There are
3
functions for each type of good
a
different good,
n
unions,
labor of type
;
i
j
indexed by
each supplying
has nominal
and each type of
labor
j
a
wage
i
=
l,...,m
different type
W
.,
.
The demand
are given by
;
of
(1)
Y,
=
Kv
(M/P)
(2)
Nj
=
Kn
(M/P)
o
(P./P)
(
-a
(Wj/W)
;
where the price and wage indices
1-6
m
-
P
(3)
(
E P.
1_
m
i
=
1;
ex
1
1
and
P
=
W
|
l_
(
n
Yi,
is
a
prices.
The elasticity of
•function
labor
j,
Nj,
the demand for goods and thus on real
respect to real money balances.
depends on the nominal wage
nominal wages.
all
wage is given by
cr.
j
1,
_1_
l-o-
)
money balances
real
of
and of
(M/P)
which is an index of all
P,
is
a
derived demand by firms.
money balances
returns to scale and is thus the elasticity
of
1,
W
f
a
is
a
6.
depends on
the degree
demand for labor with
specific type of
relative to the nominal
It
the inverse of
the overall
of
The demand for
j
the
nominal
demand with respect to the relative price is given by
The demand for type of
index
!
Z Wj
j«l
relative to the price level
price
1
1-a
n
1-6
i,
>
cr
i
1
ire given by
W
1
nominal
of
>
_1_
)
The demand for good
Pi
e
wage level
labor
W,
j
also
which is an
The elasticity of demand with respect to the relative
The letters
Ky
and Kn are constants which depend on the
parameters of technology and utility
they play no important role in what follows.
;
The price and wage rules are given in turn by
(4)
(Pi/P)
=
(K p
(9/(6-1))
(W/P)
k-1
(M/P)
(5)
(Wj/W)
=
(K„
<cr/(cr-l>)
(P/W)
(M/P)
i
1
)
1+eior-l)
a(p-l)
i
=
l,...,m
1
)l+cr<p-l)
j«=l
n
.
ml e
Consider the pri ce
function given by equation
The parameter
the price.
price.
(«-l)
8
monopolist, •facing
a
the degree of
returns to scale to labor
would be the elasticity
is
of
to
an
a
;
and 6.
firms
if
output supply with respect to
the elasticity of demand with respect
To guarantee the existence of
assumed greater than or equal
demand
a
The price rule depends on two parameters,
(1).
The parameter a is the inverse of
acted competitively,
Each fir» is
first.
the relative
to
interior maximum to profit maximisation,
unity and
is
t»
is
assumed to be strictly greater than
uni ty*
increase in the real wage shifts the marginal
An
an
increase
the relative price.
in
leading under decreasing returns,
for
parameters
(8/(6-1))
;
monopoly power
elasticity
existence
of
marginal
an
.
Each union is also
At
a
a
of
disutility
of
j,
and
a
term
cost and reflects the degree
subject to the demand function for labor given
a
p
and a.
is
(p-1)
work with respect to employment.
demand with respect to the relative wage.
p
is
is
the
The parameter
To guarantee the
assumed equal
to or
assumed to be strictly greater than unity.
given relative wage Wj/W,
received by union
KP
monopolist, maximising labor
interior maximum to utility maximisation,
greater than unity,
constant
each firm in its market.
of
elasticity
is the
a
depends on the various structural
The wage rule depends on two parameters,
(2).
of
KP
the ratio of price to marginal
is
income minus the disutility of work,
by equation
Under
increase in the relative price.
reasons which will be clear below.
Consider now the wage rule
v
shifts the demand curve out,
The constant term has been written as the product of
(8/(6-1))
of
to an
(M/P)
the firm accomodates the increase at an unchanged relative
constant returns however,
price.
increase in
An
leading to
curve upward,
cost
Wj/P;
an
increase in W/P increases the real wage
this increase in the real
wage leads the union to want to
supply more labor, thus to decrease its relative wage.
decreases the relative wage
labor and leads,
for
if
p
wage.
An
increase in
in
two terms
parameters and the second reflects the degree
its market
from equations
(1)
a
higher relative wage
;
;
the same relative
the first depends on
of
monopoly power
of
each
.
later on be interested
We shall
to
the union supplies more labor at
The constant term is again separated
in
increases the derived demand
(M/P)
under increasing disutility of work,
to unity however,
is equal
structural
uni on
(Wj/W).
Thus an increase in W/P
and
(3),
in
fluctuations
of
aggregate output. Note that,
aggregate output it given by
m
(6)
where
2)
£
Y
K
is
The Equi
In
E Pi
i=l
Y,
a
constant
1 i
br
i
)/P
;
K
(M/P)
aggregate output is proportional to real money balances.
urn
equilibrium, symmetry, both across price setters and wage setters,
relative prices and all relative wages must be equal to unity.
that all
for all
(
i
and Wj
=
W
for all
j
in
equations
(4)
and
(5)
implies
Using
Pi
=
P
gives
r-1
(7)
(P/W)
=
(9/(0-1))
KP
(M/P)
(8)
(W/P)
=
,j/(cr-D)
K-
(M/P)
o(p-l)
The first equation,
which we shall
equilibrium relation between the markup
refer to as the
of
m arkup
equation, gives the
prices over wages and real
money balances
»
%r>
«—
•s
(j
>
o
"~
,
a>
en
o
a>
D.
E
o
o o
to
O)
>
^»
^_
O
a
u
a
=3
E
o
o
^—
E
—
>-
o
o
a
e»
o
c
o
y
•fro*
the point of
view of
(«!), an
Unless firas have constant returns
•firm*.
s
increase in real money balances increases aggregate demand and requires an increase
in
the markup.
The second equation,
which we shall
the equilibrium relation between real
view of unions.
in
Unless the marginal
refer to as the real
wages and rial
disutility
of
gives
wage equation,
money balances from the point of
work
is
constant
(p«l),
increase
an
money balances increases the derived demand for labor and requires an
real
increase in the real wage.
The equilibrium is characterised graphically in Figure
log(W/P),
If
p
log(M/P)
space so that both the markup and the real
strictly greater then unity,
determines the level
it
It
1 i
wage loci
br
wage and the level
Given equation
(6),
it
of
real
linear.
are
i f
j
a
i
The equilibrium
money balances and is
determines output.
Given nominal
determines the price level.
is useful,
i
A.
locus is downward sloping.
the markup
the real
of
characterised by point
equi
drawn in the
is
It
strictly greater than unity, the real wage locus is upward sloping
is
money,
1.
um_ whi ch
for
later reference,
would prevail
if
to compare this equilibrium with
the
firms and unions had the same technology and
objective functions, but took prices and wages as given, that is, did not exploit
their monopoly power.
equilibrium.
We
shall
refer to this equilibrium as the competitive
The competitive eouilibrium is very similar to the monopol
l
sti cal
competitive one. The equations characterising it are identical to equations
(8)
except for the absence of
(6/(6-1))
Firms do not use their monopoly power,
output.
lower at
in
so
tne first
and
of
employment.
in
(7)
and
the second.
that their mark up is lower at any level
Unions do not exert their monopoly power either,
any level
(o7(cr-l))
1
The competitive loci
so that
the real
are drawn in Figure
wage is
1.
The
of
competitive equilibrium is given by point
monopol
i
sti cal
ultimate goal
Our
dynamic effects
to better
is
nominal
of
the monopol
in
whether
|
it
understand the presence and the nature
money on wages, prices and output.
introducing monopolistic competition
i
ihows the
A
hat higher
wages is ambiguous.
lower real
or
and
B
competitive equilibrium to have lower output
y
1
Comparing
B.
1
sti cal
1
?
In
we appear
way,
a
competitive equilibrium,
y
equilibrium, nominal money is still neutral,
of
the
What have we gained by
to have
gained very little
just as in the competitive
leading to an instantaneous proportional
increase in wages and prices, and leaving output unchanged.
In
as an
in
another way, we are very close to having gained something.
introduction to the next section,
it
is
to rewrite equations
useful
logarithmic form and to characterise the equilibrium
(8)
p
=
(10)
w
=
cP
s
(
cP
+
a
w
+
(l-a)m
;
a
£
l/«,
a
£
(0,1]
c
+
b
p
+
(l-b)m
;
b
s
l-B(p-l)
b
<
1
1
og (6/ (0-1
)
)
+
log(K P ))/n
and
The markup equation gives the nominal
nominal wage and nominal
returns to scale.
i
ncrease
and
(B)
equations
(7)
become, with some reorganisation
(9)
where
(7)
the price wage space.
in
Denoting by lower case letters the logarithms of upper case letters,
and
and
To see this,
p
gi ven
money =
.
c
=
log (o7 (er-1)
price as
a
)
+
log(K-)
linear combination of the
The coefficient on the wage,
a,
is
the degree of
Unless firms operate under constant returns, an increase in
w.
m
will
v£
The real
wage equation gives the nominal
nominal price and nominal
but
money.
not necessarily positive.
is
wage as
a
are large enough,
6
and
ire close to unity,
p
may even require
a
and
we shall
markups and real
and
a
value of
The price rule has slope
m.
is useful
later to give
for
may be reached through
so that
in
initial
Figure
B.
a
as
and
a
in
the p,
space in Figure
w
or
equal
to one.
w
and p,
are close to
b
j
inflexibility
of
to one
;
if
2,
b
for
a
given
positive,
is
The equilibrium is given by
a
heuristic description
that real
how this equilibrium
Suppose that nominal money increases,
A
higher markup
a
;
higher real
and the new equilibrium at
given w,
wage.
Given p,
wages and prices.
B
'.
.
These two
This process
prices and wages have increased in proportion to nominal money
money balances ere back to their previous level
in
1
Attempts by workers and firms to increase real
;
desired real wages and
desired markups are then again consistent and equilibrium is reached.
adjustment
E
they want to go to
they want to go to point
wages and markups only lead to increases in nominal
ends when both nominal
of
aggregate demand increases, increasing output and
Workers therefore, want
Firms want
a
equilibrium is at
claims are obviously inconsistent.
of
both
If
wages respectively
reflecting the degrees
tatonnement process.
the initial
2,
values of
employment.
so
If
«
If
E.
It
point
decrease in the nominal wage.
a
less than or equal
the wage rule has slope greater than
at
b
wage.
the real
in
wages respectively
The equilibrium is characterised
point
decrease
a
are also close to unity.
b
what follows refer to
in
less than unity
is
b,
increase in the price level, which decreases real
An
shifts in demand have little effect on markups and real
unity,
of
it
linear combination of the
The coefficient on the price,
money balances and the demand for labor, requires
and
a
A
possible path
which prices and wages adjust in turn is ABC..E in Figure
2.
In
this
10
the
cate,
less flexible real
This is only
a
wages and mark ups,
tatonnement process
|
we
the adjustment process.
the slower
now see that staggering leads to
shall
a
similar process in real time.
II.
Most nominal
prices -and wages- tre set for discrete periods of time.
price setters prefer the simplicity of
such period,
a
Staggering and Demand Fluctuations
contingent price path or even
a
a
constant nominal price to both
predetermined -but not necessarily constant- price
Moreover, nominal price changes do not take place all
path.
rather uniformly through time.
This may be partly because
considerations on the part
of
unavoidable consequence
the existence of
some price setters.
a
is
it
simply the
large number of uncoordinated price and
of
explicit contracts;
they are not.
experience
a
when they change their wage or
change in their relative wage or relative price.
process of adjustment to
a
nominal
shock is
a
To study
manageable, one must focus on one particular aspect
of
The actual
involving changes
complex one,
relative wages, relative prices and real wages.
example,
strategic timing
of
More often,
The implication is that wage or price setters,
price,
the same time but
at
Sometimes predetermined prices or wages are part
wage setters.
more often,
of
For each
it
and
in
keep the analysis
that process.
One may for
concentrate on the interaction among price decisions, assuming continuous
wage setting
;
this was done by Akerlof
interaction among wage decisions,
the
[1969],
One may instead concentrate on the
"wage wage spiral",
assuming continuous price
11
as was done by Taylor
setting,
[1980].
Given our focus on the "wage price spiral", we
focus on the staggering between wage decisions on the one hand and price decisions on
the other.
1)
Price and Wage Rules Under Stagge r ing
This leads us to formalize the staggering of decisions in the -following rather
mechanical but convenient way
Time is discrete.
The economy is described in the same way as before
for price and wage setting*".
Thus,
times.
:
All
,
except
price decisions are taken every two periods, at even
nominal prices are set at time
for periods
t
t
and
t+1,
and so on.
decisions are taken every two periods, at odd times, thus at t-1 for t-1 and
so on.
The unit period should be thought as fairly short,
month,
so that
after two months all
The length of
revised.
the order of
say of
price and wage decisions have all
and
a
been freely
the period during which prices and wages are fixed
exogenous and so is the staggering structure 7
t,
Wage
is
taken as
.
Firms and workers are assumed to satisfy demand at the quoted prices and wages
return to this assumption below and characterize the conditions under which
we shall
it
indeed optimal
is
As all
price.
(11)
pt
It
=
is
them to do so.
for
firms take price decisions at the same time,
choose the same
they all
given by
(l/2)[(a wt-i
+
(l-a)mt)
+(a E<w**».lt)
+
(
1-a)
E (nu ,
,
!
t
)
)
]
|
E
12
where the constant term is ignored for notational
expectation of
a
wage chosen at time t-1
prevailing at time
for t-1
Equation
t.
price is
the nominal
t
for
t
and
t
and
(11)
is
is
t+1
the optimal
price for t+1,
money for time t+l
and nominal
denotes the
which the nominal
e
.
price is fixed,
p
t
denotes
therefore the nominal wage still
extension
of
(9)|
states that
it
price for time
the optimal
of
t.
similarly Wt-i denotes the nominal
|
the natural
weighted average
a
and
depends on the current nominal wage and current nominal
value of
It)
variable conditional on information available at time
price chosen at time
the nominal
simplicity. E(
t,
which
money, and of the expected
which depends on expectations of the nominal
Equation
(11)
wage
implies that for each interval during
the expected average markup
is
non decreasing
a
function of expected average aggregate demand.
wage Betters decide about wages at the same time,
As all
In
a
way similar to prices,
all
wages trt the same.
wage chosen at time t-1 for example is given
the nominal
by
(12)
wt-i
(l/2)E(b
=
p
t
-2
+(l-b)m t _,) +(b E(p t !t-1)
+
1
(
-b
where the constant term is again ignored, for notational
chosen at time t-1
depends on
at
pt
-2,
time t-1, and
level
and nominal
implies that,
average real
for
is
weighted average
the price level
(2)
of
still
of
(1)
t
!
t-1
)
]
simplicity.
the optimal
the expected optimal
wage for
at
time t,
each period during which the nominal
a
<m
The nominal
wage for time t-1,
wage
which
prevailing at time t-1, and on nominal money
money expected to prevail
wage is
demand for labor.
a
)
non decreasing function of
t,
which depends on the price
as of
time t-1.
wage is fixed,
Equation
(12)
the expected
the expected average aggregate
13
The dynamic behavior of the economy if now characterised by equation!
and
(12),
specification
a
of
procen.
I
solve the system for
the text,
I
focus on the effects of an
the money
process for money in the appendix;
unanticipated permanent increase
in
nominal
in
money.
It
is
a
The Adjustment of
appropriate normalisation).
money increases at time t«0,
The
intuition.
the system.
from zero to dm
?
(12)
gives in this case
dm
=
Pt
=
At
time t=0,
1
and
(11)
po
(
and
easy to derive unoer static expectations and helps develop the
is
Using
general
increase is both unanticipated and permanent.
What are its effects on prices over time
The answer
of
and
The Price Level
Starting from steady state, nominal
(by
a
counterf actual
unexciting experiment but one which shows most clearly the dynamics
2)
(11)
-a)
(13)
ab
p t
-2 +
(l-ab)dm
|
t= 2,4,...
after the increase in money,
wages have not yet increased
:
firms
increase their nominal price only to the extent they want to increase their markup to
supply the higher level
time t=0 as a=l.
because,
labor.
At
unless b=l,
time t=2,
We can
if
it
Thus,
is
At
of
output.
time t=l,
a
Under constant returns,
wages increase both because prices are higher and
higher real
wage is required to supply
think of the coefficient on
higher level
ab
p
t
-r
as the degree of
price level
of
inertia
nominal prices adjust slowly to an increase in nominal
under static expectations there is
inertia,
a
prices adjust again and so on.
close to one,
price level
there is no increase at
,
a
direct relation between the degree
and the inflexibility of
mark ups and real
wages,
as
;
money.
of
1
(
.
14
measured by
The more inflexible markups and real
and b.
a
the higher the
inertia.
degree of price level
Under rational expectations,
Appendix
wages,
path is instead given by
the price level
(see
)
-1
po
(1
pt
X
-
(
1/2)
pt-2
+
where
X
-
[1
a
<l/4)ab(l+X)D >dm,
(l-X)dm
t«2,4,
|
.
<
pc
1-X
<
.
(14)
X
The initial
<
ab
jump
degree of price level
1
(
|
X
in
-/
(
-
-ab
if
)
ab
nominal
)
/
«=
l+/( 1-ab
0,
-
1
)
if
and
X
has the following properties
ab
-
1
prices is larger than under static expectations.
inertia is now given by
function of ab, but is smaller than ab.
rational
X
)
expectations is obvious
i
at
X
rather than by ab.
X
is
The
increasing
an
That the adjustment should be faster under
time t»0 for example,
price setters take into
account not only the increase in demand but the forthcoming increase in nominal wages
at
time t=l.
and current
price and wage setters take account of current demand
Along the path,
prices and wages, but also of expected increases in prices and wages.
Although the adjustment is faster under rational expectations, there is stitl
direct relation between the inflexibility of markups and real
and b,
and the degree of
price level
adjustment is well described as
a
inertia, measured by X*.
wage price spiral
in
wages,
a
measured by
a
The process of
which the speed of the spiral
depends on the desire of workers and firms to increase or maintain their real wages
and markups in response to the increase in demand.
A
0.99.
numerical
example
of
a
path of
adjustment is given
in
table
1,
for
a
b
=
Tibli
Increaie in Honey on Relative and Nominal Pricei,
1
The Effect*
o-f
an
Time
avenge
w-p
real
0.133
0.0
-0. 133
0.677
144
.677
Mage*
average
mark up**
•0.076
0.009
133
.247
2
.346
.247
-. 100
.654
3
.346
.432
.065
,654
4
.50B
.432
-.076
.492
5
.50B
.572
.064
.492
6
.629
.572
-.057
.371
7
.629
.67B
.049
.371
E
.721
.676
-.043
.279
9
.721
.757
.036
.279
10
.790
.757
-.033
.210
11
.790
.617
.027
.210
12
.B42
.617
-.025
.156
1
.
.
.007
.007
.005
.006
.003
004
.003
.003
.002
.003
.001
.002
0.99
All
numbers in the table should be multiplied by dm
The "average real wage" is the average value of the real wage for the two
period interval during which the nominal wage is fixed.
** The "average mark up" is the average value of the mark up during the two
period interval during which the nominal price is fixed.
+
15
3)
wages during the adjustment process
Real
start with
We
a
higher markup, wage setters
fail
to take
After the increase
puzzle.
a
price setters desire
money,
in
both sides
Under static expectations,
higher rial wage.
a
into account future movements in either prices or wages and »re
systematically disappointed. This cannot happen however under rational expectations
in
particular, as there is no unanticipated movement
expectation path is, after t"0,
(12)
hold for actual
wage
;
during which nominal
firms on the other hand must also,
prices are fixed,
Table
appendix).
1
obtain
a
higher markup.
for
it
Thus,
equations
as
wages are fixed, obtain
every interval
during which nominal
?
(the algebra
is
given in the
They can be consistent because the two intervals described above do not
:
there is then
paradoxical path is the result
a
path of
increases
of
the assumption of
rational
of
a
prices and wages
nominal
in
wage are higher
relevant result is not the paradox, but the existence
in
that there is no persistent deviation of the real
This
turn.
expectations
j
the
expectation path.
rational
The other and directly related characteristic of the process of
is
and
higher real
a
How can these be consistent
such that the average markup and the average real
It
(11)
must be the case that workers
shows that they can be indeed be consistent
coincide but overlap
the real
the rational
money after t"0,
perfect foresight path.
values of prices and wages,
for every interval
must,
a
in
|
adjustment is
wage from its equilibrium value
i
wage simply oscillates around this value as output returns to equilibrium 10
the very nature of
the process of
adjustment under staggering
of
.
wage and price
decisions which implies that there be no systematic relation between real wages and
output in response to demand shocks.
The two paths of
represented
in
Figure
adjustment, under static and rational expectations are
3,
the static expectation path by the ootted
line,
the rational
L
K^or^
3 J
16
expectation path by the thick line. Note that the average nominal Mage, denoted by
is
price,
denoted by
is
u,
always on
locus.
the plw)
4)
the average nominal
locus,
always on the w(p)
u
Aggregate Demand and Output
now we have assumed that firms and workers satisfy demand,
Until
adjustment, output and employment are proportional
the path of
balances.
This may not be the case
i
even after
either supplying or rationing demand.
the option of
determines the outcome, we must return to Figure
to real
monopolist has set
a
1
To see when
along
so that
a
money
price,
it
has
aggregate demand
which is redrawn for convenience
as Figure 4.
The labor market equilibrium condition under monopolistic competition,
gives real wages as an increasing function of real
money,
is
drawn as LL
j
which
the goods
market equilibrium condition, which gives markups as an increasing function of real
money,
is
is
drawn as GG.
given by ABC...E
prices,
:
The path of adjustment following an increase in nominal
after an increase of
nominal
increasing markups and decreasing real
goes to point
B
;
in
the following period,
money
money, price setters increase
money balances,
so that
the economy
wage setters take the economy to point
C
and so on.
Let us now draw the equilibrium loci
under perfect competition,
firms nor unions exert their monopoly power
drawn as L'L',
implying
a
lower real
equilibrium is drawn as G'G',
Consider now point
mark up at
a
F
on
given level
of
demand
;
a
of
output,
lower markup at any level
which gives the monopol
we
can
neither
The labor market equilibrium locus is
wage at any level
implying
the GG locus,
.
i.e if
i
the goods market
output.
of
sti cal
1
y
competitive
ask by how much we can decrease the
o
o
17
markup, and still
have firms willing to supply this given level
that we can decrease the markup until price equals marginal
is
precisely on the competitive equilibrium locus, at point F'.
firms will ration demand.
markup further,
any level
of
of
demand.
cost
In
we decrease the
If
The same reasoning applies to workers
employment we can decrease the real wage until
this shaded region,
Thus,
entirely
If
demand will
will
i
stical
1
y
region
;
general
the degree of
determines the degree
of
of
the change in nominal
of
real
know that the
we
leave the path of adjustment entirely within the
depend in
money will
in
substitution between goods and between labor types, as this
monopoly power and the size
money and the parameters
a
of
oscillations
of
the real
the region,
and b,
wage movements during the process of adjustment.
unity imply small
as
and
and
cr
Values of
wage and the markup,
increase the amount the monopoly power
increase the size
of
of
on
the size
they determine the size
and
a
and
b
close to
thus make it more
likely that the path of adjustment remains outside the shaded region.
9
4.
competitive equilibrium lies strictly inside that region, so that
whether this is the case for larger movements
on
|
adjustment lies
This is the case for the path drawn in Figure
enough increases in money will
small
ration demand
the path of
if
there is some monopoly power in both goods and labor markets,
monopol
either L'L' or
of
both satisfy it.
determine output and employment
the non shaded region.
in
at
|
reaches its
it
either firms or workers or both
outside of this region, they will
this happens
|
competitive equilibrium value. Let us shade the region to the right
G'G'.
The answer
Small
values of
firms and workers respectively,
the non shaded region and thus also make demand determination of
output more likely.
Note that monopolistic competition plays an important role here
than provide
a
convenient price setting environment.
To aet
and does more
demand determination
of
le
output to both decreases and increases in demand,
needs to start from an equilibrium in which,
cost and the wage exceeds marginal
marginal
•for
at
least within some bounds, one
whatever reason, price exceeds
utility
of
leisure.
This is what
monopolistic competition provides here.
To summarize
the results of
initial
pair of prices and wages,
and its
inverse,
too low
:
in
money,
the markup).
firms desire
a
this section,
movements
money create,
desired changes in relative prices
After an increase in money,
higher markup, unions
they are both too high.
in
a
As workers and
If
movement of nominal prices is slow.
aggregate demand,
monotoni cal
1
y
to
if
(the real
wage
higher real
wage
|
after
a
decrease
firms reestablish in turn their
aggregate demand
relative prices are relatively inflexible, the
During the process of adjustment,
oscillates around its equilibrium value.
in
the
both relative prices are
desired relative prices, nominal prices and wages adjust until
returns to its equilibrium value.
at
During the process
they are not too large,
its equilibrium value.
of
the real
wage
adjustment, movements
determine output which returns
19
Cone us on
III.
the process of
that
We have seen
1
1
aggregate demand is well described as
demand,
adjustment
a
of
nominal
wage price spiral.
a
general
increase
back to its equilibrium value.
in
nominal
richer menu
of
The model
the higher the degree of
is
of
if
at
a
:
we allow for
Suppose for example that,
output by partially accomodating the increase in nominal
the higher the degree of
longer lasting the wage price spiral.
maintain output at
higher level
accomodation, the stronger and the
The monetary authority is indeed able to
for
a
longer period of time but at the cost of
increase in prices and
a
longer period of
a
does not easily generate however
the rate of
is
an
inflation
and then decreases over
is
price increases,
a
What the model
In
the example
largest at the beginning, when output and
in
real
wages and mark ups are largest,
time as output returns to normal.
accomodation goes to unity,
inflation.
accelerating wage price spiral.
employment are highest and desired increases
nominal
inertia.
increase in nominal money, the monetary authority attempts to
this case,
,
is
presented in this section
generates more interesting wage price dynamics
maintain the higher level
sketched above
price level
shocks, monetary policies and staggering structures
after the initial
higher initial
output
relatively straightforward and involves looking
monetary policy to respond to wage and price developments.
In
wages and mark
prices and wages which last until
There are at least two directions in which the model
The first
change in
The smaller the desired increase in relative prices,
the slower the wage price spiral,
should be extended.
a
After an increase in
attempts by workers and by firms to maintain or increase real
ups lead to
prices.
prices to
As the
degree
of
is
as
the monetary authority accomodates one for one
the result
is
not
that
high inflation but an infinite value of
20
the price level
the initial
the time 0+
at
Learning by agents over
increase in money.
time 0* the goals of the monetary authority it needed to generate accelerating
inflation.
We have focused only on
demand shocks.
can be used to look at the
The model
effects of supply shocks instead, be they technological
other shocks to labor supply.
the real
wage and
a
decrease
An
and mark ups are inconsistent.
At
This starts
the initial
a
,
a
union cost push or
shock requires
adverse technological
output.
in
shocks
level
of
wage price spiral
a
output, real wages
which stops when real
money balances and output have decreased to the new equilibrium level.
efforts by the monetary authority to slow the decrease
decrease in
Here again,
output lead to more
in
inflation along the path of adjustment.
Finally,
one would want to study the effects of
structures, and
in
particular to relax the assumption
and simultaneous wage decisions.
of
Staggering
Staggering
of
of
demand with respect to relative wages will
adjustment
of
the price level'
now affect the
also affect the speed of
1
.
extensions is more difficult and more important.
The second set of
presented here to generate large and prolonged effects
aggregate demand, both
supply more output at
a
price decisions implies
wage decisions implies that the
elasticity
more labor at
of
demand with respect to relative prices will
speed of adjustment of the price level.
For the model
simultaneous price decisions
This can be done by extending the continuous
staggering structure suggested by Calvo C19B2],
that the elasticity of
more realistic staggering
a
a
and
p
must be close to unity
:
of
firms must be willing to
slightly higher markup, and unions must be willing to supply
slightly higher real
wage.
This seems indeed to be true
:
21
mi
croeconomi
evidence on markups suggest that they respond weakly to shifts in the
c
demand for goods and evidence on real
and slowly to shifts in demand for
wages suggest that real
labor.
wages respond weakly
there are serious issues in reconciling
But
this observed behavior with what we know about technology and tastes
cost
not
In
our model,
is
constant
constant
constant desired markup
(o"l).
But
!)
(a
indeed justified
is
overtime payments,
our model,
disutility
a
costs of changing production
incurred because of costs of changing the number
constant desired real wage
employment is constant
of
equally shared among workers, and
if
(p«l)
.
(b»l)
is
justified
of
This suggests two directions of research,
be smaller
research,
which has
than individual
is
p's.
long
a
There is substantial mi croeconomi
The second,
to study the role of
(p-1)
both aimed at explaining why
tradition,
contracts
is
b
of
the level
if
If
this real
the paper
c
large.
may be close
p
may
which is now the subject of active
in
labor markets,
contracts take for example the form
of
is
to explain why the unions'
and to see whether
contracts can explain why real wages seem to respond little to movements
employment.
labor
the individual
evidence however that this elasticity is small, that the individual
The first,
the marginal
unions maximize the utility of their
supply elasticity with respect to the real wage.
to unity.
if
fluctuations in employment ire
If
representative members, then p-1 corresponds to the inverse
and
cost it
workers employed, point to increasing short run marginal cost CBils 19833.
In
of
marginal
if
there is much evidence that short run marginal
inventory behavior points to substantial
i
[Blanchard 19B33,
of
a
i
of
in
free determination by the firm
employment subject to an agreed upon real wage employment schedule,
wage employment schedule is relatively flat,
6re likely tc go through 11
.
the qualitative results
x
)
22
Append
i
the Price Level
l)The Behavior of
The behavior of prices is first derived for
then for the specific process described
Using equation
for both t-1
(12)
expectations and replacing in
where
zt
ab
[p
t
-2
taking E(w t *ilt)
t+1,
using iterated
gives
E(pt!t-1)
+
process for money, and
+
p
E(p t *alt)]
+
t
+
(l/4)z
t
given by
is
z t
(1/4)
=
pt
(10)
general
the text.
in
and
a
=
a(l-b)tiH-,
+
E(mtlt-l)
2(l-a)[m t
+
E(m e .i It)]
+
EUfilt)
+
EUtoalt)]
(Al)
+
Equation
the second for
(Al)
pt
.
must be solved in two steps.
Denote by
a
star the expectation of
information available at time t-1.
on
a
is
to solve for E(p t lt-1),
variable conditional on
Then taking expectations of both sides conditional
information available at time t-1 and rearranging gives
(2ab-4)
p*
be the smallest root
of
ab
(A2)
Let
The first
X
\
p* t -2
=
(1
-
+
/(1-ab)
)/ (1
t
+
abX
+
ab
2
p* t
+
* 3
=
-z* t
(2ab-4U
/(1-ab)
+
ab
=
0,
so that
23
This root is an increasing •function of ab, equal
ab B
Solving
l.
by factorization,
(A2)
for ab-0 and to
to
subject to the constraint that
for
1
does not
pt
explode, gives
«
p*t
(A3)
p«t-j
X
+
(X/ab>
i
E X
i-0
z* t
* 2
»
i
i
so that
E(ptlt-l)
X
pt- 2
(X/ab)
+
E
E(lt* 2 ilt-1)
X
i-0
The second step is to solve for
E(p** 2
tt)
and E(p t lt-1)
in
p
gives
(Al)
t
.
Deriving E(pt»slt) from
p
t
i
»
<4-ab(l+X)
I
)p
t
ab(l+X)p
=
to dm
holds for actual
»
p*+=
;
i
E X
i-0
[E (Zt* si
I
t-i +E <z** 2 i
)
*2
1
1)
]
increases at
m
the increase in unanticipated and permanent.
values of
p
note that for t>0,
and
z
there is no uncertainty and thus
rather than for their expectations.
Note also
=
i
Zt* 2
E X
1=0
X
pt
+
i
=
(l-X)dm,
(l-X)dm
This gives in particular,
provides,
I
X
for t>0
(X/ab)
E (p 2
+
z t
the price path,
To solve for
that,
+
now consider the specific path of money described in the text,
time t=0 from
(A3)
t _2
and replacing
(A3)
0) =p 2
for
,
t
= 0,
we have
for
so that
t
>
for t=0,
p2
as
a
function
another relation between po and
p2
.
of
p
.
Equation
Noting that
E
(
p
!
(Al)
-
1
)
in
=0 and
turn
24
(l-(lM)ab) po
(l/4)ab
-
Solving the two equations in
path
the price level
[i-« +(l/2)a(l-b) Ddm
+
p2
and
p
gives the following characterization of
p2
i
-1
2)
po -
(1
p t
X
(l/2)«
-
p*-2
(l-X)dm
+
The Behavior of
x
t .*,
wage at time
=
Wo
-
po
c
-
=
wt*,
-
pt
=
C
a,b
Kf2
<
w t *,
5
-
ab
1
+
(1
(l/2)b(l+(l/X)
so that
a
=
<
1
=
•
(1
/(1-ab)
(l/2)b (1+(1/X)
1/2)
b
)
)
-
)
-
from equation
;
(12)
at
time t-1 and
prices,
d+X)-l]
1
-
(p t
dm)
* »,.,
<
>
13(pt* 2
-
-
dm)
we have
+
/(l-ab))/(l
=
b/(l
(l/2)b(l+(l/X)
-
<
t
[Q/2)b(l+(l/X>)
=
pt *2
From the definition of X,
(1+(1/X))
(
po
(l/2)b(l+X)
t
1
)dm
]
Wage
the above characterization of
Xo
+ X)
for t»2,4,...
the Real
Let Xt be the real
•from
(l/4)ab(l
-
CI
/
(1
1
>
)
+
(1
Massachusetts Institute
-
/(1-ab)
+
of
>=
2/(1
-
/( 1-ab)
)
/(1-ab))
ab/(l
>
/(1-ab))
-
/(1-ab))
-
)
*
/(1-ab))
-1
Technology
=
/(1-ab)
>
=>
x** 2
<
t
+ 1,
and
.
.
,
25
References
"Relative Wages and the Rate
Akerlof, George,
Economics LXXXIII
,
(anc
j
(
1
969
),
Janet Yellen,
353-74
"A
Inflation," Quarterly Journal
of
of
.
Near Rational
Model
Wage and Price Inertia," Quarterly Journal
of
of
the Business Cycle,
Economics
with
forthcoming LXXXIII
,
(19B5)
Bils,
Mark,
August
"The Production and
Industry," Journal
__»______,
(
"p r
i
Simonsen, eds
.
(
of
Political Economy
in
(Cambridge
an[
j
an
,
Martin,
:
Calvo,
Thesis,
Ph.D.
MIT,
Noouhiro Kiyotaki
of
Indexati on
Inertia," in
Rudiger Dornbusch and Mario
"Monopolistic Competition, Aggregate Demanc
Nominal
and Franklyn Holtzman,
I
the American Automobile
365-400.
91-3,
,
of
pp. 3-24.
MIT Press)
Surveys of Economic Theory Vol
196B)
,
Inflationary World
Externalities, and Real Effects
Bronf enbrenner
Inventory Behavior
ce Asynchronization and Price Level
Contracting and Debt
,
Cost and Price",
of
19B5.
Blanchard, Olivier,
__.
Behavior
"Essays on the Cyclical
"A
Money," mimeo MIT, November
Survey
of
19B5.
Inflation Theory,"
(American Economic Association:
in
MacMillan,
pp. 46-107.
Guillermo,
"On
the Mi crof oundat l ons of
Staggered Nominal Contracts
i
a
First
Approximation," mimeo, Columbia University, January 19B2.
Fellner, William,
"Demand Inflation,
Cost
The Public Stake in Union Power
,
Inflation and Collective Bargaining,"
P.
Bradley ed
.,
(Char 1 ottesvi
1
1
e:
1
in
959 pp
)
26
225-54.
Fethke,
Gary and Andrew Policano,
Aggregate Implications
Monetary Economics
Taylor, John,
of
XIV
the Pattern of
,
LX
X
XV
1
1 1
(19B4),
(19B0),
151-71.
Governors
the Federal
of
Overview
Price Determination
of
of
of
Political
1-24.
"The Wage Price Mechanismi
Econometrics
Negotiation and
Alternative Contract Structure*," Journal
"Aggregate Dynamics and Staggered Contracts," Journal
Economy
Tobin, James,
,
"wage Contingencies,
,
0.
Reserve System,
of
the Conference,"
Eckstein, ed.,
1970).
in
The
(Washingtoni
Board of
.
27
Footnotes
See for example
written in
2
"A
Inflation Theory," by
M.
Brof enbrenner and
This point was in fact made many years before the rational
The model
W.
Fellner
(1959,
pp
expectation
235-236).
agnostic as to whether unions are maximising the utility
is
representative member, or maximising some other objective function.
affects the interpretation and the likely value of the parameter
issue to which we shall
*
the fixed cost
of
of
a
their
This however
below,
raising an
firms as given, we do not need to introduce explicitly
The analysis in the text
faced by each firm.
such
p
of
return later.
As we take the number
presence
Holtzman,
F.
1965.
"revolution" by
3
Survey of
fixed cost.
is
consistent with the
Thus while we rule out decreasing marginal
cost,
we do
not rule out decreasing average cost.
Whenever we refer to the nominal
relevant,
the logarithm of
and nominal
*
In
period,
the reader
price,
the nominal
price.
is
to understand,
whenever
The same applies to the nominal
wage
money.
the absence of
is the
staggered price and wage setting, the equilibrium, each
equilibrium described in Section
only from the presence of
I.
Thus,
dynamics arise
staggered price and wage setting.
this model
in
Eliminating all
sources of dynamics allows to focus more simply on the dynamic effects
of
other
price and
wage stagger ng
i
The staggering structure we consider
that
it
would not survive endogeni
the interest
of
z
at
l
on
is
particularly vulnerable to the criticism
of
staggering decisions.
It
firms to coordinate price chanoes with wage chanaes.
is
clearly
in
Replacing the
2B
decisions would be more attractive
aloebra substantially.
Fethke and Policano
e
Equation
(11)
the rule which comes out of expected profit maximisation by
not
subject to the constraint that the nominal
the equilibrium condition that all
and
to compare
may be useful
It
would however complicate the
It
further discussion and work on endogenous staggering, see
and t+1,
t
same in both periods,
to one.
this respect.
(1984)
is
firms over periods
For
in
price be the
relative prices be equal
the two rules in the simple case of
constant
returns to scale.
Under constant returns,
Pt
(1/2)
=
(wt-i
E(w**i
+
reduces to
(11)
It)
i
)
whereas the price obtained from explicit profit maximisation is,
discount factor on second period profit to be equal to
not
Pt
1
=
ogari thms)
KP
p
(letters now denote levels,
:
[(M*/(Mt+pE(M t *iit))Wt
+
(pE(Nt*iH«*s
It)
/(Nt+pE(M«*i It))
Comparing the two expressions shows three main differences.
of
the discount rate.
The third is that P t
and
t+1.
An
assuming the
The second
is
an
is
the presence of
arithmetic rather than
a
3
The first
is
the covariance of
M
geometric average
of
the presence
and
W
W
at
time
other way of stating the differences between the two rules is that,
the correct rule,
the price is an average of
t+1.
at
t
under
current and expected wages, with weights
which depend on current money and the joint disribution of future money and future
nominal
If
wages.
the unit
then
(11)
1=
period is short,
a
oood
so
that
p
is
close to one and E(Mt-nlt)
approximation to the correct Drice rule.
Our
is
close to Mr,
reason for using
29
that the approx mat 1 on
i
9
it
not
the tource of
the results Me locus on.
This suggests that explaining the behavior of relative prices,
nominal
quite apart from
rigidities should be high on the research agenda. This appears indeed to have
been the approach 'followed
in
the
1960s
(as
summarized by Tobin [1970] lor example).
Research was focused on documenting and explaining the slow and small
wages to unemployment,
inflexibility
of
the slope of
mark ups.
Nominal
the short run Phillips curve,
or
reaction
of
the
price and wage inertia were then obtained not from
staggering but from assumptions about expectations.
10
use.
The oscillations are partly the result of
For
more complex structures,
wage decisions,
11
the aggregate real
the simple staggering
structure we
such as continuous uniform staggering of price and
wage may not oscillate at all.
One can also allow for an n-step
(rather than one-step as in the text)
production process and allow for staggering of price decisiosn along the production
process.
This has two relevant
implications.
It
increases tne degree
of
price level
inertia and may generate systematic movements in the structure of relative prices in
response to changes
in
nominal money.
See Blanchard
[19B3D.
Akerlof and Yellen C19B5] have recently constructed
these lines
;
a
macroeconomi
c
model
along
they formalize the labor market as characterized by efficiency wages.
^353 0/5
MIT
3 ^
60
UBJWUfS
M*
476
3
^
Date Due
5 '89
AG
0EC2
81989J
12
MAR
mi
H
19
OlK
fa
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