Theoretical Economics Letters, 2011, 1, 114-117
doi:10.4236/tel.[phone] Published Online November 2011 (http://www.SciRP.org/journal/tel)
On the Dynamic Role of Monopolistic
Competition in the Monetary Economy
Masayuki Otaki1, Yoshihiro Tamai2
1Institute of Social Scienc e, University of Tokyo, Tokyo, Japan
2Department of Economics , Kanagawa University, Yokohama, Japan
Received August 21, 2011; revised October 22, 2011; accepted October 30, 2011
Abstract
Much static research on the new Keynesian economics is based on the distortion caused by monopolistic
pricing. When the theory of monopolistic competition is extended to monetary dynamics in an overlapping
generations (OLG) model (Otaki 2007, 2009), the underemployment problem is resolved by a proper mone-
tary policy. However, even in the full-employment equilibrium, the market mechanism does not attain the
socially optimal allocation. Since the rate of population growth is assumed to be zero, the optimal gross in-
flation rate in the model is unity. There is no such coordination motive in a monetary economy, and hence,
the inflation rate may exceed unity. The monopolistic power lowers the inflation rate. The prices of the cur-
rent goods relative to the future goods increase by virtue of the monopolistic power. This improves the life-
time utility because the lowered inflation rate corrects the consumption stream, which is biased toward the
current goods.
Keywords: Overlapping Generations Model with Money, Monopolistic Competition in Dynamics, Inflation,
Dynamic Inefficiency
1. Introduction
It is well known that monopolistic competition plays an
important role in the new Keynesian economics.1 The
price of goods relative to that of leisure becomes too
high, resulting in a shortage of consumption and an ex-
cess of leisure. The deadweight loss of monopoly makes
room for government intervention. Thus, the results of
partial equilibriu m analysis can be applied to the general
equilibrium of preceding research. However when we
extend the theory to monetary economic dynamics in the
OLG model (Otaki [1,2]), we see that a proper monetary
policy can resolve the underemploymen t problem.
Nevertheless, another distortion remains. Even when
the economy enjoys the full-employment equilibrium,
the socially optimal allocation differs not only from mo-
nopolistic competition but also from the Walrasian equi-
librium.
When the population growth is zero, the optimal gross
inflation rate is unity. The reason for this is that the
quantity of goods transferred to old individuals is the
same as that given by them to the previous generation.
Since such coordination is impossible in the monetary
economy, where decision making is separated generation
by generation, the equilibrium gross inflation rate possi-
bly exceeds unity.
In the dynamic model, the monopolistic competition
lowers the inflation rate. Since the workers’ reservation
wages depend on the current and future price levels,
monopolistic pricing heightens the current price relative
to the future price, and lowers the inflation rate. Thus,
the monopolistic competition dominates the Walrasian
equilibrium in the inflationary monetary economy.
The paper is organized as follows. Section 2 constructs
a model based on Otaki [1]. The welfare comparison
between the monopolistic competitio n and the Walrasian
equilibrium is treated in Section 3. Brief concluding re-
marks are made in Section 4.
2. Model
2.1. Structure of the Model
1For example, see Mankiw [3, 4], Blanchard and Kiyotaki [5], and
Stratz [6]. We consider a model based on Otaki [1]. Consider a

115 M. OTAKI ET AL.
standard two-period OLG model with money. There is a
continuum of perishable goods indexed by [0,1]z

.
There is no fixed cost for production. Numerous poten-
tial competitors exist in each industry . We consider
two cases for the market structure. One is that each good
is monopolistically produced by a firm. The other is the
Walrasian equilibrium where entry is free in each indus-
try and every firm behaves as a price taker. Individuals
are born at a continuous density . They can
supply one unit of labor and do so only when they are
young.
z
[0[0,1] ,1]
2.2. Individuals
Individuals have identical lifetime utility functions,

U

12 12
11
(, ,)(, )
tj tjtjtj tjtj
UC CUC C,



 

(1)
11
1
111
0() .
ii
tj tj
Cczdz










(2)
( )U
1<is a well-behaved linear homogeneous function and

. is the consumption of good at
the i th stage of life during period .
()
i
tj
cz
z
tj

is the disu-
tility of labor. tj

 is a definition function that is one
when an individual is employed, and zero when unem-
ployed.
We can obtain the following indirect utility function
by solving the optimization problem:
V
(), <0
tj tjtj
tj tj
tj
W
Vv v
P


 


  
 


 ,

(3)
where
1
11
1
1
0
(),.
tj
i
tjtjtj tj
P
P
Ppzdz



 

 






(4)
tj
W denotes the nominal wage. denotes the
profit that is equally distributed to each individual inde-
pendent of employment. Using Equation (3), we can cal-
culate the nominal reservation wage
tj

R
tj
W as

=.
tj R
tj
tj
P
Wv





(5)
Because our main concern is an underemployment
equilibrium where some ind ividuals are unemployed, the
equilibrium nominal wage is equal to
tj
W
R
tj
W

.2
2.3. Firms
The demand function of good during period t zj

is
()
()= ,
d
tj
tj
Y
PP

tj
tj tj
pz
cz
 





 (6)
where d
tj
tj
Y
P


is the real effective demand defined by

1
,
tj
L


d
tjtj tj
tj tj
tjtj tj
tj t
tj t
YW
ya
PPP
MG
PP



 



 




)
(7)
where (
tj
a

 is the marginal propensity to consume.
tj
L

is the current employment level. 1tj denotes
the nominal money stock carried over from the previous
period. Thus, the first term on the right-hand side of
Equation (7) is the aggregate consumption function of
the younger generation. The second is the aggregate con-
sumption of the older generation. The last term is the
government expenditure.
M
2.3.1. Case for Mon opolistic Competition
The profit maximization problem of a monopoly firm for
good is
z
2The nominal wage is negotiated between a firm and the employed
individuals when the economy attains the full-employment equilibrium.
If the nominal wage is determined by an asymmetric Nash bargaining
solution where the threat point is , the equilibrium nominal
wage, , becomes
(, )0R
tj
W
*
tj
W
*() ()
()=(1 ).
tj tj
R
tj tj
p
zc z
Wz W



 

denotes the parameter that represents the firm’s bargaining power.
is the inverse of the production function with a decreasing mar-
ginal product. The profit function of a firm, , is
()
tjz 

*
()=[()()() (())]
=[( )()(( ))].
tjtj tjtjtj
R
tjtjtj tj
zpzczWzcz
pzczW cz


 


Thus, the production decision process of the firms in 2.3 can be applied
intact independent of the aggregate demand level. See Otaki [2]fo
r
more details.
() ()
()=[()()( ())],
max max
> 0, 0,
tj tj
R
tjtjtjtjtj
pz pz
zpzczWcz






(8)
where ( )

 is the inverse of the production function.
The solution is
**
1
()=( ()),.
1
R
tj
tj tj
W
pzcz z






(9)
Substituting (5) into (9), we obtain





**
*
**
,
11
*,
==
11
tj tj
tj
tj Mtj
Mt j
yy
P
Pv
v













. (10)
Thus the equilibrium inflation rate, *
M

, is the
non-increasing function of the real GDP per firm *
tj
y

.

M. OTAKI ET AL.
116
(10) is the difference equation that the equilibrium price
sequence, , must satisfy. It is noteworthy that
has no relationship with the sequence of
nominal money supply, 0. This implies the non-
neutrality of money in the sense that real cash balance,
*0
{}
tjj
P
*0
{}
tjj
P {}
tjj
M
*
tj
tj
M
P


, can be determined independently of the price
level, .
*
t
Pj
tj
2.3.2. Case for the Walrasian Equilibrium
We assume that every firm in any industry behaves as a
price taker. It is clear from Equation (8) that the maxi-
mization yields . Substituting (5)
into this result, the equilibrium inflation rate,

(
tj
pz y
*
=
R
tj
W


* )
*
W

, satis-
fies
*
= (
W



* .
tj
y() )v (11)
Because is a decreasing function of v

, it is
straightforward from Equations (10) and (11) that
**
()
Wt
j
tj tj
GS

t
**
(),
Mtj
yy


**
(
Wt
y 

1
=
tj tj
MM
 

*
j tj
 .y

)
0.
(12)
The equality holds when is not larger than
unity. Thus, the inflation rate in the monopolistic compe-
tition is lower than that in the Walrasian equilibrium
when inflation occurs.3
j
2.4. Government
The role of the government in this model is very simple.
It finances the wasteful expenditure by seign-
iorage . Namely, tj
G
t
S
, j


(13)
We specify the money supply rules as follows:
1). The government arbitrarily chooses the current
money supply
M
. This decision does not affect the
initial price level, , because the equilibrium price se-
quence, , is determined by Equation (10) or
Equation (11) (Rul e 1).
t
P
*0
{}
tjj
P
t
2). From period onward, is controlled so
as to keep the real cash balance equal to
1tj M
t
t
M
mP .
Namely, =,
tj
tj
M
m
P


1j

 holds (Rule 2).
From rules 1 and 2, and Equation (13), the current
budget constraint of the government is
==
tj t
tj t
SG
m
mg
P



.
P
(14)
2.5. Market Equilibrium
There are three kinds of markets: goods, labor, and
money. We focus on the first two. The labor markets are
in equilibrium when the equilibrium nominal wage is
equal to the nominal reservation wage. It is expressed by
Equation (10) or Equation (11). The equilibrium condi-
tion for the goods markets in the stationary state is
***
=( ).
j
ya ym   (15)
Equation (15) is the Keynesian cross in this model.
Suppose that real money supply, , is sufficiently small.
Then, the solution for (15), m
*
y
, is located within .
Such a case corresponds to the stationary underemploy-
ment equilibrium.
(0,1)
To sum up, for the arbitrarily given initial price level,
, is determined by Equations (10) and (15)
or by Equations (12) and (15).
t
P** (,)
jy

3. Welfare Analysis
In this section, we first show that the allocation by the
monopolistic competition dominates that by the Walra-
sian equilibrium for all production levels *
y
. Second,
we explain the reason for th is by considering th e socially
optimal allocation.
To keep the GDP level at *
y
, the real money supply,
*
j
m, must satisfy the following equation: 3
***
=[1(())= .
jj
ma yjMor  ] ,y W
Using Equations (3) and (5), the lifetime utility at the
stationary underemployment equilibrium, *
j
V, is repre-
sented as
*
****
** *
()=(())
=(())(),= .
t
jj
t
j
VyvyP
vyyy jMorW




(16)
3When an equilibrium falls into deflation, i.e., *
j

becomes less than
unity, the effective inflation rate that the individuals face is fixed at
unity. This is because the deflation levies the money holding of the old
generation proportionately to its negative inflation rate. See money
supply rule 2 and Equation (14) below.
4Although the sign of the first derivative of a(
・ ) is ambiguous, the real
money supply
From Inequality (12), we obtain the following theo-
rem.
Theorem 1 In any stationary equilibrium,
y

, the al-
location of the monopolistic competition weakly domi-
nates that of the Walras ian equilibrium. Namely,
*
j
mfor attaining some fixed *
y
can be determined,
independent of the sign.

M. OTAKI ET AL.
117
** ***
()(), (0,1],
MW
Vy Vyy
where *
M
V is the utility of each individual in the mo-
nopolistic competition, and is that in the Walrasian
equilibrium.
*
W
V
Inflation, which makes the Walrasian equilibrium dy-
namically inefficient, is a true social cost incurred from
using money, and hence, the monopolistic competition
can contribute to the economic welfare through a reduc-
tion in such cost.
In addition, the gain obtained by the monopolistic
competition is actually attributed to the monopoly rent
*
*
t
t
P
, because the real reservation wage is reduced by the
disinflation as appears in Equation (16). It is also note-
worthy that although the increasing marginal cost is the
only cause of underemployment in the static monopolis-
tic competition model, it is not a crucial factor in the
dynamic model as long as the fiscal monetary policy is
properly executed.
4. Concluding Remarks
This paper investigated the dynamic role of the monop o-
listic competition in the monetary economy. The follow-
ing results are obtained.
First, the monopolistic competition lowers the infla-
tion rate. This is because the monopolistic power in-
creases the current price level relative to the future price
level, which is woven into the nominal reserv ation wage.
Second, the monopolistic competition weakly domi-
nates the Walrasian equilibrium in resource allocation. If
coordination between generations is possible, the marginal
transformation rate is unity. In the monetary economy, how-
ever, decision making is diversified with each generation.
Hence, there is no guarantee that the inflation rate is
equal to the marginal transformation rate, except for in
the special case. As compared to the social optimum, the
current consumption becomes too large under inflation.
Thus, inflation is the deadweight loss intrinsic to the
mon eta r y e co no my. To su m u p, th e mo no po lis ti c c omp e -
tition contributes to economic welfare through a reduc-
tion in the inflation rate.
It is also noteworthy that the sou rce of distortion sh ifts
from the relative price between the goods and leisure in
statics to the intertemporal relative price of the goods in
dynamics. The welfare-economic results of the dynamic
monopolistic competition contrast sharply with those of
the preceding static analyses.
5. References
[1] M. Otaki, “The Dynamically Extended Keynesian Cross
and the Welfare-Improving Fiscal Policy,” Economics
Letters, Vol. 96, No. 1, 2007, pp. 23-29.
doi:10.1016/j.econlet.2006.12.005
[2] M. Otaki, “A Welfare Economic Foundation for the
Full-Employment Policy,” Economics Letters, Vol.102,
No. 1, 2009, pp. 1-3. doi:10.1016/j.econlet.2008.08.003
[3] N. G. Mankiw, “Small Menu Costs and Large Business
Cycles: A Macroeconomic Model of Monopoly,” Quar-
terly Journal of Economics, Vol. 100, No. 2, 1985, pp.
529-539. doi:10.2307/1885395
[4] N. G. Mankiw, “Imperfect Competition and the Keynes-
ian Cross,” Economics Letters, Vol. 26, No. 1, 1988, pp.
7-14. doi:10.1016/0165-1765(88)90043-2
[5] O. Blanchard and N. Kiyotaki, “Monopolistic Competi-
tion and the Effects of Aggregate Demand,” American
Economic Review, Vol. 77, No. 4, 1987, pp. 647-666.
[6] R. Starz, “Monopolistic Competition as a Foundation for
Keynesian Macroeconomic Models,” Quarterly Journal
of Economics, Vol. 104, No. 4, 1989, pp. 737-752.