On the Dynamic Role of Monopolistic Competition in the Monetary Economy

doi:10.4236/tel.2011.13024

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Theoretical Economics Letters, 2011, 1, 114-117

doi:10.4236/tel.2011.13024 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

E-mail: [email protected], [email protected]

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.

[0[0,1] ,1]

2.2. Individuals

Individuals have identical lifetime utility functions,



12 12

(, ,)(, )

tj tjtjtj tjtj

UC CUC C,





 



(1)

111

0() .

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 .

()

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:

(), <0

tj tjtj

tj tj

Vv v





 







 

 



 ,



(3)

where

(),.

tjtjtj tj

Ppzdz









 













(4)

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



W as









(5)

Because our main concern is an underemployment

equilibrium where some ind ividuals are unemployed, the

equilibrium nominal wage is equal to

W



2.3. Firms

The demand function of good during period t



()

()= ,



tj tj













 (6)

where d



is the real effective demand defined by







tjtj tj

tj tj

tjtj tj

tj t

PPP





 







 







)

(7)

where (



 is the marginal propensity to consume.



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

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

W

*() ()

()=(1 ).

tj tj

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

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

more details.

() ()

()=[()()( ())],

max max

> 0, 0,

tj tj

tjtjtjtjtj

pz pz

zpzczWcz













(8)

where ( )



 is the inverse of the production function.

The solution is

()=( ()),.

tj tj

pzcz z













(9)

Substituting (5) into (9), we obtain











tj tj

tj Mtj

Mt j



























(10)

Thus the equilibrium inflation rate, *



, is the

non-increasing function of the real GDP per firm *



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,

{}

tjj

P

{}

tjj

P {}

tjj

M



, can be determined independently of the price

level, .

Pj

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,



(

pz y





*

)

*



, satis-

fies

= (







*

y() )v (11)

Because is a decreasing function of v



, it is

straightforward from Equations (10) and (11) that

()

tj tj



(),

Mtj





(





tj tj

 



j tj



.y



)

(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

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

S

, j





(13)

We specify the money supply rules as follows:

1). The government arbitrarily chooses the current

money supply

. 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).

{}

tjj

P

2). From period onward, is controlled so

as to keep the real cash balance equal to

1tj

M

.

Namely, =,





 holds (Rule 2).

From rules 1 and 2, and Equation (13), the current

budget constraint of the government is

tj t





.

(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

***

=( ).

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

, 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).

P**

(,)



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 *

. Second,

we explain the reason for th is by considering th e socially

optimal allocation.

To keep the GDP level at *

, the real money supply,

m, must satisfy the following equation: 3

***

=[1(())= .

ma yjMor



] ,y W

Using Equations (3) and (5), the lifetime utility at the

stationary underemployment equilibrium, *

V, is repre-

sented as

****

** *

()=(())

=(())(),= .

VyvyP

vyyy jMorW









(16)

3When an equilibrium falls into deflation, i.e., *



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,



, the al-

location of the monopolistic competition weakly domi-

nates that of the Walras ian equilibrium. Namely,

mfor attaining some fixed *

can be determined,

independent of the sign.

M. OTAKI ET AL.

117

** ***

()(), (0,1],

Vy Vyy

where *

V is the utility of each individual in the mo-

nopolistic competition, and is that in the Walrasian

equilibrium.

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

, 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.