international relocation, the real exchange rate and effective demand

International relocation, the real exchange

rate and effective demand

Wataru Johdo a,*, Ken-ichi Hashimoto b

a Department of Economics, Tezukayama University, 7-1-1 Tezukayama, Nara 631-8501, Japanb Graduate School of Economics, Kobe University, 2-1 Rokko-dai, Nada, Kobe 657-8501, Japan

Received 18 February 2006; received in revised form 1 May 2007; accepted 18 September 2007

Abstract

By introducing an international relocation mechanism into a two-country model, we analyze the effects

of an increase in the corporation tax in the richer country on employment and effective demand in both

countries. This taxation policy proves to produce not only enterprise relocation, but also depreciation in the

real exchange rate. The latter is also shown to dominate the former, such that rich-country employment and

effective demand are stimulated. However, the two countries respond in opposing ways regarding enterprise

relocation and real exchange rate adjustment. Consequently, employment and effective demand in the poor

country will fall.

# 2007 Elsevier B.V. All rights reserved.

JEL classification: E24; F23; F31; H32

Keywords: Enterprise relocation; Real exchange rate; Effective demand; Corporation tax

1. Introduction

The main purpose of this paper is to investigate whether enterprise relocation from a home to a

foreign country under synchronized stagnation worsens conditions in the former and improves

conditions in the latter. Recently, the possible existence of stagnated equilibrium was

investigated by Ono (2001). Ono (2001) shows that stagnation may occur in a closed economy

when two assumptions not found in the neoclassical literature are fulfilled: namely insatiable

liquidity preference and sluggish price adjustment. In such a model, Ono (2001) considers the

effect of fiscal and monetary policy on effective demand. Furthermore, Ono (1999, 2006) extends

the closed economy model to an open economy setting and examines the effect on the two

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Japan and the World Economy

21 (2009) 39–54

* Corresponding author. Tel.: +81 742 48 9380; fax: +81 742 46 4994.

E-mail address: [email protected] (W. Johdo).

0922-1425/$ – see front matter # 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.japwor.2007.09.001

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countries’ effective demand of one country’s fiscal and monetary policy. However, Ono’s model

does not embody any form of international location behavior between the two countries.

Alternatively, in the multinational firm literature, Fukao (1997) uses a dynamic model to

derive an equilibrium where enterprise relocation does not work completely, and examines the

impact of relocation by comparing it with free-entry equilibrium. However, since the regulation

of enterprise relocations among developed countries has been substantially liberalized, we

believe it is appropriate to examine the impact of the relocation of unrestricted firms at the initial

point. In addition, because Fukao (1997) assumes a small open economy, he cannot consider the

impact of enterprise relocation on another country that faces an inflow of firms. We consider it is

then appropriate that a two-country model should be adopted to examine the impact of enterprise

relocation among economic powers, including the U.S. and Japan.1

As a point of further comparison, Johdo and Hashimoto (2005) investigate the effects on welfare

of a corporation tax in a world in which production is globalized so that firms can relocate easily

using a two-country monopolistic trade model. However, this model lacks the adjustment

mechanism between relocation and effective demand under stagnation, because the model assumes

that demand is always met with supply in the labor market. Our contribution to the literature is to

present a two-country monopolistic trade model incorporating the international relocation of firms,

and show how it can be used to shed light on the relationship between the corporation tax rate and

effective demand under stagnation. The main result is as follows. If the home country increases

the corporation tax rate that led to international relocation under stagnation, this could improve

employment and effective demand in the home country and worsen employment and effective

demand in the foreign country if the home country is rich (or the foreign country is poor). The

remainder of thepaper is structured as follows. Section 2 outlines the features of the model. Section 3

describes the steady-state equilibrium. Section 4 presents the comparative steady-state results and

explains the underlying intuition. Thefinal section summarizes the findings andconcludes thepaper.

2. The model

2.1. Definitions of various prices

We assume a two-country (home and foreign) world economy in which monopolistically

competitive producers exist continuously in the range of [0, 1], each of which produces a single

differentiated product. An individual producer must choose either the home or the foreign

country as its production location, and productive activity cannot be carried out in both locations

simultaneously. We assume that the home location consists of those producers in the interval [0,

n], and the remaining [n, 1] producers are in the foreign location, where n is endogenous. This

paper adopts a consumption index of the Dixit and Stigliz (1977) type (shown below), in which

case the consumption-based price indexes are

P ¼� Z 1

0

P1�sj d j

�1=ð1�sÞ

¼� Z n

0

P1�sj d jþ

Z 1

n

ðeP�jÞ1�s

d j

�1=ð1�sÞ

; (1)

W. Johdo, K.-i. Hashimoto / Japan and the World Economy 21 (2009) 39–5440

1 Ethier and Markusen (1996) show that 80 percent of total foreign direct investment is between developed countries. In

addition, Stevens and Lipsey (1992) and Fukao (1996) are examples of empirical research in which enterprise relocation

is represented by foreign direct investment.

P� ¼� Z 1

0

P�1�sj d j

�1=ð1�sÞ

¼� Z n

0

�P j

e

�1�s

d jþZ 1

n

P�1�sj d j

�1=ð1�sÞ

; (2)

where P and P* are the price indexes of the home and foreign countries respectively and e is the

nominal exchange rate.2 There is a one-to-one correspondence between firms and varieties of

models after the Dixit–Stiglitz–Krugman types, so s is the elasticity of substitution between any

two varieties, and Pj is the price of product j. Here we assume that there are no impediments to

trade, so that ‘‘the law of one price’’ holds for each good. Since the price of the same good is

equalized across countries by the law of one price, purchasing power parity (P = eP*) must be

consistent with (1) and (2). Assuming symmetry between firms, (1) and (2) reduce to

P ¼ ½nP1�sh þ ð1� nÞðeP�f Þ

1�s�1=ð1�sÞ; (3)

P� ¼�

n

�Ph

e

�1�s

þ ð1� nÞP�1�sf

�1=ð1�sÞ

; (4)

where Ph is the price of the home good and P�f is the price of the foreign good. Adopting the above

definitions yields the real exchange rate of v� eP�f =Ph. In addition, the real prices of the two

goods are respectively

ph ¼Ph

P; pf ¼

eP�fP; p�h ¼

Ph=eP�

; p�f ¼P�fP�; (5)

which, from (3), (4), (5) and v� eP�f =Ph, yield

ph ¼ p�h ¼ v�1½nvs�1 þ ð1� nÞ�1=ðs�1Þ; (6)

p�f ¼ pf ¼ ½nvs�1 þ ð1� nÞ�1=ðs�1Þ: (7)

Considering (6) and (7), the real exchange rate reduces to v� p�f = ph. The nominal rate of return

from holding the equities of the home-located (respectively foreign-located) firm is defined as R

(respectively R*). If the two equities are perfect substitutes, these assets must yield equal rates of

return; i.e., R ¼ R� þ e=e, where e=e is the spot rate of exchange. Furthermore, differentiating

P = eP* with respect to time yields purchasing power parity in terms of inflation rates as

P=P ¼ P�=P� þ e=e, where P=P and P

�=P� are the spot rates of inflation. Moreover, defining the

real rates of return to home and foreign equities, respectively, as r (�R� P=P) and r*

(�R� � P�=P�) yields r = r*, where

r ¼ ph

qþ q

q; r� ¼ p�f

q�þ q�

q�; (8)

W. Johdo, K.-i. Hashimoto / Japan and the World Economy 21 (2009) 39–54 41

2 Foreign-country variables are indicated by an asterisk.

In expression (8), q (respectively q*) is the real price of equities and ph (respectively p�f )

represents the real flow of dividends from holding the equities of the home-located (respectively

foreign-located) firm, respectively.

2.2. Households

The size of the world population is normalized to unity. We assume that the shares of

households in the home and foreign locations are s and s* (�1 � s), respectively. In addition,

each household is endowed with one unit of (inelastically supplied) labor. The households in

each country consume a group of differentiated goods and obtain utility vðmÞ by holding real

money balances m (i.e., money-in-the-utility-function model). The consumption index c,

which is defined below, is assumed to be symmetric both within and across countries. A home

country’s household allocates total assets a between real money balances m, equities of home-

located firms bh, equities of foreign-located firms bf. Hence, the intertemporal maximization

problem is

max U ¼Z 1

0

½uðcÞ þ vðmÞ�expð�rtÞ dt; (9)

u0ðcÞ> 0; u00ðcÞ< 0; v0ðmÞ> 0; v00ðmÞ< 0; v0ð1Þ ¼ b> 0 (10)

s:t: a ¼ mþ bh þ bf ; (11)

a ¼ raþ wxs � c� Rm; (12)

xs ¼ min

�1;

n‘h

s

�: (13)

In Eq. (9), r is the subjective discount rate, and is identical in both countries. In Eq. (10),

v0ð1Þ ¼ b> 0 implies that there is no saturation point in the individual’s liquidity preference

even if real money balances m keeps increasing.3 Eq. (11) represents the stock constraint, and

Eq. (12) is the flow budget equation, where w (�W/P) denotes the real wage rate and xs is

realized labor supply. Eq. (13) implies that realized labor supply is determined on the short

side as either the potential labor supply or as the actual labor demand n‘h/s by the home-

located firms, where ‘h is labor input of each home-located firm, and hence n‘h/s is the per

capita actual labor demand.


3 Ono et al. (2004) attempt to provide a justification for the existence of an insatiable liquidity preference by testing for

it empirically in Japan using two data sets, prefectural and individual. In their study, they use two different econometric

methods—parametric and nonparametric. They show that insatiable liquidity preference is significantly positive at

standard levels of significance.

Before turning to the dynamic problem, we consider the composition of a given level of

nominal expenditure, E, in each instant to maximize the consumption index c. The consumption

index, aggregating across the differentiated varieties, is given by

c ¼�Z 1

0

cðs�1Þ=sj d j

�s=ðs�1Þ

; s> 1: (14)

We take a particular point in time and define E at that point of time as

E ¼R 1

0P jc j d j ¼

R n0

P jc j d jþR 1

n ðeP�jÞc j d j. Subject to this, the individual determines cj to

maximize (14). Then we obtain the following demand functions

ch ¼EP�s

h

P1�s; h2 ½0; n�; cf ¼

EðeP�f Þ�s

P1�s; f 2 ðn; 1�; (15)

where ch (respectively cf) denotes the demand function for a good produced in the home

(respectively foreign) country. Similarly, we obtain the following demand functions for a foreign

household

c�h ¼E�ðPh=eÞ�s

P�1�s; h2 ½0; n�; c�f ¼

E�P��sf

P�1�s; f 2 ðn; 1�; (16)

where E� ¼R 1

0P�jc

�j d j ¼

R n0ðP j=eÞc�j d jþ

R 1

n P�jc�j d j. From (1), (14), (15) and P = eP*, we

obtain c = e, where e � E/P.

We now turn to the dynamic optimization problem. Since each household

maximizes (9) subject to c = e, (11), (12) and (13), the Hamiltonian is given

by H ¼ ½uðeÞ þ vðmÞ� exp ð�rtÞ þ l½raþ wxs � e� Rm�. The first-order optimality

conditions for this problem are u0(e) exp(�rt) = l, v0ðmÞ exp ð�rtÞ ¼ Rl and �l ¼ rl,

and the transversality condition is limt!1 la = 0. From the above conditions, we

derive

rþ me

�e

e

�þ P

P¼ R ¼ v0ðmÞ

u0ðeÞ ; (17)

where me � �u00(e)e/u0(e) is the elasticity of marginal utility. Similarly, from the first-order

conditions for a foreign household, we derive

rþ me�

�e�

e�

�þ P

�

P�¼ R� ¼ v0ðm�Þ

u0ðe�Þ : (18)

Following the terminology in Ono (2001), we refer to (17) and (18) as ‘‘Keynes’s rule’’.

2.3. Firms

We require all monopolistically competitive firms throughout the world to have identical

technologies, and we assume that the number of firms is fixed, which allows for

strictly positive profits. These firms use constant returns to scale technology to produce


the differentiated consumption products, according to yj = ‘j, where yj is the production of

home-located firm j and ‘j represents labor input. Summing the private demand functions

and equating the resulting equation to the output of good j produced in the home country

yields

y j ¼ sc j þ s�c�j : (19)

In expression (19), scj (respectively s�c�j) is aggregate home (respectively foreign) consumption

demand for product j. Since home-located firm j hires labor domestically, home-located firm j

faces the following profit-maximization problem:

maxp j

p jy j � w‘ j; (20)

s:t: y j ¼ sc j þ s�c�j ¼ p�sj ðseþ s�e�Þ; (21)

where (21) is derived by substituting e � E/P into (15) and e* � E*/P* into (16), taking account

of (5). Given W, P and (se + s*e*), the price markup is chosen according to

p j ¼�

s

s � 1

�w: (22)

Since w (�W/P) is given, (22) yields pj = ph, j 2 [0, n]. These relationships imply that each firm

supplies the same quantity of goods: yj = yh, j 2 [0, n]. Similarly, the price markups of foreign-

located firms are identical, so that yields p�j ¼ p�f , j 2 (n, 1] and y�j ¼ y�f ; j2 ðn; 1�. Substituting

(21) and (22) into (20) yields the real profit flows of the home-and foreign-located firms,

respectively as

ph ¼�

1

s

�p1�s

h ðseþ s�e�Þ; p�f ¼�

1

s

�p�1�s

f ðseþ s�e�Þ: (23)

2.4. Market adjustment

The money markets and the equities market are assumed to be always in equilibrium:

Money market : sm ¼ M

P; s�m� ¼ M

�

P�; (24)

International equities market : sbþ s�b� ¼ nqþ ð1� nÞq�: (25)

In expression (24), M (respectively M�) represents total money supply in the home

(respectively foreign) country. In expression (25), nq (respectively (1 � n)q*) represents

the total real value of home-located (respectively foreign-located) firms. From (21), goods

markets are represented by


y j ¼ p�sj ðseþ s�e�Þ; j2 ½0; n�; y�j ¼ p��s

j ðseþ s�e�Þ; j2 ðn; 1�: (26)

Here, we assume sluggish nominal wage rate adjustment in the labor market, and we

formulate the nominal wage rate adjustment process for each country as follows:4

W

W¼ aðx� 1Þ; W

�

W¼ a�ðx� � 1Þ4; (27)

where a and a* are the parameters that represent the speed of nominal wage-rate adjustment, and

the employment rate of each country in (27) can be defined as

x ¼ n‘h

s; x� ¼ ð1� nÞ ‘

�f

s�: (28)

Expression (27) and (28) imply that the instant rate of nominal wage rates W (respectively W*) are

positively related to the excess labor demand (n‘h � s) (respectively (1 � n)‘�f � s�).5

3. Steady state with stagnation

We now present the conditions required in the steady state for both the home and

foreign countries to be in stagnation. The steady state with stagnation is six-fold (vss, nss, xss, x*ss,

ess, e*ss) in which r ¼ 0; r� ¼ 0; R ¼ 0; R� ¼ 0; v ¼ 0; q ¼ 0; q� ¼ 0; e ¼ 0; e� ¼ 0; n ¼

0; P=P< 0; P�=P�< 0; m> 0; m�> 0; v0ðmÞ ¼ b and n0ðm�Þ ¼ b� hold. The above definition

means not only that the real and nominal rates of interest, the real exchange rate, and the real price

of equities are fixed, but also that e, e* and n remain constant. In addition, the steady state with

stagnation requires that involuntary unemployment exists, consequently causing nominal wages,

nominal prices, and the price level to continue to decline, and hence real balances to continue to

increase. This is because that P=P ¼ Ph=Ph ¼ W=W ¼ aðx� 1Þ holds in the steady state from

(5), (6), (22) and (27).6 Since the money supply in each country is constant, from (24), the

dynamics of m and m* are represented by

m

m¼ � P

P;

m�

m�¼ � P

�

P�: (29)

Here, we assume that initial stockholdings per capita of the two countries, i.e., b0 (�bh0 + bf0)

and b�0 �ðb�h0 þ b�f0Þ; are

b0 ¼u½nqþ ð1� nÞq��

s; b�0 ¼

ð1� uÞ½nqþ ð1� nÞq��s�

; (30)


4 Johdo (2002) and Matsuzaki (2003) also use this type of sluggish adjustment mechanism.5 Naturally, when full employment holds, i.e., n‘j = s, (27) yields W=W ¼ 0, 8a.6 Appendix A presents the parametric conditions required for unemployment to exist in the steady state.

where u and (1 � u) denote the share of the total value of world equities, held by home and

foreign agents, respectively.7 Then, from (8), (11), (12), (22), (29), and (30), the employment

levels of the two countries are as follows8

x ¼ e� u½nph þ ð1� nÞp�f �=s

phðs � 1Þ=s ; (31)

x� ¼ e� � ð1� uÞ½nph þ ð1� nÞp�f �=s�

p�f ðs � 1Þ=s : (32)

Since v and n are constant, from (6) and (7), P and P* change parallel to Ph and P�f , which results

in, from (22), (27) and (28):

P

P¼ Ph

Ph

¼ W

W¼ aðx� 1Þ; P

�

P�¼ P

�f

P�f¼ W

�

W�¼ a�ðx� � 1Þ: (33)

Moreover, since e and e* remain constant, from (17) and (18), we obtain

rð¼ r�Þ ¼ r: (34)

Now, and for the purposes of simplicity, we assume that firms do not face any relocation costs

so that it does not take any time to relocate in another country. If any firm is indifferent between

home and foreign location, then returns from the two locations must be equalized. Arbitrage

behavior regarding location then ensures the following location-equilibrium condition:

ph ¼ p�f : (35)

From (23), (35) and v� p�f = ph, the steady-state value of v is

vss ¼ 1: (36)

We explain (36) intuitively as follows. The profits of the enterprises of both countries are equal

from (35). In addition, since the preferences of the two countries are symmetrical, the real prices

of the home country’s product and the foreign country’s product are equal. Thus, the real

exchange rate, which is the price ratio, is vss = 1. Here, for simplicity, we specify the utility

function for consumption as u(e) = ln e. Then (17) and (18) reduce to

bess ¼ rþ aðxss � 1Þ; b�e�ss ¼ rþ a�ðx�ss � 1Þ: (37)

Eq. (37) shows that an increase in xss (respectively x*ss) raises ess (respectively e*ss), i.e.,

dess/dxss > 0 and de*ss/dx*ss > 0. This is because an increase in xss (x*ss) reduces the deflation


7 The values of b0 and b�0 turn out to be consistent with (25).8 In this paper, the steady state with stagnation requires that unemployment exists in both countries, hence nominal

wages and nominal prices continue to decline. Therefore x < 1 and x* < 1 must hold in the steady state. On the other

hand, the full-employment steady state requires that x = x* = 1.

rate (or increases the inflation rate) according to (33), which raises the time preference rate and

hence consumption increases. In addition, we assume that population size, the wage-adjustment

speed and the minimum level of the marginal utility of money are the same in both countries; i.e.,

s = s*, a = a*, b = b*. From (31), (32), (36), and (37), we obtain the following steady-state

employment rates:

xss ¼ ðb=aÞfðr� aÞ½ðb� aÞððs � 1Þ=sÞ � 2ðau=sÞ�gðb� aÞ½bððs � 1Þ=sÞ � a� � ðr� aÞ=a ; (38)

x�ss ¼ ðb=aÞfðr� aÞ½ðb� aÞððs � 1Þ=sÞ � 2ðað1� uÞ=sÞ�gðb� aÞ½bððs � 1Þ=sÞ � a� � ðr� aÞ=a : (39)

If we substitute xss and x*ss from (38) and (39) respectively into (37), we obtain the following

steady-state consumption values:

ess ¼ ðr� aÞ½ðb� aÞððs � 1Þ=sÞ � 2ðau=sÞ�ðb� aÞ½bððs � 1Þ=sÞ � a� ; (40)

e�ss ¼ ðr� aÞ½ðb� aÞððs � 1Þ=sÞ � 2ðað1� uÞ=sÞ�ðb� aÞ½bððs � 1Þ=sÞ � a� : (41)

In addition, from (6), (7), (13), (23), (26), (31), (36) and yj = ‘j, the steady-state distribution of

enterprises between locations for enterprises is as follows9:

nss ¼ 1

2ðs � 1Þ

�s � 2u þ ½asð1� 2uÞ�½bðs � 1Þ � as�

�: (42)

Here, we find the parametric condition required for nss to be between 0 and 1 as follow (see

Appendix A).

sðb� aÞ> 2b: (43)

In addition, for a steady state with stagnation in which there are unemployment and effective

demand shortages in both countries, the employment levels given above must satisfy 0 < xss < 1

and 0 < x*ss < 1, and the steady-state consumption values given above must satisfy

up/s < ess < ef and ð1� uÞp=s�< e�ss < e�f , where p� ½nph þ ð1� nÞp�f �, and ef and e�f are

the full-employment production levels of each country compatible with xss = 1 and x*ss = 1,

respectively. In what follows, we assume that (43) and the conditions required for 0 < xss < 1 and

0 < x*ss < 1, up/s < ess < ef and ð1� uÞp=s�< e�ss < e�f are valid, so that a steady state with

stagnation exists in this economy.10


9 When u = 1/2 holds, (42) reduces to nss = 1/2.10 See Appendix A for the condition required for 0 < xss < 1 and 0 < x*ss < 1, up/s < ess < ef and ð1�

uÞp=s�< e�ss < e�f to hold together in the steady state.

4. International relocation, employment and consumption

In this section, we investigate the impact on the effective demand of both countries of an

increase in one country’s corporation tax rate that causes the relocation of some firms to the other

country.11 Suppose that the home government imposes a corporation tax rate on the profits of

home-located firms. Then the location equilibrium condition (35) is rewritten as ð1� tÞph ¼ p�f ,

where t is the corporation tax rate. In addition, we assume that all tax revenue is shared equally by

home-located households in a lump sum. Then, in a steady state with stagnation, the model is

reduced to the following four equations:

vss ¼ ð1� tÞ1=ð1�sÞ; (44)

nss ¼ ð1� tÞfu � s½ess=ðess þ e�ssÞ�gf1� t � s½1� t½ess=ðess þ e�ssÞ��g ; (45)

bess ¼ rþ a½nssvsssðnssvsss�1 þ 1� nssÞ�s=ðs�1Þðess þ e�ssÞ � 1�; (46)

be�ss ¼ rþ a�½ð1� nssÞðnssvsss�1 þ 1� nssÞ�s=ðs�1Þðess þ e�ssÞ � 1�; (47)

where Eq. (44) is the location equilibrium condition, Eq. (45) is the current account equilibrium

of the home country and Eqs. (46) and (47) are the steady-state conditions of consumption

behavior in the home and foreign countries, respectively. From (44), we easily obtain @vss/

@t � 0. The mechanism can be explained intuitively as follows: an increase in t leads to

ð1� tÞph <p�f . On the other hand, an increase in v increases ph and decreases p�f , since s > 1

implies that the price elasticity for each product is greater than unity. Thus, an increase in the

corporation tax rate leads to an increase in v required for after-tax profits to be equalized

worldwide. Totally differentiating (44)–(47) with respect to t gives:

1 0 0 0

0 h2 h3 h4

h6 h7 h8 h9

h10 h11 h12 h13

2664

3775

dvss

dnss

dess

de�ss

2664

3775 ¼

h1

h5

0

0

2664

3775dt;

where

h1�1

ð1� sÞð1� tÞs=ðs�1Þ ;

h2� 1� t � s

�1� t

�ess

ess þ e�ss

��;


11 The validity of adopting corporation tax as an influence upon enterprise relocation is empirically supported by

Grubert and Mutti (1991) and Wheeler and Mody (1992).

h3�se�ssðnsst þ 1� tÞðess þ e�ssÞ2

;

h4� �sessðnsst þ 1� tÞðess þ e�ssÞ2

;

h5� nss � u þ sð1� nssÞ�

ess

ess þ e�ss

�;

h6� � ansssvsss�1ðnssvsss�1 þ 1� nssÞ�s=ðs�1Þðess þ e�ssÞ

� ½1� nssvsss�1ðnssvsss�1 þ 1� nssÞ�1�;

h7� � avsssðnssvsss�1 þ 1� nssÞ�s=ðs�1Þðess þ e�ssÞ

� ½1� nssðs=ðs � 1ÞÞðvsss�1 � 1Þðnssvsss�1 þ 1� nssÞ�1�;

h8� b� anssvsssðnssvsss�1 þ 1� nssÞ�s=ðs�1Þ;

h9� � anssvsssðnssvsss�1 þ 1� nssÞ�s=ðs�1Þ;

h10�asnssð1� nssÞvsss�2ðnssvsss�1 þ 1� nssÞð1�2sÞ=ðs�1Þðess þ e�ssÞ;

h11� � aðnssvsss�1 þ 1� nssÞ�s=ðs�1Þðess þ e�ssÞ

� ½1þ ð1� nssÞðs=ðs � 1ÞÞðvsss�1 � 1Þðnssvsss�1 þ 1� nssÞ�1�;

h12� � að1� nssÞðnssvsss�1 þ 1� nssÞ�s=ðs�1Þ;

h13� b� að1� nssÞðnssvsss�1 þ 1� nssÞ�s=ðs�1Þ:

The impact of an increase in the corporate tax rate on vss, nss, ess and e*ss evaluated at t = 0 is

then:

dvss

dt

��t¼0

¼ 1

s � 1> 0; (48)

dnss

dt

��t¼0

¼ D�1ðb� aÞnss

�abð1� uÞ þ 2�1ðb� aÞ½bþ s½sðb� aÞ � 2b��

bðs � 1Þ � as

�< 0; (49)

dess

dt

��t¼0

¼ 2�1asðb� aÞð2u � 1Þnssðess þ e�ssÞ½ðbðs � 1Þ � as�2

; (50)

de�ss

dt

��t¼0

¼ �2�1asðb� aÞð2u � 1Þnssðess þ e�ssÞ½ðbðs � 1Þ � as�2

; (51)


where D = � (b � a)as[(b/a)((s � 1)/s) � 1] < 0 is the determinant of the matrix, nss equals

(42) and ess and e*ss equal (40) and (41), respectively. Expression (48) shows that an increase in

the corporation tax in the home country produces depreciation in the real exchange rate. Since

b > a from (43), expression (49) shows that an increase in the home country’s corporation tax

rate stimulates enterprise relocation from the home country to the foreign country. In expressions

(50) and (51), since b(s � 1) > as from (43), we find the effects of corporation tax on each

country’s consumption depend on the sizes of u:

dess

dt

��t¼0

> ð< Þ 0; de�ss

dt

��t¼0

< ð> Þ 0; when u> ð< Þ 1

2: (52)

Furthermore, Eq. (37) shows that dess/dxss > 0 and de*ss/dx*ss > 0 in the steady state with

stagnation. Therefore, from (37) and (52), the impact of an increase in the corporate tax rate of the

home country on the steady-state employment rates are as follows:

dxss

dt

��t¼0

> ð< Þ 0; dx�ss

dt

��t¼0

< ð> Þ 0; when u> ð< Þ 1

2: (53)

From (52) and (53), the effects of t on xss, x*ss, ess and e*ss can be stated as follows.

Proposition 1. In the steady state with stagnation, when u > (respectively<) 1/2, an increase in

the corporation tax rate of the home country raises (respectively lowers) both employment and

effective demand of the home country. Conversely, the tax increase lowers (respectively raises)

both employment and effective demand in the foreign country.

Proposition 1 is intuitively explained as follows. First, from (28) we find that the effect of

an increase in the corporation tax rate on employment in the home country is decomposed into

a negative effect from the decrease in production due to enterprise relocation (i.e., dnss/

dtjt = 0 < 0) and a positive effect of the increase in production due to the depreciation of the

real exchange rate (i.e., dyss/dvssjt = 0 = d‘ss/dvssjt = 0 > 0). Therefore, the net effect on

employment in the home country, xss = nss‘ss/s, is ambiguous. However, if the home country is

rich (respectively poor) in the sense that its agents hold a more (respectively less) than

proportionate share of world equities, the positive effect of an increase in production due to the

depreciation of the real exchange rate exceeds (respectively is exceeded by) the negative effect

of a decrease in production due to the enterprise relocation. Hence, employment in the home

country is stimulated (respectively falls). Then from Keynes’s rule (37), an increase in

employment in the home country leads to an increase (respectively decrease) in the rate of time

preference through an increase (respectively decrease) in the inflation rate. Consequently,

consumption or effective demand (or aggregate consumption) in the home country rises

(respectively falls). By way of contrast, in a foreign country that is poor (respectively rich), the

negative effect of a decrease in production due to the appreciation of the real exchange rate

exceeds (respectively is exceeded by) the positive effect of an increase in production due to

enterprise inflow; hence, employment in the foreign country falls (respectively increases).12

Then the decrease (respectively increase) in employment due to the increase in the home


12 When the home country is rich, the foreign country must be poor in the sense that its agents hold a less than

proportionate share of world equities.

country’s profit tax rate leads to a decline (respectively rise) in the rate of time preference

through a decline (respectively rise) in the inflation rate. As a result, consumption or effective

demand in the foreign country falls (respectively increases).

5. Conclusion

This paper employed a two-country monopolistic trade model to examine the impact on

employment and effective demand of a rise in one country’s corporation tax rate leading to

international relocation. In such a model, both the real exchange rate and enterprise relocation

offer the key to understanding the impact of the corporation tax policy. It was found that

the effects of the rise in the corporation tax rate on the effective demand of the home country can

be decomposed into the negative effect of a decrease in aggregate consumption due to enterprise

relocation, and the positive effect of an increase in aggregate consumption due to the

depreciation of the real exchange rate. The former effect is intuitively explained as follows. The

relocation due to the rise in the corporation tax rate reduces production in the home country and

then reduces employment. This lowers the inflation rate, thereby decreasing consumption

through a decline in the rate of time preference. On the other hand, the latter effect is intuitively

explained as follows. The depreciation of the real exchange rate, which is brought about by

arbitrage behavior over the location of enterprises, increases world demand for the home

country’s good, which stimulates production and labor demand, thereby increasing

consumption through a rise in the inflation rate. Therefore, the latter effect must exceed the

former if the relocation-promoting tax policy is to be effective in stimulating effective demand.

However, if the home country is rich (respectively poor), the increase in consumption due to the

depreciation of the real exchange rate exceeds (respectively is exceeded by) the decrease in

consumption due to enterprise relocation. The opposite happens in the foreign country.

Therefore, in this paper, we show that if the home country increased the corporation tax rate that

led to international relocation under stagnation, this would improve effective demand in the

home country and worsen effective demand in the foreign country if the home country is rich (or

the foreign country is poor).

From the above results, whether the increase in the home country’s corporation tax rate

improves its economy depends on whether the country is rich in the sense that its agents hold a

more than proportionate share of world equities. We suggest that the U.S. is the poor country and

Japan the rich country. This is because, at least for the past few decades, the balance of the current

account deficit between the two economies was in the U.S., while the balance of the current

account surplus was in Japan.

Acknowledgments

We are very grateful to Yoshiyasu Ono for his considerable help. We have also benefited from

comments and suggestions by Shin-ichi Fukuda, Ichiro Gombi, Shinsuke Ikeda and two

anonymous referees. Any remaining errors are due to us alone.

Appendix A. The conditions for the steady state with stagnation

First, we find the condition required for nss to be between 0 and 1. To ensure that nss is between

0 and 1, the following inequality must satisfy from (42):


0< nss ¼ 1

2ðs � 1Þ

�s � 2u þ ½asð1� 2uÞ�

bðs � 1Þ � as

�< 1: (A1)

For (A1) to be valid, the following conditions must hold:

�b

a

��s � 1

s

�> 1; sðb� aÞ> 2bu and sðb� aÞ> 2bð1� uÞ: (A2)

Then the following are the sufficient condition for (A2) to be valid:

sðb� aÞ> 2b: (A3)

Thus, nss is between 0 and 1 if (A3) is valid. Next, we find the condition required for

unemployment to exist in the steady state with stagnation, i.e., 0 < xss < 1 and 0 < x*ss < 1.

From (38), for 0 < xss < 1, the following condition must hold:

0<

�b

a

��ðr� aÞ½ðb� aÞððs � 1Þ=sÞ � 2ðau=sÞ�

ðb� aÞ½bððs � 1Þ=sÞ � a�

�� r� a

a< 1: (A4)

For (A4) to be valid, the following conditions must hold:

�b

a

��s � 1

s

�> 1; r>a; ðb� aÞðs � 1Þ> 2au; and

s

b<

ðb� aÞðs � 1Þ � 2au

½ðb=aÞðs � 1Þ=s � 1�ðb� aÞ < rsbðr� aÞ: (A5)

Similarly, from (39), for 0 <x*ss < 1, the following condition must hold:

�b

a

��s � 1

s

�> 1; r>a; ðb� aÞðs � 1Þ> 2að1� uÞ; and

s

b<ðb� aÞðs � 1Þ � 2að1� uÞ½ðb=aÞðs � 1Þ=s � 1�ðb� aÞ <

rs

bðr� aÞ : (A6)

From (A5) and (A6), we find the conditions that satisfy 0 < xss < 1 and 0 < x*ss < 1

simultaneously so that both countries have unemployment in the steady state:

�b

a

��s � 1

s

�> 1; r>a; ðb� aÞðs � 1Þ> 2a; and

s

b<


½ðb=aÞðs � 1Þ=s � 1�ðb� aÞ <rs

bðr� aÞ : (A7)

Finally, we find the condition required for the steady-state consumptions to exist

under stagnation, i.e., the existence of effective demand shortages. Under effective

demand shortages, the steady-state consumptions of each country not only must exceed the


interest incomes from equities, but also must be below the full-employment production levels.13

Thus, the steady-state consumption values defined above must satisfy up/s < ess < ef and

ð1� uÞp=s�< e�ss < e��f , where p� ½nph þ ð1� nÞp�f �, and ef and e�f are the full-employment

production levels of each country compatible with xss = 1 and x*ss = 1, respectively. Substituting

xss = 1 and x*ss = 1 into (31) and (32), respectively, and using (6), (7), (23), (35) and (36), yields

the following full-employment production levels of each country:

ef ¼s � 1

sþ 2u

sand e�f ¼

s � 1

sþ 2ð1� uÞ

s: (A8)

In addition, from (6), (7), (23), (35) and (36), the interest incomes from equities of each country

are as follows

up

s¼ 2u

s; and ð1� uÞ p

s�¼ 2ð1� uÞ

s: (A9)

From (40), (A8) and (A9), for up/s < ess < ef, the following condition must hold:

�b

a

��s � 1

s

�> 1; r>a; ðb� aÞðs � 1Þ> 2au; and

2u

r� a<


½ðb=aÞððs � 1Þ=sÞ � 1�ðb� aÞ <s � 1þ 2u

r� a: (A10)

Similarly, from (41), (A8) and (A9), for ð1� uÞp=s�< e�ss < e�f , the following must hold:

�b

a

��s � 1

s

�> 1; r>a; ðb� aÞðs � 1Þ> 2að1� uÞ; and

2ð1� uÞr� a

<ðb� aÞðs � 1Þ � 2að1� uÞ½ðb=aÞððs � 1Þ=sÞ � 1�ðb� aÞ <

s � 1þ 2ð1� uÞr� a

: (A11)

From (A10) and (A11), we find the conditions that satisfy up/s < ess < ef and ð1�uÞp=s�< e�ss < e�f simultaneously so that both consumptions are below the full-employment

consumption levels in the steady state:

�b

a

��s � 1

s

�> 1; r>a; ðb� aÞðs � 1Þ> 2a; and

2

r� a<

ðb� aÞðs � 1Þ � 2auÞ½ðb=aÞððs � 1Þ=sÞ � 1�ðb� aÞ <

s � 1

r� a: (A12)


13 Interest income from equities occurs even if production in the home country is zero in this model.

Therefore, the parameters of this model must satisfy (A3), (A7) and (A12) for (nss, xss, x*ss, ess,

e*ss) to exist together in the steady state with stagnation. The conditions above reduce to the

following conditions:

sðb� aÞ> 2b; r>a; ðb� aÞðs � 1Þ> 2a;

s

b<


½ðb=aÞðs � 1Þ=s � 1�ðb� aÞ <rs

bðr� aÞ ;

and2

r� a<


½ðb=aÞððs � 1Þ=sÞ � 1�ðb� aÞ <s � 1

r� a: (A13)

Thus, the sufficient condition required for the steady state with stagnation to exist is (A13).

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