GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.140

Who gains from capital market integration: Tax competition between unionized and non-unionized countries

Hikaru Ogawa, Yasuhiro Sato, and Toshiki Tamai

June 2010

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Who gains from capital market integration: Tax competition between unionized and non-unionized countries∗
Hikaru Ogawa†Yasuhiro Sato‡

Toshiki Tamai§

June 8, 2010

Abstract
The welfare eﬀects of capital market integration are examined under a model of tax
competition with two asymmetric countries. The asymmetry is expressed through the labormarket: one country has a perfect labor market whereas the other country is unionized. Our
results show that the welfare eﬀects of capital market integration are diﬀerent dependingon whether governments play an active role in attracting capital: in the absence of active
governments, the capital market integration benefits the country with a competitive labormarket and harms the unionized country. If the governments are active and compete formobile capital using tax/subsidy, the market integration benefits both countries. The government’s incentive to participate in a tax/subsidy game is also examined in the integrated
capital market. We find that the unionized country always prefers to participate in the
tax/subsidy game, but the non-unionized country avoids the game if it is a capital importer.

Keywords: Capital Market Integration, Capital Mobility, Tax Competition, Trade Unions,Welfare.
JEL Classification Number : F21, H73, J51∗

We thank Tomoya Mori, Se-il Mun, Jun Oshiro, Itsuro Otaki, and the participants of Urban Economics
Workshop held in Kyoto University for their useful comments and discussions. Of course, we are responsible forany remaining errors. We acknowledge the financial support by the JSPS Grants-in-Aid for Scientific Research(S, A, B, and C) and the MEXT Grant-in-Aid for Young Scientists (B).
†
School of Economics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8601, Japan, e-mail:ogawa@soec.nagoya-u.ac.jp.
‡
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka 560-0043, Japan, e-mail:ysato@econ.osaka-u.ac.jp.
§
Faculty of Economics, Kinki University, 3-4-1 Kowakae, Higashi-Osaka 577-8502, Japan, e-mail:tamai@eco.kindai.ac.jp.

11Introduction

Given the increases in capital flows among countries, many scholars have analyzed the eﬀects
of capital market integration during the past few decades. One of the most important strands
in this field is the tax competition theory, which has a long history dating back at least to
Zodrow and Mieszkowski (1986) and Wilson (1986). The theory has investigated the role ofgovernments in attracting capital to their jurisdiction. Taking into consideration the fact that
regions diﬀer in many aspects, quite a few studies in tax competition have analyzed the caseof asymmetric regions. They have given due weight to regional characteristics and disparities
in population, technology, preference, and the initial endowment.1 The aim of this paper is tointroduce new aspect of regional disparities in terms of the domestic labor market: one country
has a competitive labor market and operates well and therefore unemployment is of limited
importance but the other country fights unemployment as the trade union has a voice in wage
bargaining.2 Given other things, such as technology, preferences, and initial endowments, being
equal, this paper examines how capital market integration changes the resulting equilibrium andthe domestic policy choices in the countries with contrasting labor markets.
A large number of tax competition works address the issue of an imperfect labor market,
i.e., the unemployment in the local market.3 Most works are in the framework of symmetric tax
competition where all countries encounter the problem of unemployment. In contrast to these
existing studies, this paper focuses on regional asymmetry in the labor market. In particular, ourmain research focus is the eﬀect on two diﬀerent countries of the lifting of the curbs on mobile
capital.4 Our paper resolves this issue using two models: (i) a benchmark model in which the1

The representative studies focusing on the regional asymmetries are as follows. The eﬀects of the diﬀerencesin population size are examined by Bucovetsky (1991), Wilson (1991), Kanbur and Keen (1993), Ottaviano andvan Ypersele (2005), and Sato and Thisse (2007). The eﬀects of asymmetric capital endowment are investigatedby DePater and Myers (1994), Peralta and van Ypersele (2005), and Itaya, Okamura and Yamaguchi (2008).
2
Other strands of studies on capital market integration include the literature on foreign direct investment(FDI), where many papers analyzed the interactions between trade unions and FDI. See Skaksen and Sorensen(2001) and Zhao (2001) among others.
3
See, for instance, Lejour and Verbon (1996), Fuest and Huber (1999), Richter and Schneider (2001), Boadway,
Cuﬀ and Marceau (2002), Koskela and Schöb (2002), Lozachmeur (2003), Leite-Monteiro, Marchand and Pestieau(2003), Ogawa, Sato and Tamai (2006), and Sato (2009).
4
The eﬀects of capital market integration on domestic policies have been examined in the unemployment modelof symmetric tax competition. Gabszewicz and van Ypersele (1996) shows that market integration initially lowers
the minimum wage in each country. Leite-Monteiro, Marchand and Pestieau (2003) shows that market integration2

government in each country plays no active role in capital attraction and (ii) a model in which
the government is active and uses capital tax/subsidy as a policy tool. The significant findingin our study is that the welfare eﬀects of market integration vary with government interference.
Our study is motivated by the work of Aloi, Leite-Monteiro and Lloyd-Braga (2009), whichshows that the workers in the unionized country receive higher income in autarky, while theworkers in the non-unionized country benefit from capital market integration. The benchmark
model in our paper is analogous to their model, and our first result is in accordance with theirs,i.e., the unionized country loses and the non-unionized country gains from the capital market
integration. The new result we find in the second model with government intervention is that thelifting of the curbs changes the welfare eﬀect so that both countries gain from market integration.
Our first result shows that when the government does not play an active role in capital
attraction, the capital market integration harms the unionized country and benefits the nonunionized country. The intuition behind this result is simple. In the unionized country, laboris overpaid as compared to its marginal product and capital rent is far below its intrinsic level.
In the non-unionized country, labor and capital are paid according to their marginal product.
Once the capital market is integrated, capital flows from the unionized country to the nonunionized country in search of higher rents. This capital flow simply benefits the non-unionizedcountry. The capital outflow from the unionized country harms the unionized country as it
reduces labor productivity, and by extension, labor demand, which results in the worsening of
the unemployment problem. It is also shown that such capital flows reduce total world output.
When the government plays an active role in capital attraction, the welfare eﬀects of themarket integration get amended: both countries benefit from the market integration. Whenthe capital market is not integrated, the amount of capital available for production in eachcountry is fixed at the endowment level. Thus, the governments can do nothing to control
capital allocation in the market, and the equilibrium with government intervention accords withthe one without. Once the capital market is integrated, the unionized country that is plagued by
reduces employment subsidy in a fixed-wage model of tax competition. Lejour and Verbon (1996) finds that the
unemployment benefit decreases as the mobility of capital increases in a wage-bargaining model, and a similar
result is obtained in the minimum-wage model of Lozachmeur (2003).

3

the unemployment problem has an incentive to attract capital since capital inflow increases the
productivity of labor, and by extension, labor demand, which reduces unemployment. On theother hand, the non-unionized country with an eﬃcient labor market still has no incentive to use
tax/subsidy policy to control the amount of capital in the domestic market. As such, the nonunionized country is not active while the unionized country actively subsidizes capital, resulting
in possible capital flow from the non-unionized country to the unionized country. While thedirection of capital flow is ambiguous and depends on the degree of labor market imperfectionin the unionized country, the tax/subsidy instrument can be employed by active governments
to improve welfare gain in both countries.
The organization of this paper is as follows. In the next section, we set up the basic model.
Section 3 examines the welfare eﬀects of capital market integration in the absence of governments.
In Section 4, the active governments are taken into account to derive the main result of thispaper. Section 5 studies the government’s incentive to participate in the tax/subsidy game in
the integrated capital market. Section 6 concludes.

2

Model

There are two countries, and in each country i(= 1, 2), there is a single government and there
are immobile residents/workers with preference u(ci ) = ci defined over the consumption of a
private good ci . Without any loss of generality, we assume each country has a continuum of
residents of size one. The two countries are identical, except for the labor market: in country
1, the labor market is imperfect due to union bargaining, whereas in country 2, there exists a
perfect competitive labor market.
The economy has a stock of capital that is perfectly mobile among countries. Each country
has capital stock K̄, so that the total supply of capital in this economy is fixed at 2K̄. The
mobile capital will be allocated between countries 1 and 2 to satisfy 2K̄ = K1 + K2 . We assume
that the capital stock in the economy is equally owned by the entire population, implying that all4

capital income is distributed to the capital owners (residents), and there is no absentee capitalowner in the economy.
Private goods are produced using labor and capital. The production technology is formulated
as Yi = F (Ki , Li ), where the production function is homogenous of degree one with respect
to two inputs. Yi is the output level, Li is the labor input, and Ki is the capital input incountry i. Denoting the capital per labor input as ki ≡ Ki /Li , we have Yi /Li = f (ki ), wheref (ki ) ≡ F (ki , 1); further, we assume that f 0 (·) > 0 and f 00 (·) < 0.
Each worker is assumed to be endowed with one unit of labor, which she/he supplies inelastically when employed. We assume that the residents in the same country are identical withrespect to preference and initial endowments. However, as the residents in country 1 may be
unemployed due to labor market imperfection, the residents do diﬀer in terms of their statusof employment. The residents are classified into two types of workers indexed by superscript
j: the resident is not employed by a firm j = u and is employed if j = e. Unemployment isseen as merely an unfortunate accident befalling individual workers, in which those fortunate
enough to be employed receive wages whereas the unemployed start their own business and earn
income w̄ ≡ 1.5 Labor income diﬀers between firm-employed and self-employed workers, but allof them earn a return on capital. By contrast, in country 2, since the labor market is perfect,
all residents are employed by firms.
The budget constraint of the residents indexed by superscript j in country 1 are given as
cj1 =

½

r1 K̄ + w1 + h1
r1 K̄ + 1 + h1

if
if

j=e
j = u.

(1)

In (1), h1 denotes the lump-sum transfer made by government 1, r1 is the net return on capital
investment, and w1 is the wage rate in country 1.6 Since all residents in country 2 are employedby firms, the budget constraint of a resident in country 2 is simply given by
c2 = r2 K̄ + w2 + h2 .
5This can also be interpreted as the value of leisure.
When the capital market is not integrated, the owner (resident) of endowed capital in country i invests all
capital in county i. In this case, the net return of capital investment, ri , diﬀers between country 1 and 2 as theamount of labor input diﬀers. Under perfect capital mobility accompanied by the capital market integration,
however, the capital owners are now able to invest their endowments in both countries, so that the net return ofcapital investment should be equalized.
6

5

The firm’s profit in country i is given by πi = [f (ki ) − (ri + τi )ki − wi ]Li , where τi is the unit
tax rate on capital in country i. The profit maximization gives
ri = f 0 (ki ) − τi ,(2)

wi = f (ki ) − ki f 0 (ki ).

(3)

Note that the capital substitutes for labor when the wage rate increases in country i:
dki
1
=−
> 0.
00
dwi
ki f (ki )(4)There is a single trade union in country 1. The trade union is concerned over job opportunities and the wage rent that is given by the union wage minus the reservation wage, w1 − 1.
The objective of the trade union is, thus, assumed to be given by U1 = Lβ1 1 (w1 − 1)β2 , where
β1 > 0 and β2 > 0 represent the concern for the level of employment and for the wage rent,
respectively.7 The union, taking the eﬀects of a change in w1 on k1 as given by (4), decides on
the wage level w1. Using ki ≡ Ki /Li and (3), given K1 , the problem of the trade union can beformulated as
max
w1

U1 =

µ

K1
k1

¶β1

(w1 − 1)β2 .

The first-order condition is
w1 dk1
βw1=,
k1 dw1w1 − 1(5)where β ≡ β2 /β1 > 0. In country 1, from (4) and (5), we have w1 = 1 − βk12 f 00 (k1 ). Combining
this equation with (3), we obtainf (k1 ) − k1 f 0 (k1 ) = 1 − βk12 f 00 (k1 ).

(6)

Under certain conditions, (6) uniquely determines the capital per labor in country 1 as k1 = k1∗ .8
In the following analysis, we assume k1∗ > K̄, which ensures unemployment in country 1 (see7The objective function follows McDonald and Solow (1981). Some empirical literature, e.g., MaCurdy and
Pencavel (1986), suggests that the union places more weight on employment rather than the wage rent, i.e.,
β1 > β2 . We, however, do not exclude the case of β1 ≤ β2 .
8One set of suﬃcient conditions for a unique k1∗ is given by the following three conditions: (i) when f (0) = 0,
f 0 (k1 ) and f 00 (k1 ) are finite, (ii) limk1 →∞ f (k1 ) − k1 f 0 (k1 ) > 1 − β limk1 →∞ k12 f 00 (k1 ), and (iii) (1 − 2β)k1 f 00 (k1 ) >βk12 f 000 (k1 ). Condition (i) implies that the left hand side of (6) is smaller than the right hand side of it at k1 = 0.
Condition (ii) requires that the opposite holds true as k1 → ∞, which ensures that there exists at least one k1
that satisfies (6). The uniqueness comes from condition (iii) because it implies that the left-hand side is steeper
than the right-hand side.

6Subsection 3.1). Using (3) and (6), the wage rate in country 1 is determined as
w1∗ = 1 − βk1∗2 f 00 (k1∗ ) > 1.

(7)

Note that k1∗ and w1∗ do not change regardless of whether or not there are curbs on the mobilityof capital.9
The government in each country imposes a tax on mobile capital. The tax revenue is distributed to the resident in each country as a lump-sum transfer. Hence, the budget constraintof a government in country i is hi = τi Ki . For the main analysis that will be developed in Section 4, we now present the optimization problem of an active government, which strategicallychooses it’s tax/subsidy rate on mobile capital so as to control capital allocation. We assume
a utilitarian government that maximizes the sum of utilities residing in the country. Then, thegovernment’s objective function in country 1 is formulated as W1 = L1 · u(ce1 ) + (1 − L1 ) · u(cu1 ).
From u(ci ) = ci , and by substituting (1) and hi = τi Ki into the objective function, we get the
optimization problem of government 1 asmax
τ1W1 = L1 · u(ce1 ) + (1 − L1 ) · u(cu1 )(8)= r1 K̄ + (w1∗ − 1)L1 + τ1 K1 + 1.
We mention here that this objective function is equivalent to the social surplus in our framework.
Since L2 = 1 holds in country 2, the maximization problem of government 2 is defined as
max
τ2

3

W2 = u(c2 ) = r2 K̄ + w2 + τ2 K2 .

(9)Equilibrium without active governments

Before introducing the model with active governments, we start our analysis from the benchmark
model. As the benchmark case, we present the equilibrium characteristics when the governments
9

We now describe how the equilibrium values of K1 , K2 , and L1 are determined. Assume that the capital
market is integrated, so that capital is freely mobile between country 1 and 2: f 0 (k1 ) − τ1 = f 0 (k2 ) − τ2 . In
country 1, the union determines the wage level as w1 = w1∗ . Therefore, following (5), k1 = k1∗ . Then, given the
tax rate in both countries, τ1 and τ2 , the equilibrium ratio of capital to labor in country 2 is determined by theequilibrium condition for capital markets f 0 (k1 ) − τ1 = f 0 (k2 ) − τ2 as k2 = k2∗ . In country 2, the equilibrium
number of workers employed by firms is equal to unity, L∗2 = 1, as the labor market is perfectly competitive.
By k2 = k2∗ and L∗2 = 1, capital input in country 2 is given by K2∗ = k2∗ . Finally, capital input in country 1 isdetermined as K1∗ = 2K̄ − K2∗ . When the capital market is not integrated, so that capital is immobile, the capitalstock of each country is equal to K̄, and the process described above can be applied.

7

play no active role, as in the model presented in Aloi, Leite-Monteiro and Lloyd-Braga (2009). In
the first part of this section, an autarky is considered where the capital market is not integrated,i.e., capital is immobile. In the second part, we attempt an analysis of the lifting of the curbs
on the mobility of capital to derive the welfare impacts of capital market integration. The
governments do not play an active part in attracting capital throughout.

3.1

Autarky

The equilibrium values in an autarky are indicated by superscript a. Since capital is immobile,
the amount of capital used in country i is Kia = K̄. As the government has no active policy,
τi = 0, and the wage bargaining of the trade union determines the capital per labor ratio incountry 1 as k1 = k1∗ , the return on capital and the employment level in country 1 are given
by r1a = f 0 (k1∗ ) and La1 = K̄/k1∗ < 1, respectively. Then, the equilibrium welfare of country 1 isobtained as
W1a = r1a K̄ + (w1∗ − 1) La1 + 1.

(10)

Since labor market clearing in country 2 requires L2 = 1, we have k2a = K̄. The return on
capital is, thus, r2a = f 0 (k2a ), and the wage rate is w2a = f (k2a ) − k2a f 0 (k2a ). In this paper, we focus
on the case in which workers in country 2 have an incentive to be employed, which, in the caseof autarky, gives the assumption that f (K̄) − K̄f 0 (K̄) > 1. The welfare of country 2 is obtainedasW2a = r2a K̄ + w2a .

(11)

In an autarky with non-active governments, we have the following characteristics in equilibrium:
Lemma 1. r1a < r2a and w1a > w2a .
Proof: See Appendix A-(i).
In country 1, the presence of a trade union increases the wage rate as compared to themarginal productivity of labor; on the other hand, in country 2, the wage rate is set in accordance8

with the marginal productivity principle. In country 1, as a consequence of higher wage, thereturn on capital decreases in country 1. At the same time, the return on capital in country
2 is given by the marginal productivity of capital and is greater than the return on capital incountry 1. Since the capital market is not integrated, the diﬀerence in the return on capital
persists.

3.2

Capital Market Integration

We now lift the curbs on capital mobility between the countries. The equilibrium values in
the integrated market are indicated by superscript m. Since capital is mobile between two
countries, the diﬀerence in capital returns is eliminated, and the net return on capital is equalin equilibrium: r1 = r2 = rm . Then, we obtain the capital flow in the equilibrium as follows.
Lemma 2. K1m < K̄ and K2m > K̄ .
Proof: See Appendix A-(ii).

Lemma 2 indicates that as the capital market is integrated, capital flows from country 1 tocountry 2. Furthermore, from Lemma 2, we easily get that r2a > r1a = r m , w2m > w2a , and
Lm
1 =

K̄
2K̄ − K2m
< ∗ = La1 ,
∗
k1
k1

(12)

showing that the market integration increases unemployment in country 1.
As shown in Lemma 1, the return on labor in the unionized country is set at a higher level
than in the non-unionized country. When the capital market is not integrated and capital ispegged in the original country, the rent for capital in country 1 decreases, and the net returnon capital in country 1 is lower than that in country 2. Once the curbs are lifted, capital flows
from country 1 to country 2 to pursue higher return, which reduces output L1 f (k ∗ ) and laborademand L1 in country 1 (Lm
1 < L1 ). Note that the capital market integration does not alter

the level of capital income f 0 (k ∗ )K. The decline in labor demand aggravates the unemployment
problem in the unionized country, which is harmful for it. By contrast, capital inflow and the9market integration result in output expansion and wage increase in country 2, which benefits
the residents in the non-unionized country.
The above argument on the welfare eﬀects of capital mobility can be formally proved asfollows. Using the equilibrium values, the welfare of countries 1 and 2 can be given by
W1m = rm K̄ + (w1∗ − 1) Lm
1 + 1,(13)

W2m = rm K̄ + w2m .

(14)Comparing (10) and (11) with (13) and (14), respectively, we obtain the welfare eﬀects of thecapital market integration when the governments are inactive. These results are similar to thoseof Aloi, Leite-Monteiro and Lloyd-Braga (2009).

Proposition 1. When governments are inactive, the unionized country loses and the nonunionized country gains from the capital market integration, W1m < W1a and W2m > W2a .
Proof: See Appendix B.

Proposition 2. When governments are inactive, the capital market integration reduces world
surplus, W1m + W2m < W1a + W2a .
Proof: See Appendix C.

The world surplus is equal to the total world output ( total world income), which is
W1 + W2 = f (k1∗ )L1 + 1 − L1 + f (K2 )K1
K1+ 1 − ∗ + f (K2 )∗k1
k1
2K̄ − K2
2K̄ − K2
+1−
+ f (K2 ).
= f (k1∗ )∗k1
k1∗= f (k1∗ )Therefore, capital inflow into country 2 alters the world surplus as∂(W1 + W2 )f (k1∗ ) − 1=−+ f 0 (K2 ).
∂K2
k1∗

10

The first term shows the decrease in output in country 1 and the second term represents theincrease in output in country 2. Though the first term is constant because of union bargaining,
the second term declines as K2 increases. In equilibrium under the capital market integration,
the eﬀect of the first term dominates that of the second term because −(f (k1∗ )−1)/k1∗ +f 0 (k1∗ ) < 0,which results in a lower total output than in the equilibrium under autarky.

4

Equilibrium with active governments

It is a natural argument that the government in each country has an incentive to employ atax/subsidy policy to exert an influence on the allocation of mobile capital. Specifically, thecountry that is plagued by an unemployment problem may have a strong incentive to employ
fiscal policy instruments to attract mobile capital. To include active governments in the model,
we solve (8) and (9) explicitly.

4.1

Autarky

Although governments can put tax/subsidy polices to use, they do not employ such policy
instruments since they have no impact on the capital allocation in autarky, where capital isfixed in each country. Thus, the equilibrium agrees completely with the equilibrium presented
in subsection 3.1.

4.2

Capital Market Integration

The government in country 1 is faced with r = f 0 (k1∗ ) − τ1 . In choosing the optimal tax/subsidy
rate on mobile capital, it takes into account the policy eﬀects on the capital price and thedomestic variables, which are shown in Appendix D. Equation (8) gives the first-order condition
for government 1’s optimal policy choice as
∂W1
∂w∗
∂K1
∂r
∂L1
= K̄
+ L1 1 + (w1∗ − 1)
+ K1 + τ1
∂τ1
∂τ1
∂τ1
∂τ1
∂τ1
w1∗ − 1
τ1
= −K̄ + ∗ 00 ∗ + K1 + 00 ∗ = 0,
k1 f (k1 )f (k1 )

11

where we used (21), (23), (24) and (26) as in Appendix D. Using (7), we solve this equation
with respect to τ1 as
τ1μ = f 00 (k1∗ )(K̄ − K1μ + βk1∗ ),(15)

where superscript μ stands for the equilibrium values under the capital market integration withactive governments.
The optimization problem of the government in country 2, (9), gives the first-order condition
as
∂W2
∂K2
∂r
∂w2
= K̄
+
+ K2 + τ2
∂τ2
∂τ2
∂τ2
∂τ2
∂K2
= τ2
.
∂τ2
Since ∂r/∂τ2 = 0 and ∂w2 /∂τ2 = −K2 , the first three terms disappear (see (21) and (23) inAppendix D), indicating that the government in country 2 has no incentive to use a tax/subsidy
instrument and chooses10
τ2μ = 0.

(16)This suggests that the government in country 2 does not employ a tax/subsidy policy on mobile
capital even if the capital market is integrated.
From (15) and (16), we have the results on optimal tax/subsidy policy in the integrated
economy.

Proposition 3. When governments are active, the unionized country subsidizes capital and thenon-unionized country does not employ a capital tax/subsidy instrument, τ1μ < 0 and τ2μ = 0,
under the capital market integration.
Proof: See Appendix E.
As capital and labor are complementary in production, as shown in (26) in Appendix D, an
increase in capital accompanied by a reduction in the tax rate increases employment in country 1,
10Note that since ∂K2 /∂τ2 = 1/f 00 (k2 ) < 0 (see (25) in Appendix D), ∂W2 /∂τ2 R 0 if τ2 Q 0, showing that W2
takes a maximum when τ2 = 0.

12

∂L1 /∂τ1 < 0. Moreover, it increases capital income suﬃciently to compensate for the reductions
in tax revenue. Thus, the government in country 1, which is troubled over unemployment, has
an incentive to provide capital subsidy in the integrated capital market.
We now state the capital flow in equilibrium with active governments. As shown in Lemma 2,
when governments are inactive, capital moves from country 1 to country 2 if the capital market
is integrated. In contrast,the eﬀects of the market integration on capital flow are somewhat
complex when governments are active. On the one hand, once the capital market is integrated,the capital owners have an incentive to invest in the non-unionized country to seek a higher
return. On the other hand, they may find the investment in the unionized country attractive
since its government provides capital subsidy. The capital subsidy works as a barrier against
capital outflow. As a matter of fact, capital subsidy may lead to capital influx into country 1even though the return on capital, f 0 (k1 ), is reduced.
To provide further insight as to how the capital migrates between two countries, consider
the familiar quadratic production function, fi = (A − ki )ki , where A > 2ki .11 In the equilibriumwith active governments, we have K1μ = (3K̄ − (1− β)(1− 2β)−1/2 )/2 and K2μ = (K̄ + (1− β)(1 −2β)−1/2 )/2, which reveals that K̄ R K2μ ↔ K̄ R (1−β)(1−2β)−1/2 .12 The combination of (K̄, β)
where the sign of K̄ − K2μ is determined is shown in Figure 1. This figure clearly shows that
capital is likely to move from country 2 to country 1 (from country 1 to country 2) to the extent
that the trade union in country 1 places high (low) weight on the wage rent. This is simply
because the government in the unionized country provides significant capital subsidy to attract
capital as the labor market is distorted to a considerable degree.13 Hence, the extensive capitalsubsidy in the unionized country results in capital outflow from the non-unionized country. The
opposite argument applies to the case in which the trade union places low weight on the wage
rent.

This condition ensures fi0 = A − 2ki > 0.
0.5(K̄ − 1)(K̄ + 1)/K̄ 2 < β < 0.5 is assumed to satisfy k1∗ = (1 − 2β)−1/2 > 0 and La1 = K̄/k1∗ < 1. We here
present the figure only for country 2 as the figure for country 1 is inextricably linked.
13
Since τ1μ = K̄ − (1 + β)(1 − 2β)−1/2 < 0, we have ∂τ1μ /∂β < 0, indicating that capital subsidy increases as βincreases.
11
12

13

[Figure 1. HERE]

Capital flow depends on the preference of the trade union, β, and therefore its direction is unclear.
However, we obtain the following proposition on the welfare eﬀects of market integration when
governments are active.

Proposition 4. When governments are active, both countries gain from the capital market
integration, W1μ > W1a and W2μ > W2a . Hence, in this case, the market integration increases
world surplus, W1μ + W2μ > W1a + W2a .
Proof: See Appendix F.
This result is in contrast to Proposition 1. The following two lemmas are useful in interpreting
this intriguing result.
Lemma 3. When governments are active, country 1 exports (imports) capital in the integrated
market if and only if (f (k ∗1 ) − 1 )/k ∗1 < f 0 (K̄ ) ( (f (k ∗1 ) − 1 )/k ∗1 > f 0 (K̄ )).
Proof: See Appendix A-(iii).
Lemma 4. Starting from equilibrium under autarky, capital export (import) by country 1
increases world surplus if and only if (f (k ∗1 ) − 1 )/k ∗1 < f 0 (K̄ ) ( (f (k ∗1 ) − 1 )/k ∗1 > f 0 (K̄ )).
Proof: See Appendix A-(iv).
These lemmas show that the government of country 1 determines the subsidy rate so thatcountry 1 exports capital if and only if the capital endowment is small enough and the marginal
productivity of capital is suﬃciently high in country 2. In such a case, capital export by country
1 increases total world output. By contrast, if the capital endowment is large and the marginal
productivity of capital is low in country 2, country 1 sets a subsidy rate that enables it to import
capital, which leads to higher total world output.
Keeping these lemmas in mind, we can explain the reason behind Proposition 3 as follows.
Once the capital market is integrated, the government in country 1 reduces the tax rate and starts
14

providing subsidy for mobile capital. Such reduction in tax rate generally produces two eﬀects.
First, it raises the net return on capital, ∂r/∂τ1 < 0. Second, it changes the allocation of capital
between countries 1 and 2, which aﬀects the labor demand and wage rate, and consequently thelabor income in each country.
Assume that the unionized country is a capital importer and the non-unionized country isa capital exporter, K1μ > K̄ > K2μ . Take country 1 as an example. The rise in capital price, r,
along with the market integration increases the payment for capital import in country 1, which
triggers welfare reduction. However, capital inflow owing to the capital subsidy increases labordemand and leads to more job opportunities, ∂L1 /∂τ1 < 0. While employment increases, wage
rate remains unchanged at w1∗ given by (7) since the trade union has bargaining power in thelabor market. This increases labor income, and by extension, welfare in country 1. In sum,
the positive and negative factors aﬀect the resulting welfare change, but the active government
can choose its subsidy rate to achieve net welfare gain when the capital market is integrated.
Note here that country 1 can attain the same capital distribution as that under autarky because
capital subsidy merely redistributes income within a country when the subsidy level is set suchthat net capital export is zero. If country 1 chooses a subsidy level other than this, it implies
that welfare in country 1 is higher than that under autarky.
When K1μ < K̄ < K2μ , the same argument applies. On the one hand, the increase in capital
price, accompanied by the market integration, increases the reward from capital export, which
increases welfare in country 1. On the other hand, the capital outflow increases unemployment,
which reduces labor income, and thus lowers welfare. The government uses a subsidy policy toensure that the positive eﬀect is stronger than the negative one. Thus, the market integration
always benefits the unionized country with an active government.
Now, we consider the eﬀects of market integration on welfare in country 2. Assume that
K1μ > K̄ > K2μ , i.e., country 2 exports capital in equilibrium. The resulting capital subsidy
attracts investment in country 1, and yields capital outflows from country 2, which decreases
wage rate in country 2. This has a negative impact on welfare in country 2. However, tax

15

reduction in country 1 increases the capital price, which benefits country 2 since it increases the
reward from capital export. As the positive eﬀect is stronger than the negative eﬀect because
capital export alleviates the low marginal productivity of capital, market integration benefits
country 2. When K1μ < K̄ < K2μ , i.e., country 2 imports capital from country 1, we can interpretthe result in a similar way. The capital subsidy in country 1 increases the capital price, which
increases the payment for capital import. This is a negative aspect of market integration for
country 2. However, with the market integration, capital flows into country 2, which increases
wage, and increases welfare in country 2. If the marginal productivity of capital is high underautarky, the positive eﬀect of capital inflow is large and stronger than the negative eﬀect, andtherefore the market integration benefits country 2.

5Comparison of equilibria with and without active governments

In this section, we perform a comparison between the equilibria with and without active governments. By ranking welfare in the integrated market, we refer to the governments’ incentives toparticipate in a tax/subsidy game in the integrated market. We start by comparing the capital
allocation with active governments and with non-active governments.

Lemma 5. Assume that the capital market is integrated. With active governments, country
1 has more capital and thus higher employment than with non-active governments, K1μ > K1m
and Lμ1 > Lm
1 . In contrast, in country 2 with active governments, has less capital than with
non-active governments, K2μ < K2m .
Proof: See Appendix A-(v).

Since capital flows from country 1 with market integration if no capital subsidy is provided;
capital subsidy works as a barrier against this flow.
Based on Lemma 3, we have the result on the governments’ incentive to participate in the
tax/subsidy game.

16

Proposition 5. Assume that the capital market is integrated. The government in the unionizedcountry becomes active and participates in a tax/subsidy game since it always gains from thisgame. By contrast, the government in the non-unionized country may become inactive and avoid
the tax/subsidy game since it may lose from it.
Proof: See Appendix G.

If the non-unionized country is a capital importer in equilibrium with active governments, thecapital subsidy policy employed in the unionized country increases the capital price, which
increases the payment for capital import and may reduce welfare in the non-unionized country.
This makes the capital-importing country develop a preference for the equilibrium without active
governments and reluctant to participate in the tax/subsidy game.

6

Concluding Remarks

This paper examined the consequences of the capital market integration for the residents’ welfare
in unionized and non-unionized countries. We first examined the model in which governments
do not play an active role and proved that once the capital market is integrated to allow capital
mobility between countries, capital moves from the unionized country to the non-unionizedcountry. This leads to an increases in unemployment, and therefore the market integration
harms the residents in the unionized country. By contrast, capital inflow in the non-unionizedcountry increases output, and therefore the market integration benefits the residents in the
non-unionized country. The necessary condition for this result is that capital outflow inducedby market integration reduces the demand for labor in the unionized country, which is assured
when the natural assumption that capital and labor are complementary in production is made.
This result, however, needs an amendment if we consider active governments. In the framework of active tax competition between unionized and non-unionized countries, our result showsthat capital market integration benefits both countries. The unionized country has an incentive

17

to provide subsidy for mobile capital since it is plagued by an unemployment problem. Unemployment gives the government in the unionized country an incentive to raise labor productivity
so as to boost labor demand. To raise labor productivity, the government tries to attract mobile
capital that is complementary in production. For this purpose, it strategically uses a subsidy
policy and succeeds in attracting capital. In contrast, the government in the country with a perfect labor market keeps choosing zero tax rates on capital even though the market is integrated,i.e., there is no point in using tax/subsidy policy instruments for the non-unionized country.
The capital subsidy provided by the unionized country changes the allocation of capital between
countries, net return for capital investment, wage, and unemployment level. All of these aﬀect
the welfare in each country, but the tax/subsidy instrument can be used to bring welfare gain
in both countries.
Finally, we examined the incentives to participate in a tax/subsidy game in the integrated
capital market. The results reveal that while the unionized country always becomes active anddesires to participate in the game by employing capital subsidy, the non-unionized country may
prefer the environment without active governments. If the non-unionized country is a capital
importer, the capital subsidy policy employed in the unionized country increases the capital
price, which increases the payment for capital and reduces welfare in the non-unionized country.
This makes the non-unionized country reluctant to participate in the tax/subsidy game.
Our argument reveals that whether the capital market integration harms or benefits theunionized and non-unionized countries depends on whether the governments in these countries
are active in controlling the capital allocation using a tax/subsidy policy, which has been recognized as the key component in the era of globalization.
It is worth pointing out that one of the most important extensions is to check the robustnessof our results in the case of three or more countries. Although we can interpret more than
two countries in our framework as the mass of unionized countries and that of non-unionizedcountries, this perspective neglects the strategic interactions among governments within eachmass (i.e., among governments of unionized (or non-unionized) countries). Investigating the18results of such strategic interactions is an important direction for future research.

Appendixes
Appendix A: Proof of Lemmas(i) Proof of Lemma 1.
Since f (·) is concave in ki , from k1a (= k1∗ ) > K̄ = K2a = k2a , we get r1a < r2a . Furthermore,from (3), we obtain w1a > w2a .
(ii) Proof of Lemma 2.
Although K1 changes, k1 does not change even if the market is integrated. Hence, k1∗ = k1a =k1m . From rm = f 0 (k1m ) = f 0 (k2m ), we readily havek1∗ = k2m = K2m > K̄.

(17)

From 2K̄ = K1m + K2m and (17), we have K1m < K̄.
(iii) Proof of Lemma 3.
In equilibrium under the capital market integration, the distribution of capital K1μ is determined by
f 0 (k1∗ ) − τ1μ = f 0 (K2 ),which is rewritten as
f 0 (k1∗ ) − f 00 (k1∗ )(K̄ − K1 + βk1∗ ) = f 0 (2K̄ − K1 ).

(18)

The left hand side (LHS) of (18) is decreasing in K1 and the right hand side (RHS) of (18) isincreasing in K1 . If and only if the LHS of (18) is smaller than the RHS of (18) at K1 = K̄, K1μis smaller than K̄, which implies that country 1 exports capital. This condition is equivalent tof 0 (k1∗ ) − βk1∗ f 00 (k1∗ ) < f 0 (K̄).
Using (6), this can be rewritten asf (k1∗ ) − 1< f 0 (K̄).
k1∗
19

Similar arguments show that country 1 imports capital if and only if
f (k1∗ ) − 1> f 0 (K̄).
k1∗(iv) Proof of Lemma 4.
Capital import by country 1 changes the world surplus as∂(W1 + W2 )f (k1∗ ) − 1=− f 0 (2K̄ − K1 ).
∂K1
k1∗
Evaluating this at K1 = K̄, we have

which gives the lemma.

¯∂(W1 + W2 ) ¯¯
f (k1∗ ) − 1=− f 0 (K̄),
∗
¯
∂K1
k
1
K1 =K̄

(v) Proof of Lemma 5.
f 0 (K2μ ) = f 0 (k2μ ) = f 0 (k1∗ ) − τ1μ > f 0 (k1∗ ) = f 0 (k2∗ ) = f 0 (K2m ). This yields K2μ < K2m andhence K1μ > K1m . Moreover, we have Lμ1 = K1μ /k1∗ > K1m /k1∗ = Lm
1 .

Appendix B: Proof of Proposition 1.
a
From w1∗ > 1 and Lm
1 < L1 in (12), we get that country 1 loses from the lifting of the curbs
asince W1m − W1a = (w1∗ − 1) (Lm
1 − L1 ) < 0. By contrast, country 2 gains sinceW2m − W2a = (rm − r2a ) K̄ + w2m − w2a¢¡= K2a f 0 (K2m ) − f 0 (K2a ) + f (K2m ) − K2m f 0 (K2m ) − f (K2a ) + K2a f 0 (K2a )= f (K2m ) − f (K2a ) − (K2m − K2a ) f 0 (K2m ) > 0,

where K2m > K2a from (17). The last inequality comes from the assumption that f 00 (·) < 0.

Appendix C: Proof of Proposition 2.
Simple comparison yields
W1m − W1a + W2m − W2a =¡¢f (k1m ) − k1m f 0 (k1m ) − 1

µ

K̄
K1m
− a
m
k1
k1

¶

+ f (K2m ) − f (K2a ) − (K2m − K2a ) f 0 (K2m ).
20

Using the results that k1m = k1a = k1∗ = k2m = K2m , K1m = 2K̄ − K2m , and K2a = K̄, we obtain
W1m − W1a + W2m − W2a = K̄µf (k1∗ ) − 1 f (K̄) − 1
−
k1∗
K̄

¶

.

(19)

Moreover, we can see that
∙

µ
¶¸
¤
£
d f (k) − 1
sgn= sgn 1 − f (k) + kf 0 (k) ,dk
kd (1 − f (k) + kf 0 (k))= kf 00 (k) < 0,dkwhich implies that1 − f (k1∗ ) + k1∗ f 0 (k1∗ ) < 1 − f (K̄) + K̄f 0 (K̄).
From the assumption that the workers in country 2 under autarky have an incentive to be
employed (f (K̄) − K̄f 0 (K̄) > 1), we haveddkµf (k) − 1k¶

< 0, ∀k > K̄.

(20)

From (19) and (20), we have W1m + W2m − (W1a + W2a ) < 0.

Appendix D: Policy eﬀects on equilibrium values
We now derive the equations representing the policy eﬀects on the equilibrium values used in
Subsection 4.2. Total diﬀerentiation of (2) gives
µ

−1
0
00
−1 f (k2 )

¶µ

dr
dk2

¶

=

µ

dτ1
dτ2

¶

.

After some manipulations, we have∂r∂r
= −1 and
=0
∂τ1
∂τ2
∂k1∗
∂k∗
∂k2
1
1
∂k2
= 1 = 0,= − 00= 00> 0, and
< 0.
∂τ1
∂τ2
∂τ1
f (k2 )∂τ2
f (k2 )

(21)
(22)

Equations (3) and (22) give
∂w1∗
∂w1∗
∂w2
∂w2
=
= 0,
= k2 > 0, and= −k2 < 0.
∂τ1
∂τ2
∂τ1
∂τ2

21

(23)

Since k2 = K2 and K1 + K2 = K̄, we have
∂K1
∂K2
∂K2
∂k2
=−
< 0 and
=
> 0,
∂τ1
∂τ1
∂τ1
∂τ1
∂K1
∂K2
∂K2
∂k2
=−
> 0 and
=
< 0.
∂τ2
∂τ2
∂τ2
∂τ2

(24)
(25)

Furthermore, as L1 = K1 /k1 , we have
∂L1
1 ∂K2
∂L1
1 ∂K2
=− ∗
< 0 and
=− ∗
> 0.
∂τ1
k1 ∂τ1∂τ2
k1 ∂τ2(26)

Appendix E: Proof of Proposition 3.
Suppose that τ1μ ≥ 0. Equation (15) implies that K̄ < K1μ because we have f 00 < 0. FromK1μ = 2K̄ − K2μ , we obtain K2μ < K̄ < k1∗ . Capital mobility requires that f 0 (k1∗ ) − τ1 = f 0 (k2μ ) =f 0 (K2μ ) > f 0 (K̄) > f 0 (k1∗ ). This implies that τ1μ < 0, which is a contradiction.

Appendix F: Proof of Proposition 4.
In autarky, we have
W1a = f 0 (k1∗ )K̄ + (f (k1∗ ) − k1∗ f 0 (k1∗ ))La1 + 1 − La1= f 0 (k1∗ )K̄ +K̄
f (k1∗ )K̄− f 0 (k1∗ )K̄ + 1 − ∗ ,∗k1k1

W2a = f 0 (K̄)K̄ + f (K̄) − K̄f 0 (K̄) = f (K̄).
Assume K1μ > K̄ > K2μ . Then, in the integrated market with active governments, we haveW1μ = f 0 (k1∗ )K̄ + (f (k1∗ ) − k1∗ f 0 (k1∗ ))Lμ1 + 1 − Lμ1 + τ1μ (K1μ − K̄)f (k1∗ )K1μ
K1μ
μ
∗
0 ∗
− f (k1 )K1 + 1 − ∗ + τ1μ (K1μ − K̄),
= f (k1 )K̄ +
∗
k1
k1
0

W2μ = f 0 (K2μ )K2μ + f (K2μ ) − f 0 (K2μ )K2μ + (f 0 (k1∗ ) − τ1μ )(K1μ − K̄)= f (K2μ ) + f 0 (K2μ )(K̄ − K2μ ).
The comparison gives
W1μ − W1a =µ¶K̄ − K1μf (k1∗ )μ0 ∗− f (k1 ) (K1 − K̄) ++ τ1μ (K1μ − K̄).
k1∗
k1∗

¡
¢2
Substituting (15) and using (6), we have W1μ − W1a = −f 00 (k1∗ ) K̄ − K1μ ≥ 0.
22

Furthermore, the comparison of W2μ and W2a gives
W2μ − W2a = f (K2μ ) − f (K̄) + f 0 (K2μ )(K̄ − K2μ ).
Combined with the concavity of f (·), W2μ − W2a takes a non-negative value, from which we findthat the market integration benefits country 2.14
When K1μ < K̄ < K2μ , a similar procedure can be applied, which leads to Proposition 4.

Appendix G: Proof of Proposition 5.
From (17) and K1m + K2m = 2K̄, we have K1m < K̄. In addition, K2μ < K2m from Lemma 5.
Thus, the simple comparison of welfare levels yields¢¡
W1μ − W1m = τ1 K1μ − K̄ + (w1∗ − 1) (Lμ1 − Lm
1 )
¶
µ
¡
K̄
μ ¢2
00 ∗
∗
m
− 1 > 0,= −f (k1 ) K̄ − K1 + (w1 − 1)L1
K1m
which proves the former result. The welfare comparison in country 2 gives
W2μ − W2m = K̄[f 0 (K2μ ) − f 0 (K2m )] + f (K2μ ) − K2μ f 0 (K2μ ) − f (K2m ) + K2m f 0 (K2m ).
If country 2 imports capital under tax/subsidy game (K2μ ≥ K̄), we haveW2μ − W2m ≤ K2μ [f 0 (K2μ ) − f 0 (K2m )] + f (K2μ ) − K2μ f 0 (K2μ ) − f (K2m ) + K2m f 0 (K2m )= f (K2μ ) − f (K2m ) − f 0 (K2m )(K2μ − K2m ) < 0,where the last inequality comes from the concavity of f (·). If country 2 exports capital, thewelfare eﬀect of the tax game is ambiguous for country 2.

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25

β = 0.5(K̄ − 1)(K̄ + 1)/K̄ 2

K̄

invalidK̄ > K2μ1

K̄ = (1 − β)(1 − 2β)−1/2

K̄ < K2μβ00.5

Figure 1. Capital flow in the integrated market with active governments.

26