Discussion Paper No. 959

THE WELFARE EFFECTS
OF ATTRACTING FOREIGNDIRECT INVESTMENT
IN THE PRESENCE OF UNEMPLOYMENT
Yoshitomo Ogawa
Yoshiyasu Ono

February 2016

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

The Welfare Eﬀects of Attracting Foreign Direct
Investment in the Presence of Unemployment∗

Yoshitomo Ogawa† and Yoshiyasu Ono‡

February 2016

Abstract
We develop a 2 × 2 × 2 model with the following features: (1) one sector is perfectly competitive while the other is oligopolistic; (2) one country has unemployment while the other attains full employment; (3) oligopolists move internationally;and (4) the ownership of each oligopolist is internationally shared. The welfare effects of various tax-cum-subsidies are examined. If the oligopolistic sector is capitalintensive, subsidizing the oligopolists’ profits, inflows, production or employment
is more likely to harm the country. The number of domestically based oligopolists,
the volume of domestic demand for the oligopoly-produced commodity, and thecountry’s ownership share of oligopolists also influence the eﬀect.

Keywords: Corporate Taxation, Production Subsidies, Unemployment, Oligopoly
JEL Classification: F12, F13, H25, H71, R38∗

We would like to appreciate a financial support from the Joint Usage/Research Center Program by
the Ministry of Education, Culture, Sports, Science and Technology, Japan. Financially supports by
the Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science to Ogawa(26380385) and to Ono (15H05728 and 22530178) are also gratefully acknowledged.
†
Faculty of Economics, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, JAPAN;
E-mail: yogawa@kindai.ac.jp‡
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 5670047, JAPAN; E-mail: ono@iser.osaka-u.ac.jp.

11Introduction

To boost domestic employment and income, many countries implement policies to retain
domestic firms and attract foreign firms, particularly when facing the threat of unemployment. Typical policies include location subsidies and corporate tax cuts. Sweden,
Germany, Ireland, and Canada respectively lowered their corporate tax rates from 56.6%,
60.0%, 50.0%, and 48.3% in 1983 to 22.0%, 30.2%, 12.5%, and 26.1% in 2013 (see Tax
Foundation Website, 2013). Location subsidies are widespread in Japan, being oﬀeredby 43 out of 47 prefectural governments (see Hamada, 2008).
However, using these policies to attract firms does not necessarily benefit a country inwhich there is unemployment. For example, the inflow of capital-intensive firms will cause
employment to decline because of the Stolper—Samuelson eﬀect. Moreover, if the firms
are mostly owned by foreigners, increase in profits promoted by tax cuts and subsidies
oﬀered to the firms will not return to home people.
To examine the welfare eﬀects of attracting foreign firms to a country that has unemployment, we develop a general equilibrium 2 × 2 × 2 model in which one sector isoligopolistic and the other is perfectly competitive.1 The model features oligopolists’location choice between two countries, international ownership of oligopolists’ equities,
and unemployment caused by wage rigidities. Haufler and Mittermaier (2011), Lahiri
and Ono (2011), and Haufler and Stähler (2013) examine international location choice byoligopolists, but they consider neither foreign ownership nor unemployment. Although
Hucka and Konrad (2003) explore the eﬀect of production subsidies by introducing an international distribution of firm ownership into the model of Brander and Spencer (1985),
they ignore location choice and unemployment. Leite-Monteiro et al. (2003), Kreickemeier (2005), and Ogawa, Sato, and Tamai (2006) analyze taxes and trade policies in an
economy that has unemployment. In their models, however, there is neither oligopolistic
behavior, firms’ location choice, nor foreign ownership of firms.
There are few studies that incorporate firm location choice, foreign ownership, andunemployment simultaneously. Johdo and Hashimoto (2009) analyze the eﬀect of corporate tax on employment and aggregate demand in a two-country model where unemployment is caused by insuﬃcient aggregate demand, and monopolistic firms produce
heterogeneous commodities using only labor. Exbrayat et al. (2012) examine international capital-tax competition by assuming technology with fixed amounts of labor andcapital inputs which are unrelated to the level of output. In our model, by contrast, unemployment is caused by wage rigidities, and Cournot oligopolists produce homogenous
commodities using constant-returns-to-scale technology with respect to labor and capital.
This setting enables us to find the role of factor intensity in the eﬀect of corporate taxcum-subsidy on employment. Furthermore, we examine the eﬀect of corporate tax on not
only employment but also welfare. The welfare eﬀects of other policy instruments, such
1

Lahiri and Ono (1995) develop a similar model.

2as production subsidies, location subsidies, employment subsidies, and minimum-wage
cuts, are also analyzed.
Our main results are summarized thus. If the oligopolistic sector is capital-intensive,(i) the more oligopolists there are in a country, (ii) the lower demand for the oligopolyproduced commodity a country has or (iii) the lower share of oligopolists a country owns,
the more likely the country is made better oﬀ by a corporate tax and worse oﬀ by locationand production subsidies. Thus, policies that attract foreign firms may make the country
worse oﬀ. This result has implications for countries that aim to stimulate their economies
by attracting more foreign firms.

2

The Model

We consider an economy in which there are two countries, home and foreign, and in which
two commodities are produced and internationally traded. One of the production sectors
is competitive and the other is a Cournot oligopoly. In the oligopoly sector, there are
N firms, of which n are located in the home country and n∗ are in the foreign country;
hence,(1)n + n∗ = N(= constant).
Throughout, the superscript ∗ denotes variables of the foreign country. Both commodities
are produced using two factors, labor and capital, based on constant-returns-to-scaletechnology. The two factors are both internationally immobile. Production technology
in the competitive sector (a) and that in the oligopoly sector (o) areA(∗) = f (ka(∗) )La(∗) ,x(∗) = g(ko(∗) )L(∗)
o ,

(2)

f 0 < 0, f 00 < 0; g 0 > 0, g 00 < 0,where A(∗) and x(∗) are the outputs of the competitive and oligopolistic sectors, respec(∗)(∗)(∗)
tively, Li and Ki are labor and capital inputs in sector i, and ki is
(∗)

ki

(∗)

(∗)

≡ Ki /Lifor i = a, o.

Using the competitively produced product as numeraire, from (2), the competitive
sector’s profit maximization and the oligopolistic sector’s cost minimization respectively
lead tof 0 (ka(∗) ) = r(∗) ,f (ka(∗) ) − f 0 (ka(∗) )ka(∗) = w(∗) ,
(∗)

w(∗)
g(ko )=− ko(∗) ,
(∗)
(∗)
0
r
g (ko )⇒ r(∗) = r(w(∗) ),ka(∗) = ka (w(∗) ),3ko(∗) = ko (w(∗) ),(3)

where w(∗) is the wage rate and r(∗) is the capital rent. From (2) and (3), the unit costfunction for each home (or foreign) oligopolist c(∗) isc(∗) = c(w(∗) ) ≡r(w(∗) )w(∗) + r(w(∗) )ko (w(∗) )=.
g(ko (w(∗) ))g0 (ko (w(∗) ))(4)

From (3) and (4), we obtainf00

1dka(∗) = dr(∗) = − (∗) dw(∗) ,ka(g 0 )2 w(∗)
dko(∗) = − 00 (∗)

gg r
ka (w ) − ko (w(∗) )(∗)dc(∗) =(∗)
g(ko )ka (w(∗) )

µ

1
1
+ (∗)
(∗)
w
ka r(∗)¶

dw(∗) ,

dw(∗) .

(5)

The utility function is quasi-linear and the second derivative of the demand function
for the oligopoly-produced commodity is zero; hence, one can ignore the second-orderdemand eﬀect. The inverse demand function for the oligopoly-produced commodity satisfies
p = p(D + D∗ ), p0 (D + D∗ ) = const. < 0,where D (or D∗ ) is home (foreign) demand for the oligopoly-produced commodity. Market
equilibrium for the oligopoly-produced commodity implies
D + D∗ = nx + n∗ x∗ .

(6)

The after-tax profits of the oligopolists located in each country are(1 − θ(∗) )π(∗) − ε(∗) = (1 − θ(∗) )(p (nx + n∗ x∗ ) − c(w(∗) ) + s(∗) )x(∗) − ε(∗) ,(7)

where π (∗) represents gross profits, θ(∗) is each country’s corporate tax rate, ε(∗) is a location tax, and s(∗) is each country’s production subsidy. The profit-maximizing conditionis(8)
p0 x(∗) + p (nx + n∗ x∗ ) − c(w(∗) ) + s(∗) = 0.
From (7) and (8), we obtain
π = −p0 x2 ,π ∗ = −p0 (x∗ )2 .

(9)

Because all oligopolists can freely move between the two countries to maximize profits,
after-tax profits are internationally equalized. Therefore,(1−θ)π−ε = (1−θ∗ )π ∗ −ε∗ ,(1−θ)dπ−(πdθ + dε) = (1−θ∗ )dπ∗ −(π∗ dθ∗ + dε∗ ) . (10)In the home country, although capital is fully utilized, labor is not fully employedbecause of wage rigidity,
w = w,
4

where w is exogenously given and above the market-clearing level. In the foreign country,
the two factors are fully utilized. Thus,
La + nLo = L,ka (w)La + nko (w)Lo = K,∗L∗a + (N − n)L∗o = L ,∗ka∗ (w∗ )L∗a + (N − n)ko∗ (w∗ )L∗o = K ,(11)∗

where K and L denote the home country’s capital endowment and labor demand, and L∗
and K are the foreign country’s factor endowments. Applying (1) to the above equations
and totally diﬀerentiating the results yields
dLa + ndL∗o + ndLo + Lo dn = dL,
ka dLa + nko dLo + nko dL∗o + ko Lo dn = 0,dL∗a + (N − n)dL∗o + (N − n)dL∗o − L∗o dn = 0,ka∗ dL∗a + L∗a dka∗ + (N − n)ko∗ dL∗o − ko∗ L∗o dn + (N − n)L∗o dko∗ = 0.

(12)

Because we assume that each household owns the same share of equities across all
oligopolists, equity ownership is not biased toward the home country. The equity shareis α for home country households and α∗ (= 1 − α) for foreign ones. Tax revenues arepaid to, and subsidy funds are collected from, each country’s households as lump-sum
amounts. Because all oligopolists earn the same net profits, as shown in (10), home andforeign national income, Y and Y ∗ , are
Y = wL + rK + n(θπ + ε − sx) + αN[(1 − θ)π − ε],∗∗Y ∗ = w∗ L + r∗ K + n∗ (θ∗ π ∗ + ε∗ − s∗ x∗ ) + α∗ N[(1 − θ∗ )π ∗ − ε∗ ].

(13)Having set up the model structure, we will analyze the eﬀects of various policies whenboth countries initially choose the same policy settings. From (9) and (10), x = x∗ ifθ = θ∗ and ε = ε∗ . Therefore, if θ = θ∗ , ε = ε∗ , and s = s∗ , from (8), c (w) = c∗ (w∗ ),which leads to w∗ = w. By applying this property to (2) and (3) one finds that initiallyx = x∗ , c(w) − s = c(w∗ ) − s∗ if θ = θ∗ and ε = ε∗ ;w = w∗ , r = r∗ , ka = ka∗ , ko = ko∗ , Lo = L∗o if θ = θ∗ , ε = ε∗ and s = s∗ .

(14)

Changes in the two countries’ welfare W and W ∗ are(1/λ(∗) )dW (∗) = dY (∗) − D(∗) p0 d(D + D∗ ),where λ(∗) is the marginal utility of each country’s income. The welfare eﬀects of thepolicies are examined in the neighborhood where all policy variables are zero. Therefore,
by totally diﬀerentiating (3), (6), and (13), substituting the results of d(D+D∗ ) and dY (∗)
5into the above equation, and making use of (10), (14) and the property that dn + dn∗ = 0
from (1), we obtain¢¡(1/λ)dW = L + Kr0 dw + wdL + n[(πdθ + dε) − xds]
−αN [(πdθ + dε) − dπ] − Dp0 (ndx + n∗ dx∗ ),∗∗(1/λ∗ )dW ∗ = (L + K r∗0 )dw∗ + n∗ [(π ∗ dθ∗ + dε∗ ) − x∗ ds∗ ]−α∗ N [(π∗ dθ∗ + dε∗ ) − dπ∗ ] − D∗ p0 (ndx + n∗ dx∗ ) .

(15)

From (5) and the last two equations in (11), we find that the change in foreign factor∗∗
income (L + K r∗0 )dw∗ to satisfy
∗

∗

∗

∗

(L + K r∗0 )dw∗ = (K − ka∗ L )f 00 dka∗ = n∗ L∗o (ko∗ − ka∗ )f 00 dka∗ .

3

(16)

Corporate Taxes

In this section, we ignore the location and production taxes, ε(∗) and s(∗) , to focus on
the welfare eﬀects of corporate taxes, θ and θ∗ . We assume that both countries initiallychoose the same tax rate. By using (1), (8), (9), (10), and (14), we obtainn∗ x(1 + n)x> 0, x∗θ |θ=θ∗ = −< 0,
2(1 − θ)(1 + N)
2(1 − θ)(1 + N)n∗ x∗
(1 + n)x∗∗∗|xθ∗ |θ=θ∗ = −
<
0,
x
> 0,
=
∗
θ θ=θ
2(1 − θ∗ )(1 + N)
2(1 − θ∗ )(1 + N )¯∂(nx + n∗ x∗ ) ¯¯
n∗ x
∗ ∗
=
n
x
|
+
n
x
|
=
−
< 0,
θ θ=θ∗
θ θ=θ∗¯ ∗∂θ
2(1 − θ)(1 + N)θ=θ¯∂(nx + n∗ x∗ ) ¯¯
n∗ x
∗ ∗
∗|
=
n
x
> 0,
∗ + n xθ ∗ |
∗ =
θ
∗
θ=θ
θ=θ
¯ ∗
∂θ
2(1 − θ)(1 + N)
θ=θxθ |θ=θ∗ =

(∗)

(17)

where xθ(∗) ≡ ∂x(∗) /∂θ(∗) . In what follows, subscripts denote partial derivatives.
Let us discuss the implications of (17). A rise in the home corporate tax lowers thenet profits of domestic oligopolists and motivates some of them to move abroad. Thischanges foreign factor prices, so that the marginal cost of each foreign-based oligopolist
increases and its output decreases. By contrast, the output of each domestically basedoligopolist increases because w is fixed at w and, thus, so too is its marginal cost. Because foreign-based oligopolists’ marginal costs increase while those of domestically basedoligopolists remain unchanged, world output decreases. A rise in the foreign corporate
tax rate encourages foreign firms to move to the home country. It boosts the output
of each foreign-based oligopolist by lowering its marginal cost. Each domestically basedoligopolist’s output decreases because its marginal cost is unchanged. Unlike a rise in
the home corporate tax rate, a rise in the foreign corporate tax rate lowers some firms’(i.e., the foreign-based firms’) marginal costs, leaving others’ (i.e., the domestically based
firms’) unchanged, which raises world output. This result yields the following proposition.
6

Proposition 1. Suppose that the home and foreign countries initially set the same corporate tax rate. If the country with (without) unemployment raises its tax rate, world
output of the oligopoly-produced commodity decreases (increases).
Next, we examine the welfare eﬀects of the home country increasing its corporate tax
rate θ from 0. From (1), (9), and (17), we obtainp0 n∗ x2
> 0,
(1 − θ)(1 + N)
p0 n∗ (x∗ )2=< 0,(1 − θ∗ )(1 + N)

π θ |θ=θ∗ = −π θ∗ |θ=θ∗

p0 (1 + n)x2
< 0,
(1 − θ)(1 + N)
p0 (1 + n)(x∗ )2π ∗θ∗ |θ=θ∗ = −> 0.
(1 − θ∗ )(1 + N)
π ∗θ |θ=θ∗ =From (1), (9), (17), and (18), dW in (15) satisfies¯
1 dW ¯¯
p0 x{2x [nN(1 − α) + n − αN] − D(N − n)}=−λ dθ ¯θ=θ∗ =02(1 + N)
¯
dL ¯¯
+w
.
dθ ¯θ=θ∗ =0

(18)

(19)

Larger values of n and smaller values of α and D contribute to the positivity of dW/dθ|θ=θ∗ =0 .
From (2), (3), (5), (8), (12), (14), and (17), we obtain
¯
xΦ
dL ¯¯
=
≶ 0 ⇔ ko ≶ ka ,(20)¯dθ θ=θ∗ 2(1 − θ)(ko − ka )ka¡∗ ¢2L∗a gp0 (N − n)(ko∗ − ka∗ )2 (N − n)p0 ka∗ + wr∗ L∗o (g0 )3+> 0.
+
where Φ ≡f 00
g(1 + N)r∗ gg 00
(See Mathematical Appendix for the derivation.) Equations (19) and (20) yield the next
proposition.
Proposition 2. Suppose that the oligopolistic sector is capital intensive (labor intensive)
and that neither country initially levies corporate tax. The larger (smaller) is the numberof oligopolists located in the home country, the lower (higher) is the share of equities
owned by the home country, or the lower (higher) is the home country’s demand for theoligopoly-produced commodity, the more likely is the home country to benefit (suﬀer) fromlevying corporate tax.
According to Proposition 1, if the home country levies corporate tax, the relative
price of the oligopoly-produced commodity increases, which raises demand for the competitively produced commodity. Therefore, if the competitive sector is more labor intensive than the oligopolistic sector, domestic employment increases, which benefits thehome country. In turn, the rise in the price of the oligopoly-produced commodity lowers
the home country’s consumer surplus. The extent of this loss rises with the home country’s demand for the oligopoly-produced commodity. Corporate tax revenue is higher,
7the more domestic oligopolists there are. Corporate tax lowers oligopolists’ net profits.
Therefore, the lower is the share of the oligopolists’ equities owned by the home country, the smaller is the loss of revenues from equities. Proposition 2 summarizes thesepredictions.
Many countries, particularly when they have unemployment, lower their corporate tax
rates in an attempt to retain their domestic firms and attract foreign direct investment tostimulate their economies. However, according to Proposition 2, a country that attracts
capital-intensive or exporting firms by lowering its corporate tax rate (from a low initiallevel) makes itself worse oﬀ.
Next, we investigate the eﬀect on foreign welfare. From (2), (5), (8), (16) and (17),the eﬀect on factor payments in the foreign country is∗∗(L + K r∗0 ) wθ∗ |θ=θ∗ = −n∗ p0 x2.
2(1 − θ)(21)

(See Mathematical Appendix for the derivation.) Applying (1), (9), (17), (18), and (21)to dW ∗ in (15) and rearranging the result yields the following eﬀect on foreign welfare
W ∗:¯
1 dW ∗ ¯¯p0 x∗{x∗ [(1 + N)n∗ − 2α∗ N(1 + n)] − D∗ n∗ }=−λ∗ dθ ¯θ=θ∗ =02(1 + N)p0 x∗
= −[n∗ (x∗ + D + 2α∗ Nx∗ ) − 2α∗ N(1 + N)x∗ ].
2(1 + N)
These two expressions for dW ∗ /dθ|θ=θ∗ =0 are used to obtain the following proposition.
Proposition 3. The larger (smaller) is the number of foreign-based oligopolists, thelower (higher) is the share of equities owned by the foreign country, or the lower (higher)
is the foreign country’s demand for the oligopoly-produced commodity, the more likely is
the foreign country to benefit (suﬀer) from the home country levying corporate tax.
There is no eﬀect on foreign employment because the foreign country attains full
employment. The intuition behind the other predictions is the same as for Proposition
2.
Next, we examine the welfare eﬀects of the foreign country levying corporate tax.
From (1), (9), (17), and (18), dW in (15) satisfies¯¯
p0 n∗ xdL ¯¯
1 dW ¯¯(D − 2αNx) + w ∗ ¯
=−
.
(22)
λ dθ∗ ¯ ∗2(1 + N)dθ∗θ=θ =0θ=θ =0From (2), (3), (5), (8), (12), (14), (17), and (20), we obtain
¯
¯
dL ¯¯
dL ¯¯
=−
≶ 0 ⇔ ko ≷ ka .
dθ∗ ¯ ∗dθ ¯ ∗
θ=θ

(23)

θ=θ

(See Mathematical Appendix for the derivation of (23).) The sign of dL/dθ∗ |θ=θ∗ isthe opposite of that of dL/dθ|θ=θ∗ . Equations (22) and (23) generate the following
proposition.
8

Proposition 4. Suppose that the oligopolistic sector is labor intensive (capital intensive).
The lower (higher) is the share of equities owned by the home country, or the higher(lower) is the home country’s demand for the oligopoly-produced commodity, the more
likely is the home country to benefit (suﬀer) from the foreign country levying corporatetax.
The number of domestic oligopolists n has nothing to do with the welfare eﬀect of theforeign corporate tax rate θ∗ because θ∗ does not aﬀect the home country’s tax revenues.
An increase in θ∗ increases world output of the oligopoly-produced commodity, as statedin Proposition 1, and reduces its price. It raises the home country’s consumer surplus andthe magnitude of the increase depends positively on the home country’s demand for theoligopoly-produced commodity. This is the opposite of the eﬀect of the home country’s
corporate tax rate, θ, as stated in Proposition 2. This is because an increase in θ lowers
world output of the oligopoly-produced commodity, as stated in Proposition 1, and raises
the oligopoly price.
Next, we examine the eﬀect on foreign welfare. From (2), (5), (8), (16), and (17), we
obtainn∗ p0 (x∗ )2
∗
∗
.
(24)
(L + K r∗0 ) wθ∗∗ |θ=θ∗ =2(1 − θ)(See Mathematical Appendix for this derivation.) Using this, (1), (9), (17), and (18), one
finds that dW ∗ in (15) is¯n∗ p0 x∗
1 dW ∗ ¯¯=−[x∗ (1 + N − 2α∗ N) + D∗ ].
λ∗ dθ∗ ¯θ=θ∗ =02(1 + N)
This result is used to establish the following proposition.

Proposition 5. The higher (lower) is the foreign country’s demand for the oligopolyproduced commodity, or the lower (higher) is the share of equities owned by the foreigncountry, the more likely is the foreign country to benefit (suﬀer) from levying corporate
tax.
From Proposition 1, an increase in θ∗ increases world output of the oligopoly-produced
commodity and reduces the price, which raises the foreign country’s consumer surplus.
From this follows the first property of Proposition 5. The second property is valid because
the foreign country suﬀers smaller losses from equity earnings the lower is its equity share.
In particular, when α∗ = 0, an increase in θ∗ unambiguously makes the foreign country
better oﬀ.

9

4

Location Taxes

The eﬀects of location taxes ε and ε∗ are basically the same as those of corporate taxes,
θ and θ∗ . Firstly, from (10) one obtains
dπ −

π∗
π
dθ = dπ∗ −dθ∗1−θ
1 − θ∗
dπ − dε = dπ∗ − dε∗when θ = θ∗ and ε = ε∗ = 0,
when θ = θ∗ = 0,(25)

implying that their eﬀects on the location choice are the same if dε(∗) = [π (∗) /(1 −θ(∗) )]dθ(∗) . Moreover, the two policies aﬀect neither the marginal conditions for profit
maximization (8) nor the gorss profits given in (9). Because the eﬀects of θ and θ∗ oneach firm’s output x and x∗ and on total output nx + n∗ x∗ are derived from (8), (9) and(10), the eﬀects of dε(∗) on them are respectively the same as those of [π(∗) /(1−θ(∗) )]dθ(∗) .
Therefore, proposition 1 also applies to the case of location tax.
Proposition 6. Suppose that the home and foreign countries initially set the same location tax rate. If the country with (without) unemployment raises its tax rate, world
output of the oligopoly-produced commodity decreases (increases).
The welfare eﬀects of the two policies in the neighborhood where ε = ε∗ = 0 andθ = θ∗ = 0 are also the same to each other, as mentioned below. From (25) in whichθ = θ∗ = 0, the eﬀects of dε(∗) on x, x∗ and nx + n∗ x∗ are respectively the same as
those of π (∗) dθ(∗) . From (8), the eﬀects on w∗ of the policies appear through changes inx and x∗ . The eﬀects on L emerge through changes in x, x∗ , nx + n∗ x∗ and w∗ so as tosatisfy (2), (3) and (12) (see Mathematical Appendix for details). Therefore, from (15),the eﬀects of dε(∗) on W and W ∗ are the same as those of π (∗) dθ(∗) .
Proposition 7. The welfare eﬀects of location tax-cum-subsidy are equivalent to those of
corporate tax-cum-subsidy; namely, Propositions 2—5 hold when location tax-cum-subsidy
rather than corporate tax-cum-subsidy is used.
In sum, neither corporate tax nor location tax changes the first-order optimal conditions of firms while changes in the two taxes aﬀect the location choice in the same way
when dε(∗) = π (∗) dθ(∗) . Moreover, from (7), when ε = ε∗ = 0 and θ = θ∗ = 0, the eﬀects
of such changes in the two taxes on each country’s tax revenue n(∗) [θ(∗) π(∗) + ε(∗) ] are thesame to each other. Therefore, the welfare eﬀect of dε(∗) is equivalent to that of π (∗) dθ(∗) .

5

Production Subsidies

This section examines the welfare eﬀects of production subsidies s and s∗ . For simplicity,
we ignore corporate taxes, θ and θ∗ , and location taxes, ε and ε∗ . From (1), (8), (9), and10

the properties on the first line of (14), we obtain
xs = x∗s = −

1
N
2x
> 0;
> 0, nxs + n∗ x∗s = −> 0, π s = π ∗s =00
(1 + N)p(1 + N)p1+Nxs∗ = x∗s∗ = 0, nxs∗ + n∗ x∗s∗ = 0, π s∗ = π ∗s∗ = 0.

(26)

From (14), the marginal costs of domestic and foreign firms are equalized through theinternational movement of firms. Therefore, if the country with the fixed wage subsidizes
production, each firm’s marginal cost falls by the same amount, which raises each firm’s
output and profits. By contrast, if the country with flexible wages subsidizes production,
firms’ marginal costs, output, and profits are not aﬀected. This result is summarized in
the following proposition.
Proposition 8. If the country with unemployment subsidizes production, each firm’s
output and profits increase, whereas subsidization of production by the full-employment
country has no eﬀect on firms’ output or profits.
From (1), the property given by the first line of (14), and (26), dW in (15) is
¯
¯
¶½ ∙
µ
¶¸
¾
µ
1+N
N
dL ¯¯
1 dW ¯¯x 2α − n+D +w=.
λ ds ¯s=s∗ =0
1+NN
ds ¯s=s∗ =0

From (2), (3), (5), (12), (14), and (26), we obtain
¯
dL ¯¯
Ω
,
=
¯
ds s=s∗ ka (ka − ko )Nxs (ka∗ − ko∗ )2 L∗a g (N − n)(g 0 )3 Lo
where Ω ≡− 00 −gf
gg 00 r∗

(27)

(28)
µ
¶2
w∗
∗
ka + ∗> 0.
r(See Mathematical Appendix for derivation of (28).) Because Ω > 0, the sign of dL/ds|s=s∗
depends on the sign of (ka − ko ). Equations (27) and (28) establish the following proposition.
Proposition 9. Suppose that the oligopolistic sector is capital intensive (labor intensive).
The larger (smaller) is the number of domestic oligopolists, the lower (higher) is theshare of equities owned by the home country, or the lower (higher) is the home country’s
demand for the oligopoly-produced commodity, the more likely is the home country to
suﬀer (benefit) from subsidizing production.
The implications of these conditions are similar to those for the corporate tax-cumsubsidy mentioned in Proposition 2.
Next, we examine the eﬀect of the home country’s production subsidy on foreign
welfare W ∗ . From (2), (3), (5), (16), and (26), we obtain∗∗(K r∗0 + L )ws∗ = −n∗ x∗ .
11

(29)

(See Mathematical Appendix for this derivation.) Therefore, using (1), (26), and (29),
we rewrite dW ∗ in (15) as
¯
µ
¾
¶½ ∙
¶¸
µ
1 dW ∗ ¯¯
1+N
N
∗
∗
∗
∗
x 2α − n+D .
=λ∗ ds ¯s=s∗ =0
1+N
N

We use this expression to establish the following proposition.

Proposition 10. The larger (smaller) is the number of foreign-based oligopolists, thelower (higher) is the share of equities owned by the foreign country, or the lower (higher)
is the foreign country’s demand for the oligopoly-produced commodity, the more likely is
the foreign country to suﬀer (benefit) from the home country subsidizing production.
The implications of the conditions are clear from those in Propositions 2 and 8. Notethat factor intensity does not matter because the foreign country achieves full employment
and the factor-intensity condition determines the direction of a change in employment if
unemployment arises.
Next, we examine the welfare eﬀects of the foreign production subsidy s∗ . Because
x and x∗ are unaﬀected by s∗ , as shown in (26), neither the oligopoly price p nor grossprofits π(= π ∗ ) is aﬀected by s∗ . Therefore, from (15), we obtain¯¯
1 dW ¯¯dL ¯¯= w ∗¯,λ ds∗ ¯s=s∗ =0
ds s=s∗ =0¯
1 dW ∗ ¯¯∗∗= (L + K r∗0 )ws∗∗ − n∗ x∗ .
(30)
∗
¯
∗
λ ds s=s∗ =0
The first equation shows that higher employment is the home country’s sole source ofincreased welfare. From (2), (3), (5), (12), (14), (16), and (26), we obtain
¯
µ
¶2
dL ¯¯
Γ
w∗
L∗a g (g0 )3 n∗ L∗o∗ka + ∗=> 0,, Γ ≡ − 00 −ds∗ ¯s=s∗ ka (ko − ka )f
g 00 gr∗r∗∗n∗ x∗ = (L + K r∗0 )ws∗∗ .

(31)(See Mathematical Appendix for the derivation of these properties.) Equations (30) and(31) are used to establish the following proposition.
Proposition 11. If and only if the oligopolistic sector is capital intensive (labor intensive) does the foreign production subsidy benefit (harm) the home country. It does not
aﬀect foreign welfare in any case.
As shown by the upper line in (14), because the home country’s wage rate is fixed atw and because oligopolists can move between countries, the foreign production subsidy
aﬀects neither oligopolists’ marginal costs, production, nor profits. The movement ofoligopolists from the home country to the foreign one reduces foreign production, and12increases home production, of the competitively produced commodity. Therefore, if theoligopoly sector is capital intensive (or if the competitive sector is labor intensive), employment in the home country increases and the home country is better oﬀ. This is the
only eﬀect on home welfare because w, r(w), and π(= π ∗ ) do not vary.
Given that earnings from equities do not change, the eﬀect on foreign welfare, if any,
operates by aﬀecting the foreign country’s total factor income minus the tax burden for
∗ ∗
∗ ∗
or
− s∗ ) as a result of thethe production subsidy. Because c(w) = c(w∗ ) − s∗ (= Lo w x+K∗international movements of oligopolists, we haven∗ x∗ c(w) = n∗ L∗o w∗ + n∗ Ko∗ r∗ − n∗ x∗ s∗ .
Therefore, from x∗ in (2), the two equations of the first line in (3), and the third and∗∗fourth equations in (11), total factor income L w∗ + K r∗ minus the tax burden n∗ x∗ s∗satisfies∗∗
L w∗ + K r∗ − n∗ x∗ s∗ = f (ka∗ )L∗a + c(w)g(ko∗ )n∗ L∗o .
(32)
This value equals total foreign production when the oligopoly price is c(w) instead of p.
Furthermore, from (3) and (4), each oligopolist’s cost minimization behavior leads toc(w)g(ko (w(∗) )) = w(∗) + r(w(∗) )ko (w(∗) ),r(w(∗) ) = c(w)g0 (ko (w(∗) )).

These equations are the same as those in the hypothetical case in which the price of thiscommodity is fixed at c(w) and the firms behave competitively. Because the other sector iscompetitive and the optimal behavior is described by the first line of (3), the hypotheticalincome represented by (32) can be regarded as that prevailing in the abovementioned
competitive economy when the relative price is fixed at c(w). The envelope theorem
implies that a marginal reallocation of the two factors between the two sectors would
not change the value of (32), which equals the foreign net factor income of the current
economy. Therefore, foreign welfare is not aﬀected by a marginal change in s∗ .

6

Minimum-Wage Reduction and Employment Subsidies

In this section, we examine the welfare eﬀects of a reduction in the minimum wage w andan increase in the employment subsidy z provided to the oligopoly sector in the homecountry. For simplicity, we assume that θ = θ∗ = ε = ε∗ = s = s∗ = 0. In this case, thesecond line of (3) and Y in (13), respectively, becomew−zg (ko )
= 0
− ko ,rg (ko )
Y = (w − z)L + rK + αNπ.
13

These expressions imply that the eﬀect of a reduction in w is the same as that of a risein z.
From (8) and (14), in which θ = θ∗ = s = s∗ = 0, we finddc = (1 + N)p0 dx.
This equation, (5), (9), and (14) yieldka − ko,(1 + N)p0 gka
2x (ka − ko )= π ∗w = −.
(1 + N)gka

xw = x∗w =
πw

(33)

If the oligopolistic sector is labor intensive (ka > ko ), a rise in w lowers each oligopolist’s
output and profits through the Heckscher—Ohlin mechanism.
From (1), the first equation in (5), (14), and (33), dW given in (15) reduces to
½ ∙
µ
¶¸
¾
1+N
1 dW
1 dW
N(ka − ko )dL
x 2α − n=−=+D −w .
(34)
λ dz
λ dw
(1 + N)gka
N
dw
Because (12) and (14) lead to∗ka dL = [N(ka − ko )Low + NLo kaw − NLo kow − (L + L )kaw ]dw,
in which Low is derived from (2), (5), and (33), thus,ka − ko(g 0 )3 Lo w
Low =+(1 + N)p0 g 2 kag 2 g00 rµ

1
1+
w ka r¶,and kaw and kow are found from (5), it follows that dL/dw satisfies
"
µ
¶2 #
dL
1 N(ka − ko )2 La + L∗a (g 0 )3 NLo
w
dL
> 0.
=−
=− 2
ka +
+
+
dz
dw
ka (1 + N)p0 g2
f 00
g 2 g00 rr(35)

Equations (34) and (35) are used to establish the following proposition.
Proposition 12. Suppose that the oligopolistic sector is labor intensive (capital intensive). The smaller (larger) is the number of domestic oligopolists, the higher (lower) is
the share of equities owned by the home country, or the higher (lower) is the home country’s demand for the oligopoly-produced commodity, the more likely is the home country
to benefit from lowering wages and subsidizing employment.
If the oligopoly sector is labor intensive, the home country’s employment subsidy
increases each oligopolist’s output, as shown in (33). It lowers the oligopoly price andincreases the home country’s consumer surplus. The magnitude of this benefit rises withthe home country’s demand for the oligopoly-produced commodity. The tax burden of
14

financing the subsidy is smaller, the fewer domestic oligopolists there are. Because thesubsidy increases every oligopolist’s net profits, the larger share of equities the homecountry owns, the more earnings from equities it earns. The employment-creation eﬀect
is unambiguously positive because the subsidy motivates oligopolists to enter the country
and employ more labor. Proposition 12 summarizes these predictions.
As is clear from (27) and (34), the welfare-improving conditions related to the employment subsidy, apart from its employment-creation eﬀect, are the same as those related
to the production subsidy. This is because the employment subsidy aﬀects the homecountry’s welfare by raising oligopoly production in the same way as does the production
subsidy.2
Next, we examine the eﬀect on foreign welfare. From (5), the last two equations in(11), the second line in (14), and (16), we obtain∗∗

L + K r∗0 =(ka∗ − ko∗ ) n∗ L∗o,ka∗dw∗ = dw.

From (1), (14), (33), and the above property, dW ∗ in (15) is
½ ∙
µ
¾
¶¸
1 dW ∗
1+N
1 dW ∗N (ka∗ − ko∗ )∗∗∗∗x 2α − n
=− ∗
=
+D .
λ∗ dz
λ dw
(1 + N)gka∗
N
From this, we establish the following proposition.
Proposition 13. Suppose that the oligopolistic sector is labor intensive (capital intensive). The smaller (larger) is the number of foreign-based oligopolists, the higher (lower)
is the share of equities owned by the foreign country, or the higher (lower) is the foreigncountry’s demand for the oligopoly-produced commodity, the more likely is the foreigncountry to benefit from the home country lowering wages and subsidizing employment.
The home country’s employment subsidy aﬀects foreign welfare by changing oligopoly
production and the international movements of oligopolists. Therefore, apart from theemployment-creation eﬀect (which does not operate in the foreign country), the implications of the conditions under which the foreign country’s welfare increases (stated in
Proposition 13) are the same as those under which the home country’s welfare increases(stated in Proposition 12).

7

Numerical Examples

From (19), (20), (27), (28), (34), and (35), we can respectively determine the conditions
on the equity share, α, required for the home country’s corporate subsidy, production
2

The employment-creation eﬀect of the employment subsidy is diﬀerent from that of the production
subsidy. The former directly stimulates employment whereas the latter aﬀects employment by raising
output in the oligopoly sector. Therefore, the former eﬀect unambiguously increases employment, asshown by (35), whereas the latter only does so when the oligopoly sector is labor intensive, as shown by
(31).

15

subsidy, and employment subsidy, to increase domestic welfare. They are¯¯∙¸D(N − n)
dL ¯¯
1
dW ¯¯
n(N + 1) −,− λw
≷0 ⇔ α≷d(−θ) ¯θ=θ∗ =0d(−θ) ¯θ=θ∗ =0
N(1 + n)2x¯dL ¯¯where λw
≷ 0 ⇔ ka ≷ ko ,d(−θ) ¯θ=θ∗ =0
¯
¯
µ
¶
D
dW ¯¯
dL ¯¯
n N +1−,− λw≷0 ⇔ α≷ds ¯s=s∗ =0
ds ¯s=s∗ =0
2
N
nx
¯
dL ¯¯
where λw
≷ 0 iﬀ ka ≷ ko ,ds ¯ ∗
s=s =0µdWdL(ka − ko )
− λw
dz
dz

¶

n
≷0 ⇔ α≷2dLwhere λw
> 0.
dz

µ

¶
D
N +1
−
,
N
nx

(36)

In this section, we present numerical examples of these conditions. We find the criticalvalues of α based on ignoring the employment-creation eﬀect. We do so because themagnitude of the employment eﬀect depends on the marginal utility of income, the firstand second derivatives of the production functions, and so on. Note that the welfare
eﬀects of corporate tax cuts and production subsidies deriving from employment creation
are positive if and only if the oligopoly sector is labor intensive, whereas that of theemployment subsidy is unambiguously positive. Therefore, the conditions relating to α
are suﬃcient in those cases.
The examples are based on data on the automobile industry in 2014, the beer industry in 2013, and the Smartphone industry in 2014. However, our examples are only
indicative of outcomes in these industries. This is because, whereas our model assumes
that a commodity is produced using only local factors, in practice, many of the parts
might be imported. Moreover, whereas our model assumes that all oligopolists have thesame technology, the same market share, and the same equity share distribution acrosscountries, in reality, these factors diﬀer between firms. Thus, our examples are merely
hypothetical examples based on market sizes and firm numbers that are similar to thoseof the three industries under consideration. To be specific, we assume the global numberof firms N to be m/ρ, where ρ is the market share of the world’s top m firms in eachindustry, and we assume the number of domestic firms n to be γ × (m/ρ), where γ is thehome country’s share of global production.

(a) Automobile Industry
In 2014, the share of the top 10 firms in the automobile industry was about 68%. Thus,
we set N to 15(+ 10/0.68). Total automobile production was about 90(= Nx) million
16

units. Thus, each firm’s production x is set to 6(= 90/15) million units. Production andconsumption levels in the top six countries are summarized in Table 1. The number offirms located in each country is assumed to be N multiplied by the production share.
For example, the number of firms located in China is assumed to be 4(+ 15 × 24/90).
Substituting the values in Table 1 into (36) yields the conditions on α under which
the subsidies make each country better oﬀ, apart from the eﬀect that operates throughemployment creation. Table 2 shows the results. In China, for example, if the worldwide
equity share is less than 57%, corporate taxation (rather than subsidization) increases
domestic welfare, apart from the eﬀect that operates through employment creation. For
the USA, the equity share must be less than 30%. For the other countries, the criticalshares are between those of the USA and China. Moreover, the employment-creationeﬀect of corporate taxation is positive if the automobile industry is capital intensive.
Therefore, taxing this industry should benefit the home country. In the USA, the welfare
eﬀect of the production subsidy (ignoring the employment-creation eﬀect) is positive.
However, the employment-creation eﬀect is negative if the industry is capital intensive.
Subsidizing employment clearly increases domestic welfare in the USA.
Table 1Country

Ã

China
USA
Japan
Germany
Korea
India

Production(million units)
24
12
10
6
5
4

Consumption(million units)
23
17
6
3
2
3

Numberof firms
4
2
2
1
1
1

Sources. Statista: http://www.statista.com/statistics/316786/global-market-share-of-the-leading-automakers/;
Global Note: http://www.globalnote.jp/post-3184.html; http://www.globalnote.jp/post-11249.html.

Table 2

3

Country

Corporate subsidy3

China
USA
Japan
Germany
Korea
India

α > 0.572
α > 0.301
α > 0.566
α > 0.416
α > 0.455
α > 0.416

Production subsidy
Employment subsidy
α > 0.216
always beneficial
α > 0.566
α > 0.283
α > 0.366
α > 0.283

Obviously, these conditions are opposite in the case of corporate tax.

17!

(b) Beer Industry
In 2013, the top 10 firms in the beer industry accounted for about 65% of the market.
Thus, we set N to 15(+ 10/0.65). Given world beer production of about 193(= Nx)billion liters, each firm’s production x is calculated to be 13(+ 193/15) billion liters.
Table 3 shows the approximate amounts of production and consumption for the world’s
top six countries. In the same way as for case (a), we calculate the number of firms
located in each country, which is reported in the final column of Table 3.
Substituting the values in Table 3 into (36) yields the conditions on α under which
the subsidies make each country better oﬀ, apart from the eﬀect that operates throughemployment creation. Table 4 shows the results. As in the automobile industry, inall countries, corporate taxation increases domestic welfare, apart from the eﬀect that
operates through employment creation, if the worldwide equity share of each country isless than 30%. The employment-creation eﬀects of corporate taxes are positive if the beerindustry is capital intensive. The welfare eﬀects of production and employment subsidies
are mixed.

Country

⎛

China
USA
BrazilGermany
RussiaMexicoTable 3
Production
Consumption(billion liters)(billion liters)
47
46
22
24
13
13
9
8
9
10
8
7

Numberof firms
4
2
2
1
1
1

Sources. Business Insider: http://www.businessinsider.com/global-beer-industry-consolidation-2014-2;⎝ Kirin Holdings: http://www.kirinholdings.co.jp/english/news/2014/0808_01.html,
http://www.kirinholdings.co.jp/english/news/2014/1224_01.html.

Table 4
Country

Corporate subsidy

China
USA
BrazilGermany
RussiaMexicoα > 0.593
α > 0.444
α > 0.300
α > 0.389
α > 0.353
α > 0.407

18

Production subsidy
Employment subsidy
α > 0.367
α > 0.145
α > 0.033
α > 0.227
α > 0.150
α > 0.266⎞⎠

(c) Smartphone Industry
In 2014, the top five firms in the Smartphone industry accounted for about 55% of themarket. Hence, we set N to 9(+ 5/0.55). Given world production of about 1220(= Nx)million units in 2014, the amount of each firm’s production x is 136(+ 1220/9) million
units. Table 5 shows the approximate amounts of production and consumption of theworld’s top two producing countries. In the same way as for case (a), we calculate thenumber of firms located in each country, which is reported in the final column of Table
5.
Substituting the values in Table 5 into (36) yields the conditions on α under which
the subsidies make each country better oﬀ, apart from the eﬀect that operates throughemployment creation. Table 6 shows the results. In China, corporate tax and production
tax are unambiguously beneficial, apart from the employment-creation eﬀect. This is also
the case for Vietnam if its worldwide equity share is less than 50%, which is plausible.
Moreover, from (20) and (28), the employment-creation eﬀects of corporate tax andproduction tax are positive if these countries’ industries are capital intensive. Therefore,
corporate tax and production tax benefit these two countries. The welfare eﬀect ofan employment subsidy that operates through employment creation is unambiguously
negative. Hence, for these two countries, the total welfare eﬀect of an employment subsidy
is ambiguous.

Country⎛

China
Vietnam

Table 5
Production
Consumption(million units)(million units)
970
420
110
10

Numberof firms
7
1

Sources. IDC: http://www.idc.com/getdoc.jsp?containerId=prUS25407215; http://www.idc.com/getdoc.jsp?

⎜⎝ containerId=prHK25437515; http://www.idc.com/getdoc.jsp?containerId=prVN25480615; JEITA (2015):
Worldwide Production of Major Electronics.

⎞⎟⎠

Table 6

8Country

Corporate subsidy

China
Vietnamalways harmful
always harmful

Production subsidy
Employment subsidy
always harmful
α > 0.520

Conclusion

We have examined the welfare eﬀects of a corporate tax, a location tax, a production
subsidy, and an employment subsidy in a 2 × 2 × 2 general equilibrium model with a19perfectly competitive sector and an oligopolistic sector. Our model incorporates unemployment caused by wage rigidities, oligopolist-location choice between countries, andforeign ownership of oligopolists. We have derived the conditions under which a corporate tax-cum-subsidy, a location tax-cum-subsidy, a production tax-cum-subsidy, and an
employment tax-cum-subsidy improve home and foreign welfare, respectively.
The literature on tax competition, as represented by, for example, Wilson (1986) and
Wildasin (1988), shows that tax competition that reduces taxes is harmful to countries
because the reduction in tax revenue from tax competition leads to an undersupply of
public goods. By contrast, tax revenue is not an important factor in the welfare analysis
based on our model because the tax revenue is returned to residents in a lump sum.
Nevertheless, a reduction in the corporate tax rate may make the country that imposes
the tax worse oﬀ.
For example, if the oligopolistic sector is capital intensive, a reduction in the corporate
tax rate increases unemployment, which is harmful to the country. Moreover, if thecountry has a low equity share, little of the extra profit deriving from the reduction
in corporate tax returns to the country. The volume of home demand for the oligopolyproduced commodity (or that of consumer surplus) and the number of domestically basedoligopolists also influence the welfare eﬀect of the tax reduction through a change in theprice and through a rise in the tax burden, respectively.

Mathematical Appendix
From (2), (3), and (17), we obtainLoθ |θ=θ∗ =n∗ x,2(1 − θ)(1 + N)g

Loθ∗ |θ=θ∗ = −When θ = θ∗ , equations (2) and (17) yield(1 + n)x∗.
2(1 − θ∗ )(1 + N)gx∗θ dθ + x∗θ∗ dθ∗ = gdL∗o + L∗o g0 dko∗ .
From (5),¶g (ko∗ ) g 00 (ko∗ ) ∗
w∗
=
−
dko ,
d
r∗
(g 0 (ko∗ ))2
f 00 (ko∗ − ka∗ ) ∗r∗ g 00 (k ∗ − k∗ )dc(w∗ ) =dka = ¡ ∗ wo∗ ¢ a0 2 dko∗ .
gka + r∗ (g )

(A-1)

(A-2)

µ

(A-3)

Equations (8) and (17) lead to
−

p0 x
p0 x∗
dθ +
dθ∗ = dc(w∗ ).
2(1 − θ)2(1 − θ∗ )From (A-2), (A-3) and (A-4),∗kaθ|θ=θ∗ = −gp0 x,2(1 − θ)f 00 (ko∗ − ka∗ )

∗
∗|
kaθ
θ=θ∗ =

20

gp0 x∗,
2(1 − θ∗ )f 00 (ko∗ − ka∗ )(A-4)

¡ ∗ w∗ ¢ 0 2
0x
ka + r∗ (g )p∗koθ
|θ=θ∗ = −,2(1 − θ)(ko∗ − ka∗ )r∗ g00
L∗oθ |θ=θ∗L∗oθ∗ |θ=θ∗¡ ∗ w∗ ¢ 0 2
0 ∗x
ka + r∗ (g )
p
∗
∗|
koθ
,
θ=θ∗ =
2(1 − θ∗ )(ko∗ − ka∗ )r∗ g00¡∗¢
p0 x ka∗ + wr∗ L∗o (g 0 )3
x∗θ
=
,
+
g
2(1 − θ)(ko∗ − ka∗ )r∗ gg00¡∗¢
p0 x∗ ka∗ + wr∗ L∗o (g 0 )3
x∗θ∗
=
.
−
g
2(1 − θ∗ )(ko∗ − ka∗ )r∗ gg00

(A-5)

Applying (A-1) and (A-5) to (12) and making use of (14) gives (20) and (23). Substituting∗∗kaθ
and kaθ∗ in (A-5) into (16), respectively, and making use of (2) yields (21) and (24).
From (2), (3), and (26),xsx∗sg 0 L∗o ∗∗dko .
Los = , dLo = ds −
g
g
g

(A-6)

Because (5) and (A-3) hold in this case, using these equations together with the first linein (26) and (A-6), one finds
µ
¶
µ
¶
1
1
(g0 )3 L∗o ka∗ w∗
xs
1(g 0 )3 L∗o ka∗ w∗
1∗∗, Los∗ = ∗
,
−
+
+
Los =
g(ko∗ ) (ka∗ − ko∗ ) gg00 r∗ w∗ r∗ ka∗(ka − ko∗ ) gg 00 r∗ w∗ r∗ ka∗
∗
kas
=
∗
kos
=

(g 0 )2 ka∗ w∗
g 00 (ka∗ − ko∗ )r∗µg

f 00 (ka∗ − ko∗ )11+w∗ r∗ ka∗

¶

,

g
∗
kas
,
∗ = −
00
∗
f (ka − ko∗ )µ¶g 0 ka∗ w∗
11∗kos∗ = − 00 ∗.
+g (ka − ko∗ )r∗ w∗ r∗ ka∗

,

(A-7)

Applying the values in (A-6) and (A-7) to (12) and making use of (14) leads to (28) and∗∗and kasthe first property of (31). Substituting kas∗ in (A-7) into (16) yields (29) and thesecond property of (31), respectively.

References
Brander, J. A. and B. J. Spencer (1985) “Export Subsidies and International Market
Share Rivalry,” Journal of International Economics 18, 83—100.
Exbrayat, N., C. Gaigné and S. Riou (2012) “The Eﬀects of Labour Unions on International Capital Tax Competition,” Canadian Journal of Economics 45, 1480—1503.
Johdo, W. and K. Hashimoto (2009) “International Relocation, the Real Exchange Rateand Eﬀective Demand,” Japan and the World Economy 21, 39—54.
Kreickemeier, U. (2005) “Unemployment and the Welfare Eﬀects of Trade Policy,” Canadian Journal of Economics 38, 194—210.
Leite-Monteiro, M., M. Marchand and P. Pestieau (2003) “Employment Subsidy with
Capital Mobility,” Journal of Public Economic Theory 5, 327—344.
21

Hamada, Y. (2008) “Hojokin Oyobi Sono Katsuyou Jirei to Kigyo Yuuchi Suisin (inJapanese),” Shoko Research Institutes.
Haufler, A. and F. Mittermaier (2011) “Unionisation Triggers Tax Incentives to Attract
Foreign Direct Investment,” Economic Journal 121, 793—818.
Haufler, U. and F. Stähler (2013) “Tax Competition in a Simple Model With Heterogeneous Firms: How Larger Markets Reduce Profit Taxes,” International Economic
Review 54, 665—692.
Hucka, S. and K. A. Konrad (2003) “Strategic Trade Policy and the Home Bias in Firm
Ownership Structure,” Japan and the World Economy 15, 299—305.
Lahiri, S. and Y. Ono (1995) “The Role of Free Entry in an Oligopolistic Heckscher—
Ohlin Model,” International Economic Review 36, 609—624.
Lahiri, S. and Y. Ono (2011) “An Oligopolistic Heckscher—Ohlin Model of Foreign Direct
Investment,” Japanese Economic Review 62, 331—347.
Ogawa, H., Y. Sato and T. Tamai (2006) “A Note on Unemployment and Capital Tax
Competition,” Journal of Urban Economics 60, 350—356.
Tax Foundation Website (2013) “OECD Corporate Income Tax Rates, 1981—2013,”
http://tax foundation.org/article/oecd-corporate-income-tax-rates-1981—2013.
Wildasin, D. E. (1988) “Nash Equilibrium in Models of Fiscal Competition,” Journalof Urban Economics 35, 229—240.
Wilson, J. D. (1986) “A Theory of Inter-Regional Tax Competition,” Journal of Urban
Economics 19, 296—315.

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