Corporate Tax Policy and Industry Location with
Fully Endogenous Productivity GrowthColin Davis
Ken-ichi Hashimoto
July 2015
Discussion Paper No.1527

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANCorporate Tax Policy and Industry Location
with Fully Endogenous Productivity GrowthColin Davis
Doshisha University∗

Ken-ichi Hashimoto
Kobe University†

July, 2015
Abstract
This papers considers how national corporate tax policy affects productivity
growth through adjustments in geographic patterns of industry in a two-country
model of trade. With trade costs and imperfect knowledge spillovers between
countries, production concentrates partially and innovation concentrates fully inthe country with the lowest tax rate. When firms have weak (strong) monopoly
power, a decrease in the tax rate of the low-tax-rate country depresses (accelerates) productivity growth. The paper also investigates the relationship between
relative tax rates and the level of product variety, and analytically characterizes
the effects of changes in tax policy on national welfare.
Key Words: National Corporate Tax Policy, Fully Endogenous Productivity
Growth, Monopoly Power, Industry Concentration
JEL Classifications: F43; O30; O40; R12∗

The Institute for the Liberal Arts, Doshisha University, Karasuma-Higashi-iru, Imadegawa-dori,
Kamigyo, Kyoto, Japan, 602-8580, cdavis@mail.doshisha.ac.jp.
†
Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe, Japan, 657-8501,
hashimoto@econ.kobe-u.ac.jp.

1

Introduction

The influence of national tax policy on geographic patterns of industry is a key concern for policy makers at local, regional, and national levels, with emphasis often
placed on the pro-growth effects of low corporate tax rates as a component of trade
policy. Indeed, Kammas (2011) and Brülhart et al. (2012) present empirical evidence
indicating that tax policies are an important factor in the location decisions of firms.1
Moreover, Devereux and Loretz (2013) survey the tax competition literature and conclude that the evidence suggests a pattern of strategic interaction in the corporate
tax rates set by national governments, which may provide one possible explanation
for the international trend towards lowering effective tax rates on corporate income(IMF, 2014). Given this policy trend, it is important to consider how economic growthis affected by shifts in production between locations, as firms respond to changes incorporate tax policy. In this paper, we attempt to address this question by studying
the effects of corporate taxes on industry location in a two-country model of tradeand fully endogenous economic growth.
In particular, we extend the framework of Davis and Hashimoto (2015a) to investigate the effects of national tax policy on industry location, productivity growth, andmarket entry. Monopolistically competitive firms employ labor in process innovation
with the objective of reducing unit production costs, and knowledge accumulation
within the production technologies of firms lowers the costs of future innovation efforts, potentially generating endogenous productivity growth (Smulders and van deKlundert, 1995; Peretto, 1996). Perfect capital mobility allows firms to locate production and innovation independently in the countries with the lowest costs. As aresult, with international trade costs, a standard home market effect causes a greater
share of firms to locate production in the country with the lowest corporate tax rate
1

Feld and Heckemeyer (2011) provide a survey of the empirical literature investigating the effectsof fiscal policy on foreign direct investment flows.

1and the largest after tax market (Martin and Rogers, 1995). In addition, imperfectinternational knowledge diffusion leads to greater knowledge spillovers from production to innovation, lower R&D costs, and the full concentration of process innovationin the low-tax-rate country.
The effects of national tax policy on firm-level employment in production andinnovation are intrinsically linked to monopoly power through free market entry andexit. Specifically, firms employ a greater share of labor in production when they
have weak monopoly power, and a greater share of labor in innovation when they
have strong monopoly power. Decreasing the corporate tax rate of the low-tax-rate
country raises its share of production, affecting employment in innovation throughtwo channels. The first is a knowledge spillover effect, through which the increased
concentration of industry lowers the cost of innovation, causing firm employment ininnovation to fall when monopoly power is weak and to rise when monopoly poweris strong. The second channel is a profit effect that is positive when the tax rate of
the low-tax-rate country is high and the rise in industry-wide profit corresponding
with lower trade costs dominates. The profit effect is negative when the initial tax
rate is low and the fall in firm-level profit resulting from greater competition in the
low-tax-rate country dominates.
The balance of the knowledge spillover and profit effects determines how changes innational tax policy affect product variety and productivity growth. When firms haveweak monopoly power, reducing the tax rate of the low-tax-rate country depresses
productivity growth, but has a positive effect on product variety if the initial tax
rate is high and an ambiguous effect on product variety if the initial tax rate is low.
Alternatively, when monopoly power is strong, a reduction in the tax rate accelerates
productivity growth, but has an ambiguous effect on product variety if the initial tax
rate is high and a negative effect on product variety if the initial tax rate is low.
In general, the empirical literature tends to find evidence supporting a negative2

relationship between corporate taxes and economic growth (Lee and Gordon, 2005;
Arnold et al., 2011; Gemmell at al., 2015), in contrast to the mixed theoretical resultsof this paper. Although, Angelopoulos et al. (2007) report that corporate taxes havea positive effect on growth, and Ojede and Yamarik (2012) find that tax policy has no
significant influence on long-run growth. As such, given the moderately mixed natureof empirical results, the framework presented in this paper emphasizes the importanceof considering the firm location decision, when estimating the size of fiscal policy effects
on economic growth (Gemmell at al., 2015).
We also investigate the relationship between corporate tax policy and national welfare levels. A decrease in the tax rate of the low-tax-rate country affects welfare levels
through three channels. The first is a fall in the average price of manufacturing goodsin the low-tax-rate country and a rise in average price in the high-tax-rate country.
The second and third channels are a love of variety effect and a productivity growtheffect. We show analytically that the balance between these channels is determinedby the degree of monopoly power. As such, national welfare levels may be increasingor decreasing in the corporate tax rate of the low-tax-rate country, depending on themonopoly power of manufacturing firms.
There is a broad theoretical literature studying the relationship between corporate
tax rates and economic growth. However, the number of studies considering firm, or
capital, mobility is limited. In a closed economy model of fully endogenous productivity growth, Peretto (2007) shows that a budget-neutral increase in corporate taxes
has a positive effect on economic growth. Iwamoto and Shibata (2008) and Palomba(2008) develop open economy models using overlapping generations frameworks tostudy the effects of capital income tax rates on the movement of capital and the economic growth rate, and find that lowering tax rates with the aim of attracting capital
may have a negative effect on growth. Both of these models exhibit scale effects, however, with a positive relationship between the size of the labor force and the rate of3

economic growth. In this paper, we develop an open economy framework that allows
for firm mobility, and study the relationship between corporate taxes and economic
growth that is not biased by scale effects.2
The remainder of the paper proceeds as follows. In Section 2, we introduce ourtheoretical framework and investigate the effects of national corporate tax rates on thelocation patterns of production and innovation. Then, we consider the implicationsof corporate taxes for the rate of productivity growth, level of product variety, andnational welfare. The paper concludes in Section 3.

2

The ModelThis section extends Davis and Hashimoto (2015a) to consider the implications of national corporate tax policy for patterns of industrial activity, productivity growth, andmarket entry. The model consists of two countries, home and foreign, that potentiallyemploy labor in three activities: traditional production, manufacturing, and process
innovation. The home and foreign labor supplies, L and L∗ , are mobile between sectors, but not between countries, with an asterisk denoting variables associated withforeign. We focus on home as we introduce the model setup.
2.1

Households

The demand side of the economy is made up of the dynastic households residing
in each country. These households choose optimal saving-expenditure paths over an
infinite time horizon with the aim of maximizing lifetime utility,

U=

Z ∞
0

e−ρt (α ln CX (t) + (1 − α)CY (t)) dt,(1)

2
This paper develops an endogenous market structure and endogenous growth framework thatis not biased by scale effects (Aghion and Howitt, 1998; Etro, 2009). Empirical support for theframework is found in Laincz and Peretto (2006), Ha and Howitt (2007), and Madsen et al. (2010).

4

where CX (t) and CY (t) are household consumptions of a manufacturing composite
and traditional goods at time t, ρ is the subjective discount rate, and α ∈ (0, 1).
Lifetime utility is maximised subject to the following flow budget constraint:Ȧ(t) = r(t)A(t) + w(t) + T (t) − PX (t)CX (t) − PY (t)CY (t),where A(t) is asset wealth, r(t) is the interest rate, w(t) is the wage rate, T (t) is a
lump-sum transfer from government to households, PX (t) is the price index associatedwith the manufacturing composite, PY (t) is the price of traditional goods, and a dot
indicates differentiation with respect to time.
The households of home and foreign have equal access to an international financial
market, leading to a common interest rate across countries, and common motions forthe evolution of household expenditure:Ė ∗Ė= ∗ = r − ρ,
E
E

(2)

where E = PX CX + PY CY . We suppress time notation for the remainder of the paper,
when doing so does not cause confusion.
The per-period demands for the manufacturing composite and traditional good
are CX = αE/PX and CY = (1 − α)E/PY , with the manufacturing composite, andits price index, taking a constant elasticity of substitution (CES) form:

CX =

Z N
0

ci

σ−1
σ

σ
 σ−1
,
di

PX =

Z N
0

pi

1−σ

1
 1−σ
,
di

(3)

where the mass of product varieties available (N = n + n∗ ) equals the sum of varieties (n) produced in home and varieties (n∗ ) produced in foreign, ci and pi are thehousehold consumption and price of variety i, and the constant elasticity of substitution between any pair of varieties is σ > 1. Given the constant level of household5expenditure allocated to manufacturing goods, the home household demands for adomestically supplied variety i and an imported variety j are
σ−1
ci = αp−σ
i PX E,

cj = α(τ p∗j )−σ PXσ−1 E,(4)where τ > 1 is an iceberg trade cost, under which τ additional units must be shipped
for every unit sold in an export market (Samuelson, 1954). We also derive analogous
demand conditions for foreign households.
2.2

Production

The traditional good sector employs labor with a unit coefficient technology thatexhibits constant returns to scale. We suppose that the share of traditional goods inhousehold expenditure is large enough to ensure both countries produce traditional
goods. Thus, with free trade in a competitive international market, the price oftraditional goods and the wage rate are common across home and foreign. Setting
the traditional good as the model numeraire, we have PY = PY∗ = w = w ∗ = 1.
The manufacturing sector features Dixit and Stiglitz (1977) monopolistic competition, with each firm supplying a single unique product variety. While there are nocosts associated with the development of new product designs, every period firms incur labor costs in the management (lF ) and implementation innovation (lR ), which are
fixed with respect to production. The production technology of a firm with production
located in home isx = θlX ,(5)

where x and lX are output and employment in production, and θ is a firm-levelproductivity coefficient. Although each firm employs a unique production technique,we assume that productivity is symmetric across all firms in all locations (θ = θ∗ ).
6

We define the degree of monopoly power associated with each firm as the ratio of
average revenue to marginal revenue (Helpman and Krugman, 1985). Therefore, with
CES preferences over product variety, the degree of monopoly power is η ≡ σ/(σ−1) >1, and firms set price equal to a constant markup over unit cost: p = p∗ = η/θ.
Matching supply with the demands from the home and foreign markets, home-based
production is x = ci L + τ c∗i L∗ , where τ > 1 units must be produced for every unit
sold in the export market. Together with (4), this condition yields optimal operating
profit on sales for a firm with production located in home:α(η − 1)π = px − lX = (η − 1)lX =ηELϕE ∗ L∗+n + ϕn∗ ϕn + n∗



,

(6)

where ϕ = τ 1−σ describes the freeness of trade.
2.3

Process Innovation

Manufacturing firms invest in process innovation with the objective of lowering production costs. In particular, each period a representative firm employs lF units oflabor in the management of innovation and lR units of labor in process innovation,with the evolution of firm productivity governed byθ̇ = kθlR ,(7)

where kθ is labor productivity in innovation. Following the in-house innovation literature (Smulders and van de Klundert, 1995; Peretto, 1996), a firm’s current state oftechnical knowledge is captured by θ, and as a result knowledge accumulates within
the production technology of the firm, generating an intertemporal knowledge spillover
through which current innovation efforts reduces future R&D costs.
Adapting the specification of Baldwin and Forslid (2000), we assume that knowl-

7

edge spillovers from production to innovation diminish with distance:k = s + δs∗ ,(8)where s ≡ n/N and s∗ ≡ n∗ /N are the shares of firms with production located inhome and foreign, and δ ∈ (0, 1) is the degree of knowledge diffusion between countries. Under this specification for knowledge spillovers, labor productivity in process
innovation is determined as a weighted average of the productivities of technologies
observable by the firm, with a stronger weighting for technologies used in production
located in proximity to the R&D department of the firm.3
We consider territorial tax systems in which the source of production, rather thanthe point of sale, is used for taxation (IMF, 2014). As such, firm value equals thepresent discounted value of net per-period profits:

V =

Z ∞
0

Rt

′

′

e− 0 r(t )dt ((1 − z)(π(t) − lR (t) − lF ))dt,(9)where z ∈ (0, 1) is the corporate tax rate set on per-period profit in the home country.4
Firms employ labor in process innovation with the goal of maximizing (9). We solve
this optimization problem using the following current value Hamiltonian function:
H = (1 − z)(π − lR − lF ) + µkθlR , where µ is the current shadow value of the firm’s
stock of technical knowledge. Combining the first order conditions, ∂H/∂lR = 0 and∂H/∂θ = rµ − µ̇, leads to the following no-arbitrage condition for a firm’s optimallevel of investment in process innovation:

r≥

k̇ θ̇
πk
− − .
η−1 k θ3

(10)

Coe et. al. (2009) and Ang and Madsen (2013) provide empirical support for the positive effects
of international knowledge spillovers on total factor productivity growth.
4
Within our framework, z is an average effective tax rate that may reflect a variety of countryspecific tax rates (Bénassy-Quéré et al., 2005).

8

The internal rate of return to investment in process innovation equals the risk-freeinterest rate when firms exhibit productivity growth.
2.4Market Entry

With zero costs incurred in the design of new product varieties, net per-period profits
determine the level of market entry.5 When firm value is positive (V > 0), new firms
enter the market causing a fall in firm-level market shares and lowering firm value
through a fall in operating profit on sales. Alternatively, when firm value is negative(V < 0), firms exit the market and firm value rises. This process is immediate, andleads to the following free entry conditions for production located in home and foreign:

π = lR + l F ,∗π ∗ = lR
+ lF .

(11)

With all firms earning zero profits, corporate tax revenues are zero in both countries(T = 0), and household expenditure equals wage income (E = 1 and E ∗ = 1). Then,from (2), r = ρ at all moments in time. For the remainder of the paper, we assume thatthe populations of home and foreign are equal (L = L∗ ), and focus on cross-country
differences in corporate tax rates.
2.5

Corporate Taxes and Location Patterns

Free to shift production between countries, at zero cost, manufacturing firms locate
production in the country that offers the highest level of operating profit, net of corporate taxes, with the aim of maximizing firm value. Accordingly, when manufacturing
occurs in both countries, net operating profit on sales equalizes between home andforeign based production: (1 − z)π = (1 − z ∗ )π ∗ . Substituting (6) into this condition5

See Davis and Hashimoto (2015b) for a similar framework with positive entry costs.

9

yields the equilibrium share of firms with production located in home:s(ϕ, Z) =(Z − ϕ) − ϕ(1 − ϕZ),(1 − ϕ)2 (1 + Z)

(12)

where Z ≡ (1 − z)/(1 − z ∗ ) describes the corporate tax gap between home and foreign.
An rise in Z indicates a fall in the home tax rate relative to foreign. In addition,Z ∈ (Z, Z), with Z = 2ϕ/(1 + ϕ2 ) and Z = (1 + ϕ2 )/(2ϕ), is required for s ∈ (0, 1).
The home share of production features a standard home market effect (Krugman,1980), with a greater share of firms locating production in the country with the larger
after-tax market.
The effect of a change in the corporate tax gap on the location of production issummarized in the following lemma.
Lemma 1 An increase in the tax gap (Z) raises the home share of production (s).
Proof: The derivative of (12) with respect to Z yields(1 + ϕ)2
ds
=
> 0.
dZ
(1 − ϕ)2 (1 + Z)2This is a standard result in the New Economic Geography literature (Baldwin et al.,2003). Intuitively, an increase in the corporate tax gap (a decrease in home’s relative
tax rate) makes home more attractive as a location for production, as the relative
size of its after-tax market increases. In order to simplify the analysis, we consider
long-run equilibria for which home has a lower corporate tax rate and a larger shareof manufacturing activity; that is, Z ∈ (1, Z) and s ∈ (1/2, 1). Accordingly, we focus
on cases for which k ∈ ((1 + δ)/2, 1) is satisfied.
The concentration of manufacturing activity leads to the full agglomeration ofprocess innovation in home. To see this, we rewrite the no-arbitrage conditions (10)10

associated with investment in innovation in home and foreign asρ(2 − η)π≥+ lf ,kη−1ρ
(2 − η)π≥+ lf ,
k∗
η−1

(13)

where we have used (11), equalized net operating profits (1 − z)π = (1 − z ∗ )π ∗ , andthe fact that ṡ = k̇ = 0 in equilibrium. With manufacturing concentrated in home,greater knowledge spillovers from production to innovation (k > k ∗ ) ensure that allprocess innovation occurs in home.
Combining the home no-arbitrage condition with (11), we solve for equilibrium
firm-level employment in production and innovation:lX =klF − ρ,(η − 2)klR =klF − (η − 1)ρ
.
(η − 2)k(14)

As discussed in Davis and Hashimoto (2015a), these conditions dictate the range ofknowledge spillovers consistent with both market entry and productivity growth.
Lemma 2 Positive employment in both production and innovation requires (i) k ∈((1 + δ)/2, (η − 1)ρ/lF ) when monopoly power is weak (η < 2), and (ii) k ∈ ((η −1)ρ/lF , 1) when monopoly power is strong (η > 2).
The degree of monopoly power dictates the ratio of labor employment in production to labor employment in process innovation that is consistent with positive
productivity growth and free market entry and exit. When monopoly power is weak(η < 2), a low range of knowledge spillovers ensures that firms employ a greater shareof labor in production (lX /(lR + lF ) > 1). On the other hand, a high range of knowledge spillovers is necessary with strong monopoly power (η > 2) in order to ensurethat firms employ a higher share of labor in innovation (lX /(lR + lF ) < 1).
Before ending this section, we derive the level of operating profit on sales associated11with the free movement of production between countries by substituting (12) into (6):π=π∗α(η − 1)(1 − ϕ)2 (1 + Z)L
=,Z
η(1 − ϕZ)(Z − ϕ)N(15)

where Z ∈ (1, Z) ensures positive operating profit since Z ∈ (ϕ, 1/ϕ).
2.6

Product Variety and Productivity Growth

We now consider the effects of changes in the corporate tax gap on productivity growthand product variety. Beginning with the rate of productivity growth, we combine (12)with firm-level employment in process innovation (14) to obtaing≡θ̇
klF − (η − 1)ρ
=
.
θ
η−2

(16)

From this expression, we can see that productivity growth is not biased by a scaleeffect, as proportionate increases in the population sizes of home and foreign do notaffect national shares of production.
We use (16) to examine how corporate taxes rates affect productivity growth.
Proposition 1 A rise in the corporate tax gap (Z) depresses productivity growthwhen monopoly power is weak (η < 2) and k ∈ ((1 + δ)/2, (η − 1)ρ/lF ), but accelerates
productivity growth when monopoly power is strong (η > 2) and k ∈ ((η − 1)ρ/lF , 1).
Proof: Taking the derivative of (16) with respect to Z gives
lF dk dsdg=,dZ
(η − 2) ds dZ(17)

where dk/ds = 1 − δ > 0 and ds/dZ > 0 from Lemma 1.
Changes in the corporate tax gap influence productivity growth through a knowledge spillover effect. In particular, a decrease in the home tax rate (a rise in Z) raises
the home share of production, resulting in a greater level of knowledge spillovers from12

production to innovation. The increase in knowledge spillovers causes adjustments
in firm-level employment in process innovation (14), the direction of which are determined by the degree of monopoly power. When monopoly power is weak (η < 2),employment in process innovation falls, dampening the rate of productivity growth.
In contrast, when monopoly power is strong (η > 2), innovation employment rises,
accelerating productivity growth.
Next, we use firm-level employment in production (14) with π = (η − 1)lX andoperating profit on sales (15) to derive the equilibrium level of market entry asN=α(1 − ϕ)2 (1 + Z)L
.
η(1 − ϕZ)(Z − ϕ)lX

(18)

From this expression, we find that product variety is determined proportionally withpopulation size.6
We investigate how changes in the corporate tax gap affect product variety (18)and obtain the following proposition.
Proposition 2 With weak monopoly power (η < 2) and k ∈ ((1+δ)/2, (η−1)ρ/lF ), arise in the corporate tax gap has an ambiguous effect on product variety for Z ∈ (1, Z̃),√and a positive effect for Z ∈ (Z̃, Z), where Z̃ = −1 + (1 + ϕ)/ ϕ. In contrast, withstrong monopoly power (η > 2) and k ∈ ((η − 1)ρ/lF , 1), a rise in Z has a negative
effect on product variety for Z ∈ (1, Z̃), and an ambiguous effect for Z ∈ (Z̃, Z).
Proof: See the Appendix.
Taking the derivative of product variety (18) with respect to Z, we have
1 dN
1 dlX dk ds(1 + ϕ)(Z − ϕ) − (1 + Z)(1 − ϕZ)
=−
+
,
N dZ
lX dk ds dZ(1 + Z)(Z − ϕ)(1 − ϕZ)(19)

where dk/ds = 1 − δ > 0 and ds/dZ > 0 from Lemma 1. Changes in the corporate
6

See Davis and Hashimoto (2015a) for a discussion of the effects of improved regional integration
through lower trade costs or greater knowledge diffusion.

13

Figure 1: Corporate Taxes and Product Variety

N

N
N (Z)

0

1

Z̃

N (Z)

Z

0

Z

(a) η < 2

1

Z

Z̃

Z

(b) η > 2

In Panel (a) we use α = 0.5, ρ = 0.15, lF = 0.07, η = 1.65, L = 1, ϕ = 0.35, and δ = 0.9. In
Panel (b) we use α = 0.5, ρ = 0.1, lF = 0.65, η = 5.6, L = 1, ϕ = 0.35, and δ = 0.5.

tax gap affect the level of market entry through two channels. The first channel isthe indirect knowledge spillover effect described by the first term on the righthandside of (19). A decrease in the relative tax rate of home (a rise in Z) increases thehome share of production, raising the level of knowledge spillovers from production to
innovation. The result is a tendency for firm-level employment in production to fall
and market entry to rise when monopoly power is weak (η < 2). On the other hand,when monopoly power is strong (η > 2), the knowledge spillover effect is negative andmarket entry tends to fall with a decrease in the relative tax rate of home.
The second channel is the direct profit effect captured by the second term on therighthand side of (19). The sign of the profit effect depends on the relative strengthsof two mechanisms. First, a decrease in the relative tax rate of home causes a shift
in production from foreign to home, improving profitability as the industry-level costof transporting goods from the smaller foreign country to the larger home country
falls. Second, the increased concentration of production in the home market raises
the level of competition, thereby reducing profitability. The negative competition14

effect dominates, and the profit effect is negative, for Z ∈ (1, Z̃), while the benefit oflower transport costs dominates, and the profit effect is positive, for Z ∈ (Z̃, Z).
The overall balance between the knowledge spillover effect and the profit effectdetermines the level of market entry. Figure 1a illustrates the case where firm’s haveweak monopoly power (η < 2). While the knowledge spillover effect associated witha rise in the corporate tax gap is positive, the profit effect is negative for Z < Z̃. As
either effect may dominate, the overall impact on product variety is ambiguous. For
Z > Z̃, however, both the knowledge spillover effect and the profit effect are positive,
and an increase in the corporate tax gap raises product variety. Similarly, a numericalexample for the case of strong monopoly power (η > 2) is provided in Figure 1b. In
this case, the corporate tax gap and product variety have a negative relationship for
Z < Z̃, and an ambiguous relationship for Z > Z̃.
2.7

National Welfare and Corporate Tax Rates

Finally, we consider the relationship between the corporate tax gap and national
welfare levels. With the governments of both countries earning zero tax revenues(T = 0), steady-state welfare levels can be derived using (1), (3), (7), and (12):(Z − ϕ)Ng(η − 1) ln,+(1 + Z)ρα(1 − ϕZ)Ng∗
U0 = ln A1 +(η − 1) ln,+
ρ(1 + Z)ρα
U0 = ln A1 +
ρ

(20)
(21)

where A1 ≡ (αθ(0)/η)α/ρ (1 − α)(1−α)/ρ ((1 + ϕ)/(1 − ϕ))α(η−1)/ρ > 0 is a constant.
Proposition 3 The welfare effects of an increase in the corporate tax gap (Z) aresummarized in the following table, where 1 < η1 < η2 < 2 < η3 .

15

Monopoly PowerHome Welfare (dU0 /dZ)
Foreign Welfare (dU0∗ /dZ)η ∈ (1, η1 )

η ∈ (η1 , η2 )η ∈ (η2 , 2)η ∈ (2, η3 )

η > η3

+

+

+

−

−

+

−

+

+

−

Proof: See the Appendix.
The effects of a change in the tax gap on national welfare levels (20) and (21) areρ dU0(η − 1)(1 + ϕ)(η − 1) dN
1 dg
=
+
+
,
α dZ
(1 + Z)(Z − ϕ)
N dZ
ρ dZ

(22)

ρ dU0∗(η − 1)(1 + ϕ)(η − 1) dN
1 dg
=−
+
+
.
α dZ
(1 + Z)(1 − ϕZ)
N dZ
ρ dZ

(23)

Changes in the corporate tax gap affect national welfare levels through adjustments in
production shares (s). A decrease in the tax rate of home raises its share of production
causing the average price of manufacturing goods to fall for home residents, but to risefor foreign residents. This price effect is captured by the first terms on the righthandsides of (22) and (23). The second term is the love of variety affect associated withchanges in the level of market entry, and may be positive, negative, or ambiguous
depending on the degree of monopoly power. Finally, the third term is the growtheffect, and is negative for η ∈ (1, 2) and positive for η > 2. The balance of theseeffects is determined by the degree of monopoly power (η).

3Conclusion

In this paper we consider how changes in national tax rates on corporate incomes affect
the geographic location of industry, the level of product variety, and fully endogenous
productivity growth without scale effects in a two-country model of trade. Economic
growth is driven by monopolistically competitive firms that invest in process innovation with the aim of lowering production costs. Faced with imperfect knowledge
diffusion and trade costs, firms shift production and innovation between countries to16the lowest cost location, leading to a greater share of firms locating production andall firms locating innovation in the country with the lower corporate tax rate and thus
the larger after tax market.
Investigating the relationships between national tax policy, productivity growthand market entry, we find that the effects of changes in corporate tax rates depend on
the monopoly power of firms and the initial levels of relative tax rates. Focusing on thepolicy of the country with the relatively low tax rate, when firms have weak monopoly
power, reducing the tax rate depresses productivity growth, but has a positive effecton product variety if the initial tax rate is high and an ambiguous effect on productvariety if the initial tax rate is low. In contrast, when monopoly power is strong,a reduction in the tax rate accelerates productivity growth, but has an ambiguous
effect on product variety if the initial tax rate is high and a negative effect on productvariety if the initial tax rate is low.

Appendix
Beginning with Proposition 1, the derivative of (18) with respect to Z yields
ρ/k dk(1 + ϕ)(Z − ϕ) − (1 + Z)(1 − ϕZ)
1 dN
=
+
,
N dZ
(ρ − klF ) dZ
(1 + Z)(Z − ϕ)(1 − ϕZ)
where dk/dZ > 0. The first term on the righthand side is positive for η < 2 and√negative for η > 2. The second term is negative for Z < Z̃ = −1 + (1 + ϕ)/ ϕ andpositive for Z > Z̃.
Turning next to Proposition 3, using (14), the marginal utilities associated with17

the corporate tax gap are
1 dU
ϕ(1 − ϕ)2 (1 + Z)2
=
+ Φ,
A2 dZ
(1 − δ)(1 + ϕ)2 (1 − ϕZ)(1 − ϕ)2 (1 + Z)2
1 dU ∗
=−
+ Φ,
A2 dZ
(1 − δ)(1 + ϕ)2 (Z − ϕ)

(A1)
(A2)

where A2 = α(η − 1)/ρ(dk/ds)(ds/dZ) > 0, andΦ=((η − 2)ρ + klF )lR.
(η − 1)(η − 2)ρklX

The thresholds presented in Proposition 3 are derived through a comparison of thefirst terms on the righthand sides of (A1) and (A2) with the sign of Φ. First, while
the numerator of Φ is negative for η < η̃ = 1 + (ρ − klF )/ρ < 2 and positive for η > η̃,the denominator is negative for η ∈ (1, 2) and positive of η > 2. Therefore, Φ > 0
for η ∈ (1, η̃), Φ < 0 for η ∈ (2, η̃), and Φ > 0 for η > 2. Then, since Φ takes large
values as η approaches values of 1 or 2 and the absolute value of the first term of(A1) is larger than that of (A2), a comparison of the sign of Φ with the signs of thefirst terms in (A1) and (A2) yields the following: dU/dZ > 0 and dU/dZ ∗ > 0 forη ∈ (1, η1 ); dU/dZ > 0 and dU/dZ ∗ < 0 for η ∈ (η1 , η2 ); dU/dZ < 0 and dU/dZ ∗ < 0for η ∈ (η2 , 2); dU/dZ > 0 and dU/dZ ∗ > 0 for η ∈ (2, η3 ); and dU/dZ > 0 and
dU/dZ ∗ < 0 for η > η3 . Note that the thresholds η1 , η2 , and η3 are within the ranges
described in Lemma 2, when lF /ρ takes sufficiently large values in the weak monopoly
power case and sufficiently small values in the strong monopoly power case.

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