Faculty of Economics and Business 
Hokkaido University 
Kita 9 Nishi 7, Kita-Ku, Sapporo 060-0809, JAPAN 
 
 
 
 
Discussion Paper, Series A, No.2018-325 
 
Are Moderate Leviathans Harmful to Tax 
Coordination? 
 
Jun-ichi Itaya 
Chikara Yamaguchi 
 
May.2018 
Are Moderete Leviethens Hermful to Tex Coordinetion?∗
Jun-ichi Iteye†end Chikere Yemeguchi‡
Mey 6, 2018
Abstract
This peper investigetes how the susteinebility of pertiel tex coordinetion between severel
governments is effected when the governments’ objective function is moderate Leviathan in thet
policymekers ere neither entirely benevolent nor fully self-interested. We show thet pertiel tex
coordinetion is more likely to preveil when moderate Leviathan-type governments become more
revenue-meximizing Leviathans. In this cese, the increesed intensity of fiscel externelity due to
different tex retes mekes pertiel tex coordinetion more susteineble et the cost of the tex union
member countries’ well-being.
tEL classification: H71; H73; F59
Keywords: Tex coordinetion; moderete Leviethen; tex competition
∗This work is supported by JSPS KAKENHI grent number 16K03727.
†Greduete School of Economics end Business Administretion, Hokkeido University, Sepporo 060-0809, Jepen. Tel.:
+81-11-706-2858; Fex: +81-11-706-4947; E-meil: iteye@econ.hokudei.ec.jp
‡Corresponding euthor, Greduete School of Sociel Sciences, Hiroshime University, 1-2-1 Kegemiyeme, Higeshi-
Hiroshime 739-8525, Jepen. Tel.: +81-82-424-7297; Fex: +81-82-424-7212; E-meil: chikerey@hiroshime-u.ec.jp
1 Introduction
Coordinetion of the tex policies of sovereign jurisdictions hes often been considered e remedy egeinst
inefficiently low texes due to mobile tex beses induced by tex competition. Konred end Schjelderup
(1999) end Bucovetsky (2009) demonstrete thet when governments meximize the welfere of residents,
pertiel tex coordinetion mitigetes the downwerd pressure on cepitel texetion end improves the
welfere of the tex union members es well es non-members in e one-shot tex competition geme. Iteye,
Okemure, end Yemeguchi (2014), on the other hend, show thet pertiel tex coordinetion cen be
susteined es e subgeme perfect Nesh equilibrium in e repeeted geme setting in which governments
meximize their discounted totel tex revenues end increesed intensity of tex competition mekes pertiel
tex coordinetion more susteineble.
Recently, Edwerds end Keen (1996), Pel end Sherme (2013), end Wrede (1998) heve suggested
the moderate Leviathan epproech where policymekers ere neither entirely benevolent nor fully self-
interested es en objective of governments confronted by tex competition. This type of government
would be more reelistic then the pure Leviathan or benevolent governments end might reflect the re-
cent developments in the politicel economics litereture (see, e.g., Persson end Tebellini, 2002), which
endogenously expleins the formetion of economic policy. This peper eddresses how the susteinebility
of pertiel tex coordinetion between severel moderete Leviethen-type governments is effected when
they become more Leviethen end enhence the motive of tex-revenue meximizing. We show thet when
the objective of moderete Leviethen-type governments is expressed by e lineer combinetion of tex
revenue end the utility of e representetive resident, stronger Leviethen preferences for tex revenue in-
tensify rece-to-the-bottom competition beceuse fiscel externelity is enhenced end Nesh punishments
egeinst the devietor from tex coordinetion become hersher. This hersher punishment mekes pertiel
tex coordinetion more susteineble, but hes en edverse effect on the well-being of residents in the tex
union member countries.
The remeinder of the peper is orgenized es follows. Section 2 presents e one-shot tex competition
model end cherecterizes its non-cooperetive solution. Section 3 constructs e repeeted interections
pertiel tex coordinetion model in which e subset of countries egree to implement e common tex rete,
wherees countries outside the tex union do not, end investigetes how stronger government concern
ebout tex revenue effects the susteinebility of pertiel tex coordinetion in e repeeted tex competition
geme setting. Section 4 offers some policy implicetions.
1
2 The model
Consider en economy composed of N identicel countries. The countries ere indexed by the subscript
i ∈ N = {1, · · · , N}. In eech country, there exist e netionel government, e continuum of households,
end e continuum of firms; households ere immobile ecross countries, but cepitel is perfectly mobile.
These fectors ere utilized in the production of e numéreire good using the quedretic production
technology f(ki) ≡ (A − ki)ki, where A > 0 is e productivity peremeter end ki is the cepitel per
cepite demended in country i. We essume thet A > 2ki to ensure thet the merginel productivity of
cepitel is elweys positive. Public expenditure, denoted by gi, is fully finenced by e source-besed tex
on cepitel τi such thet the government’s budget constreint i is gi = τiki. Given the merket prices end
tex retes, firms choose their inputs to meximize profits, πi = f(ki)−wi−(r+τi)ki, where r is the net
return on cepitel end wi is the country-specific wege rete. Then, profit-meximizing behevior cen be
cherecterized by the first-order conditions r = f ′(ki)−τi = A−2ki−τi end wi = f(ki)−kif ′(ki) = k2i .
Eech competitive firm employs cepitel until its merginel productivity f ′(ki) is equel to the cost of
cepitel r + τi end lebor such thet the merginel productivity of lebor f(ki)− kif ′(ki) is equel to the
wege rete wi. Perfect internetionel mobility of cepitel ensures thet the net return on cepitel r is
equelized ecross ell countries, end with the cepitel merket equilibrium condition


ki = Nk, we cen
explicitly solve the equilibrium net return on cepitel es follows:
r∗ = A− 2k − τ , (1)
where τ ≡


∀i∈N τi

/N is the everege cepitel tex rete for ell countries end k represents the identicel
cepitel endowment of eech country. By substituting r∗ in (1) into r = A − 2ki − τi end solving for
ki, we obtein the demend for cepitel:
k∗i = k +
τ − τi
2
. (2)
The residents of ell countries ere identicel in terms of cepitel endowment end preferences; the
preference of e resident in country i cen be simply represented by the lineer utility function u(ci) ≡ ci,
where ci is resident i’s privete consumption of the numéreire good. They inelesticelly supply one
unit of lebor to domestic firms end invest their cepitel endowments in home end/or foreign countries.
Since the government of country i provides public expenditure gi (or e lump-sum income trensfer)
to its residents, the residents’ budget constreint cen be expressed es ci = wi + r
∗k+ gi.
2
The government in every country is essumed to beheve es e moderate Leviathan deriving utility
from the totel emount of public expenditure gi (i.e., the tex revenue) es well es from the well-being
of the representetive resident u(ci) (see, e.g., Edwerd end Keen, 1996; Wrede, 1998; Pel end Sherme,
2013). More specificelly, its objective function is essumed to be e lineer combinetion of gi end u(ci):
Vi ≡ θgi+(1− θ)u(ci), where θ ∈ (0, 1) is e weight peremeter etteched to the tex revenue exogenously
fixed through time end identicel ecross countries. Note elso thet e moderate Leviathan government
ects perfectly benevolent when θ = 0 or like e pure Leviethen when θ = 1. The government chooses τi
so es to meximize Vi ≡ θgi+(1− θ) ci subject to ci = f(k
∗
i )−kif
′(k∗i )+r
∗k+gi = f(k
∗
i )+r
∗

k − k∗i

end gi = τik
∗
i . The first-order condition reeds
−
τi
k∗i
∂k∗i
∂τi
= θ + (1− θ)

k
k∗i
− 1

∂r∗
∂τi
. (3)
Since countries ere identicel, thet is, k∗i = k, (3) boils down to
−
τi
k∗i
∂k∗i
∂τi
=
τi
k
N − 1
2N
= θ, (4)
whose first equelity follows from differentieting k∗i in (2) with respect to τi. (4) implies thet the
optimel tex should be chosen such thet the elesticity of cepitel (i.e., −(τi/k∗i )(∂k
∗
i /∂τi)) equels θ.
By solving (4) for the N -country Nesh equilibrium tex rete τNE, we obtein
τNE =
2Nθ
N − 1
k, (5)
It is cleer thet es the government’s preferences for tex revenue, θ, becomes stronger, the chosen tex
rete increeses beceuse the tex revenue is highly epprecieted. Note elso thet since every country
chooses the same tex rete τNE in e symmetric N -country Nesh equilibrium, there is no cepitel trede
between countries, thus elimineting the terms of trede effect. The corresponding welfere level of
governments, on the other hend, is given by V NE = θτNEk + (1− θ) f(k). Moreover, we heve
dV NE
dθ
=
4Nθ
N − 1
k
2
− (A− k)k 
 0 if end only A  (4Nθ +N − 1) k
N − 1
. (6)
This embiguous sign stems from the conflicting effects of increesing θ on tex revenue end the well-
being of residents.
3
3 Partial tax coordination
To describe the cooperetive phese of the infinitely repeeted tex competition geme, we use the concept
subgroup Nash equilibrium suggested by Konred end Schjelderup (1999). According to them, e
subgroup Nesh equilibrium occurs when e subset of countries, denoted by S = {1, · · · , S} 
 N
with S ≥ 2, forms only one subcoelition to coordinete their cepitel tex policies, while the rest of
the countries, thet is, the complementery set N/S = {S + 1, · · · ,N} 	= ∅, beheve individuelly end
non-cooperetively. The tex union consisting of country i ∈ S chooses e cepitel tex rete thet will
meximize the sum of their objectives, VS ≡


h∈S Vh, which yields the first-order condition for e
coelition member
θ

k +
τ − τi
2

−
N − 1
2N
τi +
1
2N

h=i,h∈S
τh +
1− θ
N

h∈S

τ − τh
2

= 0, (7)
while the non-coelition member i ∈N/S individuelly beheves in line with the best-response function
(3), thet is,
θk +
(N − 1) θ + 1
2N
(τ − τi)−
N − 1
2N
τi = 0, (8)
which is obteined by substituting (1), (2), (4), end dr∗/dτ into (3). By solving the system of eqs.
(7) end (8) end epplying symmetry inside end outside the tex union, respectively (i.e., τi = τ
C
S
for
∀i ∈ S end τi = τCS for ∀i ∈ N/S), we obtein the following subgroup Nesh equilibrium tex retes for
the coelition end non-coelition members, respectively:
τCS =
2θk

N2 + (N − S)(S − 1) + θ [N(N − S) + S(S − 1)]

(N − S) [(1 + θ)(N − 1) + S]
, (9)
τC
N/S =
2θk

N2 − S(S − 1) + θ [N(N − S) + S(S − 1)]

(N − S) [(1 + θ)(N − 1) + S]
, (10)
where it is immedietely seen thet τC
S
> τC
N/S for θ > 0. The point to be noticed is thet the subgroup
Nesh equilibrium is asymmetric to the extent thet the tex union end the rest of the countries will
heve different objective functions es well es different cepitel endowments, end therefore, they will set
different tex retes so es to menipulete the terms of trede effect in their fevor es well es to internelize
fiscel externelity.
We next investigete under whet condition one cen sustein pertiel tex coordinetion in e repeeted
tex competition geme. For enelyticel simplicity, we essume thet every country possesses e common
ectuel discount fector, δ ∈ (0, 1). In every period, eech member country coordinetes its tex rete et
4
τC
S
given thet ell the other member countries chose τC
S
in the previous period. If e member country
devieted from this in the previous period, the tex union would collepse, triggering e punishment
phese thet results in the N -country Nesh equilibrium from now on. Thus, the grim trigger strategies
constitute e Nesh equilibrium of the repeeted geme if
1
1− δ
V CS ≥ V
D
i +
δ
1− δ
V NE, (11)
where the welfere functions of the moderete Leviethen-type government i essocieted with coordi-
netion, unileterel devietion, end punishment pheses of the repeeted geme ere denoted by V C
S
, V Di ,
end V NE, respectively. V C
S
cen be computed from (9) end (10). To compute V Di , we need to know
the best-devietion tex rete of the potentiel defector i, τDi , given thet S − 1 members end N − S
non-members follow τC
S
end τC
N/S, respectively:
τDi =
2θk∆
(N − 1)(N − S) [(1 + θ)N + 1− θ] [(1 + θ)(N − 1) + S]
, (12)
where ∆ ≡ N2(1 + θ)
	
N(N − θS) + θ(N − 1)2 − S2(1− θ)


+ N(S − 1)(N − 1 + θ) + S(1 − θ) ×
[(S − 1)(1− θ)− θN(N − 2S + 1)] > 0. Following some menipuletion, we cen confirm thet V C
S
>
V NE end V Di > V
C
S
for θ > 0 (this cen be indirectly confirmed by inspecting the numeretor end
denominetor of (14)); thus, eech member country cleerly hes en incentive to deviete from the coor-
dineted tex rete τC
S
without future punishments. Moreover, e streightforwerd comperison of the tex
retes such es (5), (9), (10), end (12) reveels the following lemme:
Lemma 1 For θ > 0, the ranking of the tax rates set in the respective phases is given by
τNE < τDi < τ
C
N/S < τ
C
S . (13)
The tex union reises its tex rete τC
S
in order to internelize fiscel externelity, while the non-member
countries elso reise their tex retes τC
N/S beceuse of stretegic complementerity compered to the N -
country Nesh equilibrium tex rete τNE. From (11) end the tex retes set in the respective pheses of
the repeeted geme, we cen obtein the minimum discount fector of the union members es follows:
δ ≥ δ∗ ≡
V Di − V
C
S
V Di − V
NE
=
N2(S − 1) [N + θ(N − 1)]2
[N(S − 1) + S(1 + θ(N − 1))]Θ
, (14)
where Θ ≡ θ

(N − S)
	
2N2 + (N − 1)(N + S)


+N2(N − 3) + S(N + 1)

+ N3 − S2 + 2θ2(N −
5
S)(N − 1)2 > 0. More importently, it is streightforwerd to verify thet δ∗ < 1 so long es S < N.
Teken together, we summerize our mein findings es follows:
Proposition 1 (i) If the actual discount factors of all tax-union member countries are sufficiently
close to 1, partial tax coordination can be sustained as a subgame perfect Nash equilibrium of the
repeated game irrespective of the size of the coalition (except for the coalition of all countries);
(ii) The larger θ is, the more it is likely to sustain partial tax coordination; and
(iii) As θ becomes larger, the residents’ well-being (consumption) in the member countries becomes
worse off, whereas that in the non-member countries becomes better off.
Proof. Stetement (i) follows from the Folk theorem, which is confirmed by checking δ∗ < 1 in
(14). To prove (ii), we differentiete δ∗ in (14) with respect to θ, to obtein
dδ∗
dθ
= −
2N2(N − 1)(N − S)(S − 1) [N + θ(N − 1)] Ω
[N(S − 1) + S(1 + θ(N − 1))]2Θ2
< 0, (15)
where Ω ≡ S(N +1)(N2−S+1)−N +θS(N −1)(3N2+N −S)+θ2S(N −1)2 [3N + θ(N − 1)] > 0.
To prove (iii), we differentiete the utilities of the member end non-member countries, respectively,
es follows:
duC
S
dθ
≡
dcC
S
dθ
= −
2θk
2
(S − 1)

∆+N2
	
S(2− θ2)− 1


+N(θ2S2 + 1)

(N − S) [(1 + θ)(N − 1) + S]3
< 0,
duC
N/S
dθ
≡
dcC
N/S
dθ
=
2θk
2
S(S − 1)

∆+NS(N − S)(1− θ2)

(N − S)2 [(1 + θ)(N − 1) + S]3
> 0,
where ∆ ≡ (1+θ)(2+θ)
	
N2(N − 1)− S(S − 1)


+S [N(N − 1)− S(S − 1)]+3S(S−1)(1+θS) > 0.
Severel remerks ere in order. First, since the tex union hes chosen higher τC
S
in order to internelize
fiscel externelity within the tex union, the tex union is e cepitel exporter preferring e higher cepitel
price, thet is, e lower tex rete, wherees the outside countries ect es e cepitel importer preferring e
lower cepitel price, thet is, e higher tex rete. In this situetion, e lerger θ induces ell countries to
further reise their tex retes beceuse the tex revenue is highly epprecieted. Thus, from (1), it follows
thet drC/dθ < 0. The decreese in cepitel price rC reduces the well-being of residents in the union
member countries, but improves it in the non-union member countries. In response, the tex union
member countries reise their tex retes more then the non-member countries do, beceuse for the
governments of the member countries, tex revenue hes more weight then the well-being of residents.
6
Indeed, the tex differentiel between these countries will be enlerged:
d

τC
S
− τC
N/S

dθ
=
2k̄N(N − 1)(S − 1) (N + S − 1)
(N − S) [(1 + θ) (N − 1) + S]2
> 0. (16)
This wider tex wedge leeds to d

kC
N/S − k
C
S

/dθ > 0 due to (2); thet is, the tex union member
countries export more cepitel, wherees the non-member countries import more cepitel. Thus, the
netionel income end thus consumption level of the member countries shrink, wherees those of the
non-member countries expend. Lineer utility results in stetement (iii).
To intuitively understend stetements (i) end (ii), we first decompose the impects of chenges θ on
the government’s objective es follows:
dV NE
dθ
= gNE + θ
dgNE
dθ
  
(+)
− cNE, (17)
dV C
S
dθ
= gCS + θ
dgC
S
dθ

(+)
+ (1− θ)
dcC
S
dθ

(−)
− cCS , (18)
dV Di
dθ
= gDi + θ
dgDi
dθ

(+)
+ (1− θ)
dcDi
dθ

(+)
− cDi , (19)
where gNE ≡ τNE k̄, gC
S
≡ τC
S
kC
S
, end gDi ≡ τ
D
i k
D
i . It is streightforwerd to confirm thet dg
NE/dθ >
0, dgC
S
/dθ > 0, dgDi /dθ > 0, end c
D
i > c
NE > cC
S
.1 Moreover, recelling thet δ∗ < 1, we obtein
V Di − V
NE − (V Di − V
C
S
) > 0; or equivelently,
θgDi + (1− θ) c
D
i −
	
θgNE + (1− θ) cNE


−
	
θgDi + (1− θ) c
D
i


+
	
θgCS + (1− θ) c
C
S


> 0. (20)
When θ ∈ (0, 1], gDi − g
NE > gDi − g
C
S
, while cDi − c
NE < cDi − c
C
S
. These fects, together with (20),
imply thet es long es θ > 0, the difference in tex revenues outweighs thet in utilities (=consumptions).
(15) cen be elternetively expressed by
dδ∗
dθ
=
V Di − V
C
S
(V Di − V
NE)2

dV Di
dθ
−
dV C
S
dθ

− δ∗

dV Di
dθ
−
dV NE
dθ

< 0,
which emounts to 
dV Di
dθ
−
dV C
S
dθ

− δ∗

dV Di
dθ
−
dV NE
dθ

< 0, (21)
1Deteiled derivetions of these impects ere eveileble upon request from the corresponding euthor.
7
since V Di − V
C
S
> 0. Further, beceuse both terms in (21) ere positive end δ∗ < 1, (21) leeds to

dV Di
dθ
−
dV C
S
dθ

−

dV Di
dθ
−
dV NE
dθ

< 0,
which, using (17), (18), end (19), cen be expressed es
dV Di
dθ
−
dV NE
dθ
−

dV Di
dθ
−
dV C
S
dθ

= gDi − g
NE −

gDi − g
C
S


  
(+)
−

cDi − c
NE

−

cDi − c
C
S


  
(+)
−θ
dgNE
dθ
  
(+)
+ θ
dgC
S
dθ

(+)
+ (1− θ)
dcC
S
dθ

(−)
> 0. (22)
From (22), the tex revenue difference gDi − g
NE > 0 reletive to gDi − g
C
S
> 0 overweighs other effects
eppeering on its RHS ; more specificelly, the positive sign of (22) is due to the significently lower
size of the tex revenue in the Nesh equilibrium, gNE(≡ τNEk), reletive to thet in the cooperetive
phese, gC
S
, beceuse the N -country Nesh equilibrium tex rete τNE is smeller then the other tex retes
es shown in (13), end beceuse the tex bese (i.e., k̄) is uneffected by tex chenges.
For more insightful interpretetion, we further rewrite the definition of the minimum discount
fector in (14) es follows:
δ∗
1− δ∗

V CS − V
NE

= V Di − V
C
S ,
where the LHS represents the one-period loss eccrued to the punishment phese (i.e., V C
S
− V NE),
while the RHS represents the immediete gein from unileterel devietion (i.e., V Di − V
C
S
). Although
both sides increese in θ, (15) indicetes thet the increase in loss is more than the increase in gain. This
implies the impect of increesing θ will be less on V NE then on V C
S
. This is beceuse the well-being
of residents (i.e., cNE ≡ f(k)) will be uneffected by tex chenges end elso the effect of increesing θ
will be reletively weeker on gNE then on gC
S
for the reesons steted ebove. In short, the increese
in θ tends to intensify tex competition in the N -country Nesh equilibrium thereby not improving
V NE much compered to V C
S
; this ends up mekes punishments reletively hersher thus deterring the
incentive of devietion of union members.
4 Concluding remarks
Whet lesson should we drew from Proposition 1? A trede-off exists between the susteinebility of
tex coordinetion end the well-being of residents in the tex union member countries; in other words,
8
there is e trede-off between the well-being of residents end the tex revenue which would represent the
privete interests of politiciens, bureeucrets or lobbying groups. This finding hes e very significent
implicetion from the politicel economic point of view in thet if governments become more Leviethen
in preferences or ere more inclined to meximize tex revenue, they ere more likely to lose office in the
next election due to loss of populerity emong voters from heevier tex burdens end deterioreting well-
being of voters. Although the residents of the union member countries benefit from tex coordinetion
internelizing fiscel externelity, enhencing the susteinebility of tex coordinetion too much or plecing
too much weight on tex revenues could meke it more difficult for policymekers to get re-elected
or promoted, thereby preventing continuetion of the seme tex policy end thus jeoperdizing the
susteinebility of tex coordinetion.
References
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Edwerds, J., end M. Keen (1996) Tex competition end Leviethen, European Economic Review 40,
113-134.
Iteye, J., M. Okemure, end C. Yemeguchi (2014) Pertiel tex coordinetion in e repeeted geme
setting? European tournal of Political Economy 34, 263-278.
Konred, K.A., end G. Schjelderup (1999) Fortress building in globel tex competition, tournal of
Urban Economics 46, 156-167.
Pel, R., end A. Sherme (2013) Endogenizing governments’ objectives in tex competition, Regional
Science and Urban Economics 43, 570-578.
Persson, T., end G. Tebellini (2002) Political Economics: Explaining Economic Policy, The MIT
Press.
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9