Abstract: “Optimal integration policy under a threat of secession”,
Moriki Hosoe, Kumamoto Gakuen University
In this paper, we analyze the possibility of integration and secession between a majority
region and a minority region. There is assumed to be an different preference for public
policy between two regions and a government is assumed to have to offer a constantlevel of public goods. We introduce two forms of governance, centralized integration anddecentralized integration. Then when small level of public good is necessary, the form ofgovernance is shown to chance from centralized integration to secession to decentralized
integration as the size of the minority region becomes large. And when large level ofpublic good is necessary, the form of government is shown to change from centralized
integration to decentralized integration . as the size of the minority region becomeslarge.

Resume:Optimal Integration Policy under a Threatof Secession
Moriki Hosoe（Kumamoto Gakuen University,Japan）
September 6, 2015

1

Introduction

In this paper we investigate the mechanism of integration and secession among
regions, focusing on the policy decision. In particular, we take a policypreference approach in the situation where there are policy conflicts between
two regions. Under the threat of secession, the optimal policy of a majority
region is obtained and the possibility of secession is shown to depend on thepolicy-gap and population-gap between two regions. By considering incentives of policy decisions in each region, we show the possibility of integrationand secession and how the welfare of each region is realized through strategic
determination of policy.

2Model2.1

two-region model

We assume that there are two region A and B, with the population NA andNB (NA > NB ) respectively. Region B is called a minority region and region
A is called a majority region. Each region is facing the decision of a single
and common public policy. For example a region may take a conservative orliberal stance about religious policy or education policy. For the simplicity, thestance X of the common public policy is located on the interval[0, 1].Then themost preferable policies, bliss points of the citizen are assumed to be X̄B , X̄A ,respectively. As the actual policy becomes remote from the bliss point, theutility of the citizen decreases. If the policies that their regions implement for
a common policy issue are different, political friction for the regional economy
may occur. This is called a policy externality, which causes the utility loss
in each region. We assume that a constant level g of a public good is needed1

to manage an independent country and the level g is the same irrespective of
the population, as in Aslea = Spolaore(1997). Of course the public good isassumed to be of non-rivality.

2.2Secession between two regions

Let us consider the situation of secession of two regions. In region i, incometax is levied to produce the level g of the public good. Then g = Ni τi yi(i = A, B)is assumed to be held.yi (1 − τi ) goes to private consumption. Letus denote the utility UA , UB of the representative citizen for each region asfollows, when each region implements a policy XB , XA respectively.
UA = −a(X̄A − XA )2 + yA (1 − τA ) + g
22UB = −b(X̄B − XB ) − s(XB − XA ) + yB (1 − τB ) + g

(1)
(2)

Here the utility at the bliss point is normalized to be zero. When there
is a conflict between the majority region and minority region, the minority
region incurs a policy external marginal cost s, while the majority region doesnot. Furthermore we assume that the policy difference between the majority
region and the minority region does not influence the utility of the majority
region, reflecting the difference of the population.

2.3

Policy decision under secession

Now let us seek the equilibrium policy that each region makes under secession.
The optimal policy for region B, given the policy XA for region A, is shownbybX¯B + sXAO
XB
=b+sOn the other hand, the optimal policy for region A is obviously the bliss
pointX̄A , whatever the policy for region O may be. Therefore, the optimal
public policy in region B is shown as follows.
bX¯B + sX¯AO∗
(3)
XB
=b+s
As a result, the utility of region O isggbs
UBO∗ = −b(X¯B − X̄A )2 +yO −+yB −+g = −(X̄B − X̄A )2+g (4)NB(b + s)
NBThen the utility of region A isUAO∗ = yA −2g+gNA(5)2.4

Policy decision under centralized integration

Let us consider the integration of two region A,B. Here there are two forms ofintegration. One is a centralized integration (CI). The other is a decentralizedintegration(DI). Under the centralized integration, the same level of public
policy is implemented. Under the decentralized integration, there is a room toimplement different level of the public policy. In this subsection, we consider
the case of centralized integration. In this case, the first effect of regional
integration for the majority region is in general a policy effect. By integration,
the majority region can dominate the policy in the minority region. But inthis two-region model, the policy effect for the majority region is neglected.
The second effect is a scale effect. By integration, the population increases
and personal income increases. So when region A and region B integrate anda policy XA is implemented, the utility of the representative citizen for region
A and B are
UACI = −a(X̄A − XA )2 + yA (1 − τA ) + g
UBCI = −b(X̄B − XA )2 + yB (1 − τB ) + g
Here we have τA yA NA + τB yB NB = g.We have the three effects of integration for the minority region. One is the deletion of the policy conflicts, whichis positive for the minority region. Second is the delegation of policy decision,
which is negative. And the third is of course a scale effect.
The region A proposes a pair of public policy XA and tax policy (τA , τB )to the region B. Region B can refuse the proposal if it makes region B worse
than in the secession. Therefore, region A has to propose the policies so as tosatisfy the following integration-acceptance condition.
−b(X̄B − XA )2 + yB (1 − τB ) + g ≥ UBO∗

(6)

Region A decides the policies to maximize the utility of the representative
citizen for region A. By making this integration -acceptance condition equalize
and considering (4), we obtain−b(X̄B − XA )2 − yB (1 − τB ) + g = −b(X̄B − X̄A )2gbs+ yB −+g(b + s)
NB

Then using the fiscal balance τB yB NB = g−τA yA NA , the integration-acceptancecondition isτA yA NAsb= b(X̄B − XA )2 −(X̄B − X̄A )2
NB(s + b)3(7)From this equality, the utility of representative citizen in region A is−a(X̄A − XA )2 + yA − b(X̄B − XA )2

NB
sb
NB+(X̄B − X̄A )2+gNA(s + b)NATherefore, using the first-order condition, we have the optimal public policy.
CI∗XA=aNA X̄A + bNB X̄BaNA + bNB(8)This is obviously the efficient public policy.
Proposition 1 Under centralized integration, the optimal public policy becomes efficient.

By substituting the value of the optimal public policy into (7), we havethe maximum utility of representative citizen in region A under integration asfollows.
UACI∗ = −a(bNB (X̄B − X̄A ) 2aNA (X̄B − X̄A ) 2 NB sb(X̄B − X̄A )2 NB) +yA −b()++g
aNA + bNB
aNA + bNB
NAs+bNAOnce we obtain the maximum utility in region A under integration, let us
examine whether the region A has the motivation of integration or not. We
compare the utility in region A under integration with the utility in region Aunder secession.
UACI∗ ≥ UAO∗
(9)This condition is shown as follows.
gaNAsb NB
bNB−(b()2 −)(X̄B − X̄A )2 ≥ a()2 (X̄B − X̄A )2
NA
aNA + bNB
s + b NAaNA + bNB
(10)
The right-hand side of this equality shows the merits of the decrease in percapita tax burden in the minority region due to the scale merit of integration.
The left-hand side shows policy adjustment loss in the minority region due
to integration. Therefore, the integration will be implemented if the former
effect is larger than the latter effect. These effects are shown as the functionof relative population in region B.
As the relative population in the minority region increases, the optimal
public policy goes to the ideal point for the minority region. This implies theincrease of policy adjustment cost for the majority region.
4

Proposition ２ While the centralized integration will occur in the case ofsmall relative population in the minority region, secession will occur when therelative population becomes larger than the certain level

The integration condition is rearranged as follows.
gbNBaNAsb NB≥ (a()2 + b()2 −)(X̄B − X̄A )2NA
aNA + bNB
aNA + bNB
s + b NA
From this inequality, the possibility of secession increases as the ideal point
gap of public policy between two regions becomes large and the cost of public
goods becomes large.

2.5tax policy

Let us examine the tax policy for each region under integration. the total
volume of tax in A is show as follows.
τA yA NA = NB (b(sbaNA)2 −)(X̄B − X̄A )2aNA + bNBs+b(11)From this equation, the total volume of tax and the tax rate in the majority
region becomes large as the ideal point gap becomes large. And when thecost of policy adjustment is small, the total volume of tax and the tax ratein the majority region increase with the relative population in the minority
region. On the other hand, the total volume of tax and the tax rate in themajority region is a convex function of the level of the relative population in
the minority region.
The total volume of tax in the minority region is written
τB yB NB = g − τA yA NA
Therefore the volume becomes small as the ideal point gap of public policy
becomes large.

3

Decentralized integration policy

3.1

Decentalized integration model

So far we assumed the public policy under integration is universal between
two regions. However even under the integration, different contents of public
policy may be allowed. We call an integration allowing different policy in5different region a decentralized integration. For example, native language
may be allowed as a formal language with a common language in a minority
region. Then under a decentralized integration the utility of the representative
citizen in the majority region is show as follows.
−a(X̄A − XA )2 − c(XA − XB )2 − yA (1 − τA ) + g
Then the optimal policies can be obtained to solve the following maximization
problem.
max −a(X̄A − XA )2 − c(XA − XB )2 − yA (1 − τA ) + g
XAs.t. max −b(X̄B − XB )2 − s(XB − XA )2 + yB (1 − τB ) + g ≥ UBO∗XB

The optimal public policy of minority region as an optimal response is shownas followsbX̄B + sXA
XB =b+s
From this, we can get the optimal public policy of majority region.
DI∗
XA=bsb 2aNA X̄A + b+s
NB X̄B + c( b+s) NA X̄Bbsb 2
aNA + b+s
NB + c( b+s) NA(12)Proposition 6 Under the decentralized integration, the public policy ofmajority region becomes near the ideal point of public policy in minorityregion.

DI∗DI∗XB− XA=3.2aNAb(X̄B − X̄A )bsb 2
b + s aNA + b+s NB + c( b+s) NA(13)Selection on integration and secession

The utility of majority region is shown as a function of the relative populationin minority region in the case of centralized integration and decentralizedintegration.

64Conclusion

In this paper we analyzed the mechanism of integration and secession between
two region, using policy-preference model with the cost of policy conflict. In
Particular, we showed that centralized integration will occur when the relative
population in minority region is small, and secession will occur when therelative population in minority region is larger than a certain level. And it
was shown that integration will occur as the policy preferences in two regions
are similar, and that secession will occur when the cost of policy adjustment
is large. Lastly we investigated about the two types of integration, centralizedintegration and decentralized integration. Then, we showed that ,dependingon the cost level of public goods, the two dynamic processes of going from
centralized integration to decentralized integration, via secession, and of goingdirectly from centralized integration to decentralized integration will occur
with the increase of the relative population in minority region.

7