Local Public Good Provision in a SegregatedSociety�

Selim Jürgen Erguny Tahir Öztürkz

January 2010

Abstract

In this paper we analyze the decision of two segregated jurisdictionswho can either provide a public good jointly or separately. We focus on thetrade-o¤ between economies of scale and preference heterogeneity wherethe preference heterogeneity has two components: the preference over thelocation of the public good and the preference over the group composition.We obtain that if the communities care equally about the composition ofthe jurisdiction, the consolidation takes place between relatively similarsized communities. When the smaller community cares more about thecomposition, consolidation will occur if it has a relatively moderate size.We also obtain that democracy leads to an excessive separation, from asocial point of view and in case of a non-excludable public good, whenpeople care more about group composition, free-riding is less likely.

1 Introduction

Neighboring jurisdictions may decide to provide a public facility together orseparately.1 There exists a huge literature on the uni�cation or secession deci-sion of jurisdictions and the stability of the grand coalition. As in this study,in general the main trade-o¤ is between economies of scale and heterogeneity.Larger jurisdictions enjoy larger economies of scale but at the same time theheterogeneity costs are higher in them. However, in this paper, we also analyzethe preferences over composition of bene�ciaries which means that individualscare about with whom they share the public good. How the approval and e¢ -ciency conditions for uni�cation is a¤ected from this kind of preferences is the�rst question that is addressed in this study. Obviously, joint provision of the

�Financial support from MEC (SEJ2007-62081/ECON) and Junta de Andalucía (P07-SEJ-02547) is gratetully acknowleged.

yGLOBE, Departamento de Teoria e Historia Económica, University of Granada, 18071,Granada (Spain), sergun@ugr.es

ztahirozturk@gmail.com1Various terms are used to refer joint provision such as uni�cation, annexation or consoli-

dation.

1

public good is more costly and so less likely. However, although the approvalconditions get more strict, their characteristics will be a¤ected since the changeswill not be equal for each jurisdiction. Moreover, free-riding and the locationdecision policies will change interestingly.Consolidation, i.e., cooperation in the provision of a local public good or

service, while providing other public facilities separately, is an important mech-anism in determining and shaping the number and size of jurisdictions. It is aprocess by which distinct jurisdictions share the costs and bene�ts of a new pub-lic good. There are many jurisdictions that have separated �re departments andpark services while cooperating in public schooling services with a neighboringjurisdiction. For instance, in less than one century the number of school districtsin the United States has fallen from 125 000 to 15 500 through consolidation.(Wiles, 1994)The decision of consolidation/uni�cation for the public good depends on the

trade-o¤between economies of scale and heterogeneity. Larger populations havelarger scale bene�ts but also the costs of increased heterogeneity. In this paper,our interest is focused on the decision of consolidation or independent provisionof a public good in two di¤erent sized jurisdictions in which individuals alsocare about the composition of the population of bene�ciaries. Consider, forexample, the potential problem of consolidating school districts of two jurisdic-tions. Larger districts have economies of scale and therefore the advantage ofbeing able to provide libraries, sports facilities, and administration on a district-wide basis with a low cost per resident. On the other hand, when consolidationoccurs, i.e. a larger district created, an agreement must be reached betweenan increased number of individuals on common educational policies or on thelocation of the school. Moreover, families have to agree to mix their childrenwith the children of another group. If prejudices exist with regard to the othergroup due to some ethnic, racial, or historical reasons, an individual�s utilitydeclines upon mixing. That is to say, if an increase in size implies an increase inheterogeneity, there may be an important trade-o¤ in terms of utility for groupmembers.This paper can also be related to country formation literature. The decision

of uni�cation or separation of two regions can be analyzed by the model usedin this paper.2 Uni�cation in the provision of the public good, which is gov-ernment, implies the bene�ts of large jurisdiction but also the resulting costsof heterogeneity. Residents of a region may prefer not to unify with the otherregion not only because of an increase in average political di¤erences in the so-ciety but also because of preferences regarding the composition of population.3

We believe that by taking into consideration preferences regarding populationcomposition in country formation, more reliable and deeper results are obtained.There are some empirical results in the literature that support considering

2The uni�cation/separation decisions between Montenegro-Serbia on May 21st 2006 andSouth Cyprus - North Cyprus on April 24th, 2004 were taken by a referendum. Recently,Kosova became independent by one-sided approval by referendum.

3For example, we believe that only an economical explanation is not enough for the opinionof some European countries about Turkey�s membership to EU.

2

preferences over heterogeneity in race, ethnicity, or religion. Alesina et al. (2004)�nd a signi�cant positive e¤ect that racial heterogeneity consistently has on thenumber of local jurisdictions. Brasington (2003) concludes as "the reasons whywhiter communities dislike educating their kids with those of less white commu-nities is beyond the realm of economics. The reasons why darker communitiesdislike educating their kids with those of whiter communities of similar incomeare also subject to speculation. But these sets of preferences discourage consol-idation." Although Austin (1999) focuses on the provision of public municipalannexation for provision of all local public services rather than consolidation foronly one public facility, his conclusion is that cities prefer annexing surroundingcommunities according to properties of population composition.Like many others, we adapt the Hotelling (1929) location framework in order

to represent the heterogeneity of preferences among voters over the provision ofpublic goods.4 With some others, this framework is mostly similar to Alesinaand Spolaore (1998) where they discuss the optimality and stability of the equi-librium number of countries in di¤erent politico-economic regimes. Di¤erentlyfrom Alesina and Spolaore but similarly to Goyal and Staal (2004), here weconcentrate on the e¤ects of jurisdictions�sizes to consolidation decision in anexogenously segregated society. Although Goyal and Staal�s paper has a verysimilar basis, most of our results are di¤erent since we also focus on the prefer-ences over bene�ciaries�composition and its e¤ects on speci�c situations. Oneof the pioneering works on the e¤ect of size in consolidation decision is Ellingsen(1998). He predicts that under some conditions large entities want to consoli-date with small ones, but small entities might not want to consolidate with bigones if they have the free riding option. Brasington (2003) empirically exam-ines the role of income and racial di¤erences on the school district consolidationdecision and �nds signi�cant relations.In our attempt to explain the consolidation decision, we consider a segre-

gated society with two jurisdictions where an excludable public good will beprovided. We call the society as segregated since in one jurisdiction we haveonly one community�s members.5 Jurisdictions have the opportunity to providethe public good independently or jointly. That will be decided by voting. Thepublic good has a �xed cost and it is �nanced by a lump sum tax from itsbene�ciaries. When two jurisdictions consolidate, individuals are happy to besharing the cost of the good since they pay lower taxes. However, in the caseof consolidation, the society becomes less homogenous. There are two reasonswhy individuals might prefer homogeneity. First, individuals who are from asimilar ethnic background, race, religion or income level may have more similarpreferences over a public good than the individuals from a di¤erent one. Theother reason is that while sharing the public good, an individual may prefer tointeract with people from her community. That is, individuals also care aboutthe composition of the group with whom they share the public good. This be-

4See, for instance, Alesina and Spolaore (1997), Le Breton and Weber (2003), Casella(1992) and Casella and Feinstein (2002).

5 In our analysis for analytical simplicity we deal with totally segregated societies. However,the results can be generalized to mixed jurisdictions as well.

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comes especially important in looking at highly diverse populations�decisions.For example, people in their school choice do not only take into considerationits location or educational system, but also the composition of the student body.This fact in turn a¤ects the decisions and well being of the society as a whole.Current study �rst looks at each jurisdiction speci�c decision over consol-

idation. However, di¤erent from the existing literature, this paper analyzesthe e¤ects and results of preferences over the composition of bene�ciaries whiledeciding for consolidation in provision of a public good. If the residents of ajurisdiction loose more utility because of sharing the public good with the otherjurisdiction, the consolidation is less likely. Di¤erent from the literature we con-clude that depending on the values of public good cost and importance of groupcomposition, the consolidation is more likely to occur when the small jurisdic-tion has a moderate or similar size compared to large jurisdiction. Similar tocommon results, we conclude that the consolidation decision increases the totalutility of the society if and only if the small jurisdiction is small enough.We also point out how the location decision of a social planner, solvability

of a disagreement and free-riding decision of small sized jurisdiction are a¤ectedby the importance of bene�ciaries�composition. When a jurisdiction cares moreabout the composition of the bene�ciaries, the social planner�s decision for thelocation of the public good changes in a way that makes the jurisdiction worseo¤. We also consider the free-riding option and show that the minority is keenerto provide their own public good when they care more about the compositionand the larger jurisdiction may take a strategic decision to make the minorityprovide their own public good.This paper is organized as follows. In the next section we present the model.

In Section 2.3, we look for the necessary conditions under which jurisdictions willprefer to consolidate or to provide the public good independently. In Section 2.4,we characterize the conditions for approval of consolidation. We provide alsothe conditions to guarantee that consolidation is an improvement, i.e., the totalutility of society increases when jurisdictions consolidate. Section 2.5 introducessome extensions with a glance to the social planner�s decision and Section 2.6introduces the implications of free-riding option. Section 2.7 concludes.

2 The Model

We consider a continuum of individuals that have preferences over the locationof a public good. The set of possible locations is a one-dimensional space,without loss of generality, given by the interval I = [0; 1]. Citizens�preferencesare single-peaked and each citizen i is identi�ed with his peak point xi 2 I:Individuals are uniformly distributed and immobile.We assume that there are two communities W and B that are separated by

an exogenous boundary at �; i.e., they have measure of 1�� and �; respectively.The community W is the one that is located to the right of � and obviouslythe community B is located to the left of �: We assume that 0 < � < 1

2 ; whichmeans that the population of the type W is larger than B.

4

Each individual has an income y and gets utility from both private andpublic consumption. After paying the tax of the public good ti, income is usedfor private consumption y � ti. We assume that the cost of public good isK for each jurisdiction.6 Then, to provide and to bene�t from a public good,individual i must pay a cost that depends on the size of the jurisdiction. Thetax gathered in each jurisdiction should cover the total cost of the public good.The budget constraint for a jurisdiction j (j 2 fB;Wg) with size Sj isZ

Sj

tidx = K (1)

With an equal sharing scheme, where all individuals of the same jurisdictionpay an equal tax for the provision of the public good, ti = K

Sj. Therefore, in the

case of independent provision, the tax for an individual from jurisdiction B isK� , and for an individual from W it is K

1�� . If they consolidate, all individualsin the society will pay the same tax, which is K:The utility derived from the public consumption is determined by the func-

tion

Zi (�i; ri) (1� di)

where di is the distance between the ideal point of individual i and the publicgood and Z is a function determining the utility depending on the compositionof the group. The variable �i is the proportion of individual i�s community ini�s jurisdiction and ri is the degree of importance of sharing the public goodwith the other community for individual i. ri can also be called as intolerancefactor of individual i. The intolerance factor ri is positive and takes the samevalue for all members of individual i�s community.For each individual, the utility obtained from the public good is decreasing

with the distance from the public good to her location. Moreover, we assumethat individuals prefer to share the good with the ones that are from their ju-risdiction, that is, the utility of an individual also depends on the combinationof the group with whom she shares the public good. For instance, a type Bindividual�s utility decreases as the proportion of the B population in the juris-diction decreases and vice versa. This e¤ect is covered by the function Z whichis is increasing in �i and decreasing in ri. Note that the function Z determinesthe maximum utility that an individual gets if the public good is located at hispeak point (di = 0):The utility an individual obtains from the public good is directly a¤ected

by a change in the composition of bene�ciaries. An individual, when choosingamong two public goods that are equally distant to her, chooses the one withthe composition in which there are more bene�ciaries from her community.Moreover, among two public goods with the same composition, she prefers the

6The results are robust even if we assume that the cost of public good is K + kSj forjurisdiction j with the size Sj where to provide a public good, individual i must pay a cost,which includes a �xed part K > 0 and a variable part that is proportional to the size of thegroup Sj with k > 0:

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closer one. Furthermore, in this framework as the group composition gets moreheterogenous, the e¤ect of changes in distance on individuals�utility is smaller.If the population composition is more heterogenous, an individual needs thepublic good closer to get the same utility as he would get in a homogenouspopulation.Then we can de�ne the total utility of the individuals as

Ui = y � ti + Zi (�i; ri) (1� di) (2)

Finally we assume that if the jurisdiction contains only one type of individ-uals, or if the individuals do not care about the composition of the jurisdictionthat they belong to, the utility obtained from the public good only depends onthe location of the public good, i.e., if �i = 1 and/or ri = 0, the Z function isthe same and �xed. The most simple form that satis�es the above mentionedcondition is �rii with Z (1; ri) = Z (�i; 0) = 1:So, given the �xed boundary at �, in a united society �B = � and �W = 1��

and if two regions separate �B = 1 and �W = 1. Then, if two jurisdictionsconsolidate, the utility of an individual i 2 [0; �) is equal to y�K+�rB (1� di)and the utility of an individual i 2 [�; 1] is y �K + (1� �)rW (1� di). If theydecide to provide the public good independently, the utility of an individual iis y � K

� + (1� di) for i 2 [0; �) and y �K1�� + (1� di) for i 2 [�; 1].

Each jurisdiction will make the decision to provide the public good inde-pendently or jointly. The consolidation decision is taken according to votes ofindividuals. We check two approval conditions; majority approval and unanim-ity approval. For majority approval, more than half of the population shouldbe in favor of consolidation and for unanimity approval, vote of each individualis needed. If the majority (or unanimity) in both jurisdictions are in favor ofproviding the public good jointly, they consolidate and there will be one publicgood provided. If one of the jurisdictions does not approve the consolidation,each jurisdiction provides its own public good. Then, the type (location) ofthe public good is decided by majority voting. We assume that individuals areforward looking and rational, that is, they are able to foresee the outcome of theconsolidation or separation. Thus, the result is a subgame perfect equilibriumof a two stage game where in the �rst stage individuals vote for consolidationand in the second stage they decide on the location of the public good.

3 Main Results

In this framework, where we have individuals with single peaked preferences ina single dimensional space, the median voter theorem applies, i.e., the publicgood will be located at median voter�s most preferred point. Since we have auniform distribution which means that the median voter is in the center of theeach neighborhood, the location of the public good will be the mid-point of the

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jurisdiction (for jurisdiction B it is �2 and forW it is 1+�2 and if two jurisdictionsconsolidate, the public good will be located at 12 :

3.1 Median Voter�s Decision

An individual votes for consolidation if and only if its payo¤ is higher underconsolidation. We introduce the approval condition as a threshold. An approvalthreshold for an individual is the minimal amount of public good cost deemednecessary to make that individual better o¤under consolidation. In this section,we analyze the approval conditions of the individuals in each community.We �rst look for the approval threshold of the median voter of the small

jurisdiction. We know that the median voter of the jurisdiction B, that is theindividual at �2 , prefers consolidation if and only if his payo¤ is higher, that is

y �K + �rB�1�

�1

2� �2

��> y � K

�+ 1

so we have the approval threshold for individual at �2

K >�

1� �

�1� �rB

�1

2+�

2

��� K�

2:

Now we check the approval conditions for the individuals that are located inthe interval [0; �2 ). That is, the condition for individual at

�2 �x where x 2 (0;

�2 ]

is

y �K + �rB�1�

�1

2� �2+ x

��> y � K

�+ (1� x)

then the individual located at �2 � x prefers consolidation if and only if

K > K�2� �

1� �x(1� �rB ) � K�

2�x

Individual at �2 + �x; where �x 2 (0;�2 ]; approves the consolidation if and only

if

y �K + �rB�1�

�1

2� �2� �x

��> y � K

�+ (1� �x)

By rearranging terms, we have

K > K�2� �

1� � �x(1 + �rB ) � K�

2+�x

First of all, note that K�2> K�

2�xand K�

2> K�

2+�x, i.e., the approval

threshold of the median voter is higher than the threshold of all his community

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members. This means, the public good cost should be higher to convince themedian voter to get the approval of her for consolidation (since higher publicgood cost means larger economies of scale). In other words, the most separatistindividual in a jurisdiction is the median voter. That is to say, when the medianvoter in a jurisdiction approves consolidation, all individuals in that jurisdictionalso do. The above arguments lead to our �rst proposition:

Proposition 1 In a society where the location of the good is determined bymajority voting, the median voter of the society is the most separatist.

This result is better understood when the gains from independent provisionare analyzed separately. If consolidation does not occur, not only the location ofthe public good provides more utility to the members but also the compositionof its bene�ciaries becomes more homogenous which implies higher utility to allmembers of the jurisdiction. However, although the gain from the change ofdistance is the same for the individuals in the interval [0; �2 ], individuals thathave higher utility, i.e., individuals closer to �

2 , enjoy the change of compositionmore than the others.

3.2 Majority approval

Most of the papers with a similar framework in the literature concentrate onmajority voting and take median voters�approval as a su¢ cient condition formajority approval. However, because of linearity, where the individuals do notcare about the composition of bene�ciaries (ri = 0), the majority and unanimityconditions are equal. To see that, �rst, we check the approval condition ofindividuals that are located at �

2 � x and�2 + �x where x; �x 2 (0;

�2 ] when rB is

equal to zero. We observe that K�2= K�

2�x> K�

2+�x, which means that if you

do not get the vote of the median voter, you do not have majority approval, butif median voter votes for consolidation, all individuals do. The same argumentapplies when rW = 0.In our framework it is possible to get majority approval without getting

the vote of the median voter. Since the median voter is the most separatistindividual of the jurisdiction, the votes for majority approval are obtained fromthe individuals that are closer to the borders. To get the majority approval ofjurisdiction B, �rst observe that K�

2�xis decreasing in x, in other words, if the

individual located at �2 � x is in favor of consolidation, all voters in the interval[0; �2 � x) will also prefer consolidation. Moreover, as K�

2+�xis decreasing in �x,

if the individual �2 + �x is in favor of consolidation, all the voters in the interval(�2 + �x; �] will be in favor of it.Hence, for the values of K that satisfy K > K�

2�x= K�

2+�xwith x+ �x = �

2 ,at least half of the population in jurisdiction B is in favor of consolidation. So

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if, K = K�2�x

= K�2+�x

and x+ �x = �2 exactly the half of jurisdiction B would

be in favor of consolidation. Thus, to �nd the critical value of K:

K�2�x

= K�2+�x

which implies that

x(1� �rB ) = �x(1 + �rB )and for majority approval we also need �x+ x = �

2 , then replacing �x with�2 � x,

we get

x(1� �rB ) = (�2� x)(1 + �rB )

that is

x(1� �rB ) + x(1 + �rB ) = �

2(1 + �rB )

so we have x = �4 (1 + �

rB ) and �x = �4 (1 � �

rB ) which leads to the followingproposition:

Proposition 2 The majority of jurisdiction B is in favor of consolidation ifand only if

K >�

1� �

�1� �rB

�1

2+�

2

�� �4(1� �2rB )

�The argument is very similar for jurisdiction W and obviously in both ju-

risdictions, the unanimity threshold for consolidation is always greater than themajority one.7 Note that, majority threshold is referred to the minimal publicgood cost that makes more than half of the population to vote for consolidationand unanimity threshold is the minimal K which is necessary to get the votesof the whole population.

4 Joint vs. Independent Provision

Individuals vote for the options of public good provision taking into accountthe costs and bene�ts of each case. In this section we �rst examine the char-acteristics of the outcomes when the majority or unanimity approval is neededfor consolidation.8 Then, we check under which conditions consolidation is awelfare improvement for the whole population.

7The majority threshold and its computation for jurisdiction W are given in the appendix.8To avoid repetition, we do remaining analyses for only jurisdiction B and also by taking

account the analytical facility, only the unanimity voting system is followed through the paper.However, our conclusions are less strict but still robust for majority voting system.

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4.1 Conditions

In section 3, we have found the necessary thresholds to get the approval of eachjurisdiction. However, for consolidation the approval of both sides is necessary.To characterize the necessary conditions for consolidation, �rst remember fromProposition 1, that jurisdiction B is unanimously in favor of consolidation ifand only if

K >�

1� �

�1� �rB

�1

2+�

2

��� KB (�; rB) (3)

Moreover, we know that all individuals in jurisdiction W will be in favor ofconsolidation, if the median voter wm = (1 + �)=2 is in favor of it. Then, theunanimity threshold for jurisdiction W is9

K >1� ��

�1� (1� �)rW

�1� �

2

��� KW (�; rW ) (4)

It is possible to �nd a value KH that assures the approval of both jurisdic-tions. There also exists a critical cost value KL, such that if the public goodcost is lower than that critical value, at least one of the jurisdictions does notapprove the consolidation.

Proposition 3 Independently of the jurisdiction sizes, if the cost of the publicgood is high enough, K > KH , both communities are in favor of consolidationand if it is below a threshold, K < KL, consolidation does not occur. If the publicgood cost is between these two thresholds, KH > K > KL, the consolidation isapproved by both jurisdictions only for some critical values of � where � 2(�W (K; rW ) ; �B (K; rB)).

Proof. For consolidation to occur, both (3) and (4) should be satis�ed. Nownote that @KW (�;rW )

@� < 0, @KB(�;rB)@� > 0. Thus for a given value of rW ,

KW (�; rW ) takes its maximum value for � = 0. @KB(�;rB)@� > 0, so for a

given rB its maximum is at � = 12 (recall that � 2 [0; 12 ]). Obviously, if

K > max�KW (0; rW ) ;KB

�12 ; rB

�� KH , both conditions will be satis�ed

and consolidation will occur for all values of �. Furthermore, the necessarycondition for approval is an increasing function of r, i.e., if the importance ofgroup composition increases, the consolidation is less likely to occur.For consolidation not to occur at least one of the two approval conditions

should not be satis�ed. Note that @KW (�;rW )@� < 0, @KB(�;rB)

@� > 0. Thus,

9See the Appendix for the derivation of this condition.

10

showing that KW (0; rW ) > KB (0; rB) and KB

�12 ; rW

�> KW

�12 ; rB

�, will

be enough to assure a unique intersection, ��. Below this intersection valueKW (��) = KB (�

�) � KL, at least one of the conditions is not satis�ed.We have KW (0; rW ) � KB (0; rB) =

12 + rW and we know that rW is a

positive parameter. It is trivial to obtain KB

�12 ; rW

�� KW

�12 ; rB

�which is

34 (0:5

rW � 0:5rB ). If rB > rW , then KB

�12

��KW

�12

�is also positive. That is,

if K < KB (��) = KW (��), the consolidation will be rejected by at least one of

the jurisdictions. Therefore, there will be one public good in each jurisdiction,independent of the jurisdictions�size. If rB � rW ; thenKW > KB for any valuesof �, which means if K < KW

�12

�, the consolidation is not approved. That is

also to say, only the threshold of the large jurisdiction is binding.If max

�KW (0) ;KB

�12

�> K > KW (��), consolidation will be approved

if and only if � 2 (�W (K; rW ) ; �B (K; rB)) with@�W (K;rW )

@K < 0; @�B(K;rB)@K > 0,i.e., for some values of public good cost, consolidation occurs if and only if thesmaller jurisdiction has a moderate size.

Intuitively, if the public good cost is high enough, the bene�ts of consolida-tion are su¢ cient to compensate the loss caused by heterogeneity and both com-munities are in favor of consolidation independent of the size of the jurisdiction:If the public good cost is below a critical level, for any size of jursidictions atleast one of the jurisdictions would reject consolidation. Thus, in that caseconsolidation does not occur regardless of jurisdictions�sizes.We also observe that large jurisdictions are less likely to consolidate. If

rB � rW , the approval threshold of jurisdiction W is higher than the approvalthreshold of jurisdiction B and the consolidation occurs if the small jurisdictionis su¢ ciently large. However, for rB > rW , when jurisdictions have similarsize, jurisdiction B is less likely to consolidate since its population is less andtherefore it enjoys less the public good. Hence, when the small jurisdictionis more intolerant, consolidation occurs if and only if the smaller jurisdictionhas a moderate size. This is a consequence of preferences over the bene�ciaries�composition. In case of consolidation, small sized jurisdiction members becomeminority, therefore, enjoy less the public good. Hence, they are less likely toconsolidate if their size is relatively too small.

4.2 Welfare Comparison

We now check the conditions under which consolidation is a welfare improve-ment. A consolidation is an improvement if the total utility of society increaseswhen jurisdictions consolidate. The total welfare under consolidation is

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Uc =

�Z0

[y � ti + �rB (1� di)] di+1Z�

[yi � t+ (1� �)rW (1� di)] di

= �

��rB

�1� 1� �

2

��+ (1� �)

�(1� �)rW

�1� 1

4

�1� �+ �2

1� �

���+ y �K

When they provide the public good independently, the total utility is

Us =

�Z0

[y � ti + (1� di)] di+1Z�

[yi � t+ (1� di)] di

= �

��1� �

4

�+ y � 2K

�+ (1� �)

��1� 1� �

4

�+ y � 2K

�

By de�nition, consolidation is an improvement if Uc > Us: That is satis�edif and only if

K >3

4+ (1� �) �

2� �rB+1

�1 + �

2

�� (1� �)rW

�3� 2�� 2�2

4

�� Kimp (�)

We de�ne Kimp (�) as the improvement threshold which means that, if thecost of the public good is greater than this threshold, the consolidation is animprovement independent of the jurisdictions�sizes. Note that @Kimp(�)

@� > 0:Hence, Kimp (�) is maximized at 12 . Then, if K > 7

8�38 (

12rB +

12rW ) � Kimp

�12

�,

the consolidation is an improvement for all values of �. If K < Kimp

�12

�,

consolidation is an improvement for the society if and only if � 2 (0; �imp (K))with @�imp(K)

@K > 0. That yields to the following proposition.

Proposition 4 If the public good cost is greater than the "improvement" thresh-old, i.e. K > Kimp, consolidation is an "improvement" for any size of jurisdic-tions. If the public good cost is not su¢ ciently high, consolidation is "improve-ment" if and only if small jurisdiction is small enough (� < �imp).

In other words, the total utility of the whole society increases by consol-idation, if the cost of the public good is high enough and if not, the smalljurisdiction should be small enough compared to the large one.

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5 Location decision

In this section, we analyze the mechanisms for the decision of public good lo-cation. First, we check under which conditions an agreement for consolidationcan be obtained by changing the location of the public good. Then, we analyzethe case where a social planner decides on the location of the public good withthe purpose of maximizing the utility of the jurisdiction.

5.1 Mediation

From Proposition 3, we know the conditions for approval of consolidation byboth jurisdictions. Those decisions are taken by residents that are aware ofthe second stage decision mechanism which is majority voting. Now, imaginethat there is a third party that may change the public good location to get theapproval for consolidation. First the location under the case of consolidationis announced, then individuals vote. Obviously, if no jurisdiction approves theconsolidation for the median voter�s location, there is no way to get the approvalby changing the location of the public good, i.e., mediation is worthless. Thatmeans, if only one of the jurisdictions is against consolidation, it may be possibleto take the majority approval of the other jurisdiction by the help of a thirdparty.Let us assume that the intolerance factor is the same for both jurisdictions,

rW = rB = r. This assures us that if community W approves the consolidation,communityB does as well. This also means that if the small jurisdiction does notapprove the consolidation for the location 1

2 , no agreement is possible. Then, theinteresting case is where the consolidation is approved by jurisdiction B but notby jurisdiction W . We should �rst �nd out under which conditions it is possibleto convince the community W to consolidate by changing the location of thepublic good. We know that if the location of the public good under consolidationmoves toward the median voter�s location of a community, individuals in thatcommunity become more likely to consolidate. Hence, the community W maybe convinced to consolidate if and only if

K >1� �� (1� �)r+1

�

However, the above condition is not su¢ cient to approve the consolidation,since while convincing one jurisdiction, the other may become against to it.Jurisdiction B continues to prefer consolidation to independent provision if thepublic good cost is higher than community�s threshold for a given location, i.e.,K > KB(L) where L is the new location of the public good.We know that since the bene�ts of economies of scale are higher for a smaller

jurisdiction, smaller jurisdictions are more likely to accept the new location orapproval of consolidation. Finally, we can observe that when � is small, althoughit is harder to have consolidation, it is easier to convince the large jurisdiction to

13

approve it. In other words, disagreements over consolidation get harder to solvewhen jurisdictions have relatively similar sizes or when they are more intolerantabout sharing a public good.

5.2 Social planner

Another alternative of majority voting mechanism in location decision is to leavethat decision to a social planner. A social planner could maximize the total util-ity of the jurisdiction by replacing the public good. Di¤erent from the previouscase, here we talk analyze the second stage where the social planner takes thedecision over consolidation as given, i.e., jurisdictions go to a social planner af-ter deciding to consolidate or not. If the jurisdictions provide the public goodindependently, the social planner decides to the location in jurisdiction B bymaximizing

�Z0

�y � ti +

�1� di(mB)

��di

That gives us mBeff =

�2 , that is to say, the public good will be located at

�2 . For jurisdiction W , the planner maximizes

1Z�

�yi � t+

�1� di(mW )

��di

and gets the e¢ cient location of the public as 1+�2 , i.e. m

Weff =

1+�2 .

In both jurisdictions the e¢ cient location of the public good is the same asthe location that is decided by majority voting.However if they consolidate, the social planner will be maximizing

�Z0

[y � ti + �rB (1� di(m))] di+1Z�

[yi � t+ (1� �)rW (1� di(m))] di

and by rearranging the �rst order conditions we obtain the e¢ cient locationmeff of the public good:

Proposition 5 In case of consolidation, the e¢ cient location of the public goodis given by

meff =1

2+�

2(1� �rB

(1� �)rW )

14

First of all note that, if individuals do not care about the composition ofbene�ciaries i.e. if r = 0, the e¢ cient location of the public good is the sameas the one decided by majority voting. However, when rB(rW ) increases, thelocation of public good gets farther from jurisdiction B(W ), i.e., when a juris-diction cares more about the composition of the bene�ciaries, for e¢ ciency, thepublic good will be located farther away from this jurisdiction, that is:

@meff

@rB> 0

@meff

@rW< 0

Note also that when (1� �)rW > �rB , the e¢ cient location of the publicgood is on the right of the median voter of the society meff >

12 . This also

means that when the location of the public good is decided by a planner, thesmall jurisdiction will be more keen on separation than when it is decided bymajority.When jurisdictions independently provide the public good or if they do not

care about the bene�ciaries�composition, the e¢ ciency requirement is equiva-lent to the majority voting requirement, i.e., each jurisdiction places the facilityat the location of its median resident. However, in case of consolidation, thee¢ cient location of the public good depends on the importance of group com-position for each type and size of jurisdictions.When people equally care about the group composition, the e¢ cient location

of the public good is greater than 12 , that means it favors the larger jurisdiction.

Moreover, when members of one group care more about the composition ofbene�ciaries, the e¢ cient location gets farther away from the median voter ofthat group. In other words, when the location of the public good is decidedby a social planner, i) the strategic choice of a group should be to reduce theimportance of bene�ciaries� composition in the group. ii) mostly the regionswhere the minority lives looses because of the existence of group compositionimportance.

6 Non-excludable public good

So far, we have concentrated on the case of an excludable public good. However,exclusion is not possible for some public goods such as parks, and if the publicgood is non-excludable, jurisdictions beside the joint or separate provision op-tions have the free-riding option. Under speci�c conditions, communities mayprefer free-riding to independent provision or consolidation. Moreover, evenif the communities prefer to provide their own public good, there may be anindividual or a group of individuals that admire the others�public good andtherefore would use that one.

15

6.1 Free-riding

If a jurisdiction chooses to free ride, it means that individuals in that jurisdictiondo not pay any taxes but they have no rights on the decision of the public goodlocation. Not surprisingly, free-riding is a matter for only small jurisdiction. Inother words, if the small jurisdiction decides to provide its own public good,large jurisdiction does as well. When jurisdiction B free rides, the location ofthe public good is determined by residents in jurisdiction W , so located at 1+�2 .If the following condition is satis�ed, the free riding option is preferred by

unanimity to consolidation.

Uc = y �K + �rB (1� (12� �2)) < y + �rB (1� (1 + �

2� �2)) = Ufr

�K + �rB (1 + �

2) < �rB

1

2

That is, if K > �rB �2 = K1, (i), they will not consolidate but free ride.

When jurisdictions have the possibility of independent provision of the publicfacility,

Us = y �K

�+ 1 < y + �rB (1� (1 + �

2� �2)) = Ufr

rearranging it the inequality can be expressed

1� �rB

2<K

�

That is, if K >�1� �rB

2

�� = K2, (ii), jurisdiction B prefers free riding to

providing the public good independently.Note that when (ii) is satis�ed, (i) is also satis�ed, that is, K2 > K1. The

small jurisdiction prefers independent provision of the public good if the publicgood cost is between those critical values, K2 > K > K1.When rB increases, free riding against consolidation is more likely (K1 de-

creases), but if independent provision is possible, free riding is less likely (K2

increases) since they prefer to provide the public good independently. However,when individuals do not care about the composition (r = 0), both equationsare equal K2 = K1, i.e. the choice of the minority against consolidation isnot a¤ected whether it has the independent provision option or not.In otherwords, if there exists no intolerance against the other group, the minority wouldconsolidate or free ride.The free riding option may also a¤ect the location decision of jurisdiction

W . For some values of the public good cost, the majority in community W mayprefer to locate the public good on the right side of the median voter�s locationto make the small community to provide its own public good. That threat isnot credible without a commitment, since there will be no more incentives tochange the location in the second stage. However, imagine that jurisdictions

16

take their decisions about location in the �rst stage as well. Instead of votingfor the location in the second stage, they vote for a pack that includes boththe choice about how to provide the public good and where to locate it. Oryou can only imagine that the large jurisdiction decides the location of its ownpublic good and after that the small jurisdiction decides to free ride or not.Those two cases create incentives for the large jurisdiction to change the loctionof its public good. If members of the community W do not care about withwhom they share the public good (rW = 0), the free riding decision does nota¤ect their location decision, i.e. it is located at 1+�

2 . However, if individualsin W value the bene�ciaries�composition (rW > 0), and the small jurisdictionis likely to free ride, K >

�1� �rB

2

��, then the majority in the jurisdiction

W chooses to locate the public good to a point x greater than 1+�2 where x

is derived from min[3+�2 � (1� �)rW ; 1]. The majority prefers strategically thepoint x if it makes the minority to provide their own public good instead of free-riding. More intuitively, in a democracy, the majority group in the populationmay move its own public good to a more extremist point as a result of theintolerance against minority.

6.2 Envy

When we have two non-excludable public goods, an individual or a group ofindividuals from a jurisdiction may prefer to use the one that is not in theirjurisdiction.10 Di¤erent from free riding, each community provides a publicgood and each individual pays an amount of tax to provide the public goodfor his community but if the public good of the other jurisdiction is su¢ cientlyclose to an individual�s ideal point, he may have an intention to use it.It is easy to verify that when ri > 0 with i = W;B, a single individual

never prefers to use the other jurisdiction�s public good, since the utility thathe gets from the other public good will be equal to zero. We check under whatconditions there exists a group that would prefer to use the other jurisdiction�spublic good. First, we observe that in jurisdiction B there exists no group ofindividuals that would prefer to use the public good in jurisdiction W if theyhave provided one in their jurisdiction. However, this is not always the casefor members of large jurisdiction. No group of individuals from jurisdiction Wprefer to use the public good of the others if there is not enough di¤erences insizes of jurisdictions and/or if the members of community W is very intolerantagainst sharing the good with other community members, i.e., if � and/or rWis high enough.

10 In the literature, this fact is mostly studied for excludable public goods for stabilitypurposes. Since in this paper we do not let any other coalition rather than the grand andsegregated ones, we take a glance to that question for the non-excludable case.

17

7 Conclusion

Although the preferences over population composition is a highly accepted con-cept, there is very little attention on its e¤ects over local public good provision.In this paper, we have studied the e¤ects of the existence and the changes ofpreferences over bene�ciaries�composition on various decisions.We �rst look at each jurisdiction�s speci�c decision over consolidation where

the trade o¤ is between economies of scale and heterogeneity. However, di¤er-ent from the existing literature, this paper analyzes the e¤ects and results ofpreferences over the composition of bene�ciaries while deciding for consolidationin the provision of a public good. If the residents of a jurisdiction loose moreutility sharing the public good with the other jurisdiction, the consolidation isless likely and we �nd that small jurisdictions are more keen to consolidation. Inthis framework, depending on the values of the public good cost and intolerancefactor, the consolidation is more likely to occur when the small jurisdiction hasa moderate or similar size compared to the large jurisdiction. Similar to theexisting literature, we �nd that the consolidation decision increases the totalutility of the society if and only if the small jurisdiction is small enough.We also point out the e¤ects of location decision and free-riding option.

We obtain that it is harder to solve the disagreement when jurisdictions havesimilar sizes. Moreover, when a jurisdiction cares more about the compositionof the public goods�bene�ciaries, the social planner�s location decision for thepublic good changes in a way that makes that jurisdiction worse o¤. Finally,the minority is more keen to provide their own public good even though theyhave the free-riding option and unlike the large community members, none ofthe small jurisdiction members would prefer to use the others�public good ifthey have their own.The current study may be developed in several directions such as analyzing

the e¤ects of di¤erent types of distributions and voting systems. Moreover,giving a strategical choice like lobbying may give interesting results. Lastly, itmay be fruitful conducting an empirical analysis that looks simultaneously onthe e¤ects of heterogeneity in the decision of consolidation for the provision ofa public good.

18

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[2] Alesina, A. and E. Spolaore (1997), "On the number and size of nations",Quarterly Journal of Economics, 112, pp. 1027-1056.

[3] Alesina, A., R. Baqir and W. Easterly (1999): �Public Goods and EthnicDivisions�, Quarterly Journal of Economics, Vol. 114. pp 1243-84.

[4] Alesina, A., R. Baqir and C. Hoxby (2004), �Political Jurisdictions in Het-erogeneous Communities�, Journal of Political Economy 112, pp. 348-396.

[5] Austin, D. A.(1999), "Politics vs economics: Evidence from municipal an-nexation". Journal of Urban Economics, 45, pp. 501�32.

[6] Bolton, P. and G. Roland (1993), "The break-up of nations: A politicaleconomy analysis", Quarterly Journal of Economics, 112, pp.1057-1089.

[7] Brasington, D. M. (1999), "Joint provision of public goods: The consolida-tion of school districts", Journal of Public Economics, 73, pp. 373�93.

[8] Brasington, D. M. (2003), "Snobbery, racism, or mutual distaste: Whatpromotes and hinders cooperation in local public good provision?", TheReview of Economics and Statistics, 85, pp. 874-83

[9] Casella, A. (1992) �On Markets and Clubs: Economic and Political Integra-tion of Regions with Unequal Productivity�, American Economic Review,Papers and Proceedings 82, pp. 115-121.

[10] Casella, A. and J. Feinstein (2002), �Public Goods in Trade: On the For-mation of Markets and Political Jurisdictions�, International Economic Re-view, 43, pp. 437-462.

[11] Ellingsen, T. (1998), "Externalities vs internalities: A model of politicalintegration", Journal of Public Economics, 68, pp. 251-268.

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19

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20

Appendix

Thresholds of Jurisdiction W:i) For unanimity approval in jurisdiction W , from Proposition 1 we know

that the median voter of jurisdictionW should be in favor of the joint provision.Thus, the below condition should be satis�ed:

y �K + (1� �)rW�1�

����12 � 1 + �2����� > y � K

1� � + 1

by rearranging terms, we obtain the unanimity threshold for the jurisdictionW :

K >1� ��

�1� (1� �)rW

�1� �

2

��� KW (�)

ii) For majority approval in jurisdiction W ; note that the individual locatedat 1+�2 � x where x < �

2 prefers consolidation if and only if

K >1� ��

�1� (1� �)rW

�1� �

2

�� x(1 + (1� �)rW )

�� K 1+�

2 �x

and an individual at 1+�2 + �x approves consolidation if and only if

K >1� ��

�1� (1� �)rW

�1� �

2

�� �x(1� (1� �)rW )

�� K 1+�

2 +�x

Notice that K 1+�2 �x and K 1+�

2 +�x are decreasing in x and �x respectively.

Thus, for values of K where K > K 1��2 �x = K 1��

2 +�x for �x+ x =1��2 , at least

the half of the population in jurisdiction W is in favor of consolidation, thatis, consolidation is approved by majority. When K = K 1��

2 �x = K 1��2 +�x and

�x+x = 1��2 exactly the half of the jurisdiction would be in favor of consolidation.

From K 1��2 �x = K 1��

2 +�x and �x+ x =1��2 we have �x = 1��

4 (1 + (1� �)rW )

and x = 1��4 (1� (1� �)

rW ).So, ifK > 1��

�

�1� (1� �)rW

�1� �

2

�� 1��

4 (1� (1� �)rW )(1 + (1� �)rW )

�<=> K > 1��

�

�1� (1� �)rW

�1� �

2

�� 1��

4 (1� (1� �)2rW )

�the majority

of jurisdiction W is in favor of consolidation.Note that if x = 1��

4 (1� (1��)rW ) > �

2 , that is,1��2 �x < 1

2 , the conditionK 1��

2 �x slightly changes. In that case,

K >1� ��

�1� (1� �)rW

�1 +

�

2

�� x(1� (1� �)rW )

�� K 1+�

2 �x

21

Notice that x = 1��4 (1� (1��)

rW ) > �2 if and only if (1��)

rW+1+3� < 1.Now, for majority approval we need to have �x+x = 1��

2 , and this is satis�ed

for x = 14 �

�4

�1+(1��)rW1�(1��)rW

�and �x = 1

4 ��2 +

�4

�1+(1��)rW1�(1��)rW

�. Then, the below

condition should be satis�ed.

K >1� ��

�1� (1� �)rW

�1� �

2

���1

4� �2+�

4

�1 + (1� �)rW1� (1� �)rW

��(1� (1� �)rW )

�which can be written as

K >1� ��

�1� (1� �)rW

�1� �

2

���1

4� 3�4� �2

�1

(1� �)rW � 1

��(1� (1� �)rW )

�after some steps of simpli�cation the condition for majority approval of juris-diction W when (1� �)rW+1 + 3� < 1 is

K >1� ��

�3 + �

4� 3 + �

4(1� �)rW )

�

Majority approval of free-riding decision:When we are looking for majority of votes to approve the free riding decision,

It is easy to show that the essence of the result does not change. Obviously, thesmall jurisdiction is more keen to free ride.If majority approval is needed for free ridingK >

�1� �rB

2 � �4 (1� �

2rB )�� =

Km2 and Km1 = K1.Km2 > Km1 since 1 > �

rB + �4 (1� �

2rB ).

22