From the tragedy of Africa to social problems of American cities, the e? ects of racial con? ict have risen to the center of attention not only of policymakers but also of academic researchers. 1 While sociologists and political scientists have long been aware of the importance of these issues, only recently economists have begun paying more systematic attention to them. The purpose of this paper is to discuss the question: is ethnic diversity good or bad from an economic point of view, and why? Its potential costs are fairly evident.

Con? ict of preferences, racism, prejudices often lead to policies which are suboptimal from the point of view of society as a whole, and to the oppression of minorities which may then explode in civil wars or at least in disruptive political instability. But an ethnic mix also brings about variety in abilities, experiences, cultures which may be productive and may lead to innovation and creativity. The United States are the quintessential example of these two faces of racial relations in a melting pot.

While much evidence points toward the problem of racial heterogeneity in US cities, the racially mixed and racially troubled New York City and Los Angeles are constant producers of innovation in the arts and business. In what follows we try to highlight the trade o? between the bene? ts of variety and complexity and the costs of heterogeneity of preferences in a multi-ethnic society. In order to bring more evidence to bear on this question we plan to examine jointly two strands of the literature that have proceeded in a parallel way: one on cross country comparisons, and one on local communities.

The latter is itself split into two sub areas with little communication between the two, namely the public and urban economics literature on US cities on the one hand, and the development literature which focuses on groups and local communities on the other. Within both strands of the literature, one approach takes the size and number of jurisdictions (countries or localities) as given, and studies the e? ects of di? erent degrees of ethnic fragmentation on quality of government, economic policies, growth, unrest, crime, civil wars etc.

A second and less developed approach focuses on the fact that the number and size of political jurisdictions is itself determined by the ethnic composition of the population. In the process of examining the existing literature we provide some new results and we highlight several open questions ranging from data and measurement problems, to unsolved empirical and theoretical puzzles, to policy implications. While we are of course perfectly aware that American cities are very di? erent from African villages, we believe that highlighting similarities and di?erences in the ?

Ndings may shed some light on the question at hand, for instance how di? erent levels of development and di? erent types of racial, linguistic or religious con? ict play out in the political economy of various parts of the world. As always when reviewing a strand of the literature one has to put We use the terms racial and ethnic interchangeably when referring to fragmentation, although we are aware that the two concepts di? er and we shall highlight the di? erences when in order. 1 1 boundaries.

We limit ourselves to direct economic e? ects of diversity; we leave aside indirect e? ects that may go trough civil wars. crime, revolutions etc. We proceed in the following way. In section 2 we discuss the theoretical underpinnings of the relationship between ethnic diversity and economic performance. We also sketch a simple model, which has no pretence of being innovative but illustrates clearly the pros and cons of ethnic fragmentation and sets the stage for the discussion of the literature (mostly empirical) that follows. Section 3 discusses the e?

ects of ethnic and racial fragmentation in various types of communities holding the number and size of communities as exogenous. We examine evidence collected on three types of communities: social groups, localities and nations. Section 4 discusses the question of endogenous formation of groups, localities and nations. Section 5 concludes by discussing several open questions in this area of research. The last section attempts to draw some tentative conclusions and policy implications. 2 Theories on diversity The goal of this section is to brie?

y highlight some economic motivations underlying the relationship between ethnic diversity and economic performance. Since no comprehensive treatment of this is available, we start by gathering di? erent contributions that can give a more or less coherent picture of the microfoundations for this relationship. Having established such microfoundations, we then move to analyze the impact of diversity on policies and productivity through a simple reduced-form model. 2. 1 Some microfoundations The most basic way in which ethnic diversity can a? ect economic choices is by directly entering individual preferences.

Early work on social identity theory has established that patterns of intergroup behavior can be understood considering that individuals may attribute positive utility to the well being of members of their own group, and negative utility to that of members of other groups (see e. g. , Tajfel et al. (1971)). A recent formalization of this concept is the analysis of group participation by Alesina and La Ferrara (2000), where the population is heterogeneous and individual utility from joining a group depends positively on the share of group members of ones own type and negatively on the share of di? erent types.

A second way in which diversity can a? ect economic outcomes is by in? uencing the strategies that individuals play. Even when individuals have no taste for or against homogeneity, it may be optimal from an e? ciency point of view to transact preferentially with members of ones own type if there are market imperfections. For example, Greif (1993) argues that traders in Medieval times formed coalitions along ethnic lines in order to monitor agents by exchanging information on their opportunistic behavior. Ethnic 2 a? liation helped sustain a reputation mechanism in the presence of asymmetric information.

But strategies can be conditional on ones ethnic identity also in the presence of perfect information. La Ferrara (2003a) shows that when contracts cannot be legally enforced (and therefore have to be self-enforcing), membership in ethnic groups allows to enlarge the set of cooperative strategies that can be supported. The reason is that both punishment and reciprocity can be directed not only to the individual but to other members of his/her group. A similar reasoning is proposed by Fearon and Laitin (1996) to explain inter-ethnic cooperation. Finally, ethnic diversity may enter the production function.

Alesina Spolaore and Wacziarg (2000) employ a Dixit Stiglitz production structure where more variety of intermediate inputs, that can be interpreted as more variety of individual skills, increases total output. This model, however, does not identify a trade o? in the production function since more heterogeneity is always better than less. The costs of heterogeneity are outside the production function. Lazear (1999 a, b) also discusses how di? erent skills in a production unit may increase overall productivity. He identi? es a trade o? between the productive bene?

ts of diversity and the possible costs that may arise due to di? cult communication between people with di? erent languages, culture etc. There is an optimal degree of heterogeneity that is identi? ed by the optimal point of this trade o? given also the nature of the production unit and its technology. An empirical paper by O Reilly Williams and Barsade (1997) brings supportive evidence on these hypothesis. They analyze 32 project teams and ? nd that more diversity lead to more con? ict and less communication, but controlling for the latter it also leads to higher productivity.

Pratt (2000) raises related points in the context of team theory. In teams where jobs are complementary homogeneity has positive e? ects and the other way around. Ottaviano and Peri (2003) also investigate the pros and cons of diversity in production. Diversity and related amenities a? ect the value of land (rents) which enters the production function. 2. 2 2. 2. 1 Costs and bene? ts of diversity: a simple model Private goods, public goods and diversity We provide here an elementary model that helps to clarify the pros and cons of ethnic diversity and o?

Ers a useful perspective for a review of the empirical literature. Consider a community, say a country, with K di? erent types of individuals, for a total population of N individuals. For simplicity, every group has the same size s = N/K. Output produced in the country is given by: Y = Nf (x; K) (1) where x is the ? xed amount of input, say labor, equal for every person and type. We assume that fx > 0, fxx < 0, where subscripts denote partial derivatives. If variety in 3 production is good then we have fK > 0, fKK < 0. This is the simplest possible way of capturing a bene?

T from variety in production, since per capita income is increasing in the number of di? erent types in the population. We also assume complementarity, i. e. fxK > 0. 2 Output can be either consumed privately or used to produce a public good, g. Individual utility is separable in the private and public good and is given by: U i = u(ci ) + v(g, K) (2) where uc > 0, ucc < 0, vg > 0, vgg < 0. We also assume vK < 0, and vgK < 0, implying that the enjoyment of the public good is decreasing and less communication, but controlling for the latter it also leads to higher productivity.

Pratt (2000) raises related points in the context of team theory. In teams where jobs are complementary homogeneity has positive e? ects and the other way around. Ottaviano and Peri (2003) also investigate the pros and cons of diversity in production. Diversity and related amenities a? ect the value of land (rents) which enters the production function. 2. 2 2. 2. 1 Costs and bene? ts of diversity: a simple model Private goods, public goods and diversity We provide here an elementary model that helps to clarify the pros and cons of ethnic diversity and o?

Ers a useful perspective for a review of the empirical literature. Consider a community, say a country, with K di? erent types of individuals, for a total population of N individuals. For simplicity, every group has the same size s = N/K. Output produced in the country is given by: Y = Nf (x; K) (1) where x is the ? xed amount of input, say labor, equal for every person and type. We assume that fx > 0, fxx < 0, where subscripts denote partial derivatives. If variety in 3 production is good then we have fK > 0, fKK < 0. This is the simplest possible way of capturing a bene?

T from variety in production, since per capita income is increasing in the number of di? erent types in the population. We also assume complementarity, i. e. fxK > 0. 2 Output can be either consumed privately or used to produce a public good, g. Individual utility is separable in the private and public good and is given by: U i = u(ci ) + v(g, K) (2) where uc > 0, ucc < 0, vg > 0, vgg < 0. We also assume vK < 0, and vgK < 0, implying that the enjoyment of the public good is decreasing with the number of types in the population. These preferences can be rationalized in two ways.

One is that sharing a public good implies contacts between people, and contacts across types produce negative utility, as in Alesina and La Ferrara (2000). A di? erent rationalization follows Alesina and Spolaore (1997). They distinguish between di? erent kinds of public goods in a context where the public good chosen is the one preferred by the median voter. The larger the number of types in the population the larger the average distance between each type an the median one that chooses the public good. 3 The budget constraint implies: g = tNf (x, K) (3).

Where t is the income tax rate. Suppose that a benevolent government can choose the tax rate, for given number of types. The problem is: max N [u(c) + v(g, K)] s. t. Nc + g = Nf (x, K) g = tNf (x, K) The ? rst order condition that de? nes an interior solution for this problem is: Nvg (·) = uc (·). (4) This equation implies that the marginal bene? t of taxation in terms of production of public good (LHS) has to be equal to the marginal cost of taxation in terms of reduction of private consumption (RHS). Distortionary taxes on, say, the labor supply would not change the basic message.

Standard applications of the implicit function theorem and of the envelope theorem lead to the following result: This can be considered a reduced form simpli? cation of a production function with a variety of inputs a la Dixit-Stiglitz as used by Alesina, Spolaore and Wacziarg (2000). 3 In Alesina and Spolaore (1997) there are multiple kinds of public goods to be supplied with ? x quantities. More generally, both the type and the quantity of public goods could change. 2 4 sign {dt/dK} = sign Note that we are holding N constant to isolate the e?

Ects of more fragmentation without changing total population size. While the sign of (5) is generally uncertain, dt/dK < 0 as long as vgK is large enough in absolute value. The intuition for this condition is clear: as long as the marginal bene? t of public consumption goes down substantially with an increase in ethnic fragmentation, then a larger K means that the social planner will choose a smaller size of the public good in favor of more private good. The only force working against this e? ect is the decreasing marginal utility of the private good.

In what follows we refer to the case where dt/dK < 0 as our benchmark case. This benchmark implies that, as a country becomes more ethnically fragmented, it may become more productive but it will choose to have a smaller size of government (remember that t = g/Y , thus t represents the size of government). More generally private consumption will increase but public consumption will decrease. This is an empirical implication which we shall test below. 4 Another application of the implicit function theorem leads to the following result: sign {dt/dx} = sign 2 ? tN vgg ? (1 ? t)ucc .

(6) 2 ? tN vgg fK + NvgK ? (1 ? t)ucc fK . (5) Note that if dt/dx < 0, then, a fortiori, dt/dK < 0. However one could have dt/dx > 0 and dt/dK < 0, i. e. , it is perfectly possible that the size of government is increasing with the level of individual productivity x, and thus in GDP, but decreasing in fragmentation. We next allow the social planner to choose not only the level of taxation but also the optimal number of types, K, again holding the size of the country constant. The ? rst order condition for an interior solution with respect to K is: uc (·)(1 ? t)fK + vg (·)tNfK = ?

VK (·) (7) and the second order conditions are satis? ed. Condition (7) equals the marginal bene? ts of letting in an additional group in terms of increased productivity and tax revenues (LHS) to the marginal costs of having one more group to share the public good with (RHS). 5 An interesting comparative statics exercise regards the e? ect of an increase in x (individual level of input/productivity) on the optimal number of groups. Straightforward algebraic computations establish, under very general conditions, the following:6 Note of course that if fk < 0, then income per capita would.

Go down as fragmentation increases and the allocation of this lower total output between private and public consumption would depend on the marginal bene? ts of the two. 5 Note that if there were no bene? ts in production from variety (fK ? 0), then the solution would be at a corner with the minimum number of groups, possibly 1, that is, a fully homogeneous society. The ? rst order condition for the choice of t is of course unchanged. 6 Intuitively, these conditions require that the indirect e? ects of a a change in t caused by a change in K do not override the direct e? ect of a change in x on K.

Details are provided in the appendix. 4 5 Remark 1 If fxK is positive and su? ciently large, then dK/dx > 0. A higher level of per capita input raises the bene? ts of variety and increases the optimal number of groups if the cross partial fxK is large enough. In this case, as the level of individual output increases the productivity gains from variety go up as well, so the bene? t from more ethnic fragmentation are increasing with the level of per capita output. This is an empirically plausible implication: the bene? ts of skill di? erentiation are likely to be more relevant in more advanced and complex societies.

2. 2. 2 On the number of jurisdictions The same theoretical framework can be extended to analyze the optimal number of jurisdictions, along the lines of Alesina and Spolaore (1997, 2003). We can think of the optimal size of a jurisdiction (say a country) to emerge from the a trade o? : the bene? t form variety and the costs of heterogeneity. In the language of our model above we could think of a social planner choosing the size s with the goal of maximizing total welfare. The trade o? between bene? ts and costs of heterogeneity would deliver an optimal size. Needless to say the larger the e?

Ect of variety in production and the lower the utility costs of heterogeneity the larger the size of the jurisdiction chosen by the social planner. 7 Given our analysis above, should we then expect larger countries to be more productive because they have more variety? The answer depends on the structure of international trade. With sever trade restrictions, country size would be very important for productivity; on the other hand with free trade countries can be small, enjoy the bene? t of homogeneity as far as public goods provision is concerned but enjoy diversity in production ( and consumption) by means of international trade.

8 Note that some ethnic fractionalization in country may favor trade as well. For instance a certain ethnic minority in country A can be a link with a country B where that ethnic group is a majority, therefore facilitating trade between A and B. The extent in which ethnic and cultural relation facilitate trade and more generally economic integration is well established See for instance Huntington (1994) for an informal discussion and Casella and Rauch (2001, 2003) for models and empirical evidence.

The same kind of trade o? between economies of scale of being large and the cost of heterogeneity public policy decisions, is applied to discuss the formation of local governments within a country with speci? c reference to the US by Alesina Baqir and Hoxby (2004). They show how an An important question is under which condition the optimal solution would or would not be reproduced by the market without a social planner, a question explored in a variety of setting by Alesina and Spolaore (2003).

In general the answer is no and the equilibrium size of jurisdictions would vary as a function of various aspect of political institutions and available rules to change borders, a set of issue that we do not purse here. 8 One implication of this is that he e? ects of the size of countries on economic success is mediated by the extent of freedom of trade, a result empirically supported by Ades and Glaeser (1995), Alesina Spolaore and Wacziarg (2000) and Alcala and Ciccone ( 2004) amongst others.

7 6 increase in heterogeneity in a county in the US leads to a formation of a larger number of smaller localities (cities and school districts). 2. 2. 3 Summing up the implications of the theory The potential bene? ts of heterogeneity come from variety in production. The costs come from the inability to agree on common public goods and public policies. One testable implication is that more heterogenous societies may exhibit higher productivity in private goods production but lower taxation.

Con? ict of preferences, racism, prejudices often lead to policies which are suboptimal from the point of view of society as a whole, and to the oppression of minorities which may then explode in civil wars or at least in disruptive political instability. But an ethnic mix also brings about variety in abilities, experiences, cultures which may be productive and may lead to innovation and creativity. The United States are the quintessential example of these two faces of racial relations in a melting pot.

While much evidence points toward the problem of racial heterogeneity in US cities, the racially mixed and racially troubled New York City and Los Angeles are constant producers of innovation in the arts and business. In what follows we try to highlight the trade o? between the bene? ts of variety and complexity and the costs of heterogeneity of preferences in a multi-ethnic society. In order to bring more evidence to bear on this question we plan to examine jointly two strands of the literature that have proceeded in a parallel way: one on cross country comparisons, and one on local communities.

The latter is itself split into two sub areas with little communication between the two, namely the public and urban economics literature on US cities on the one hand, and the development literature which focuses on groups and local communities on the other. Within both strands of the literature, one approach takes the size and number of jurisdictions (countries or localities) as given, and studies the e? ects of di? erent degrees of ethnic fragmentation on quality of government, economic policies, growth, unrest, crime, civil wars etc.

A second and less developed approach focuses on the fact that the number and size of political jurisdictions is itself determined by the ethnic composition of the population. In the process of examining the existing literature we provide some new results and we highlight several open questions ranging from data and measurement problems, to unsolved empirical and theoretical puzzles, to policy implications. While we are of course perfectly aware that American cities are very di? erent from African villages, we believe that highlighting similarities and di?erences in the ?

Ndings may shed some light on the question at hand, for instance how di? erent levels of development and di? erent types of racial, linguistic or religious con? ict play out in the political economy of various parts of the world. As always when reviewing a strand of the literature one has to put We use the terms racial and ethnic interchangeably when referring to fragmentation, although we are aware that the two concepts di? er and we shall highlight the di? erences when in order. 1 1 boundaries.

We limit ourselves to direct economic e? ects of diversity; we leave aside indirect e? ects that may go trough civil wars. crime, revolutions etc. We proceed in the following way. In section 2 we discuss the theoretical underpinnings of the relationship between ethnic diversity and economic performance. We also sketch a simple model, which has no pretence of being innovative but illustrates clearly the pros and cons of ethnic fragmentation and sets the stage for the discussion of the literature (mostly empirical) that follows. Section 3 discusses the e?

ects of ethnic and racial fragmentation in various types of communities holding the number and size of communities as exogenous. We examine evidence collected on three types of communities: social groups, localities and nations. Section 4 discusses the question of endogenous formation of groups, localities and nations. Section 5 concludes by discussing several open questions in this area of research. The last section attempts to draw some tentative conclusions and policy implications. 2 Theories on diversity The goal of this section is to brie?

y highlight some economic motivations underlying the relationship between ethnic diversity and economic performance. Since no comprehensive treatment of this is available, we start by gathering di? erent contributions that can give a more or less coherent picture of the microfoundations for this relationship. Having established such microfoundations, we then move to analyze the impact of diversity on policies and productivity through a simple reduced-form model. 2. 1 Some microfoundations The most basic way in which ethnic diversity can a? ect economic choices is by directly entering individual preferences.

Early work on social identity theory has established that patterns of intergroup behavior can be understood considering that individuals may attribute positive utility to the well being of members of their own group, and negative utility to that of members of other groups (see e. g. , Tajfel et al. (1971)). A recent formalization of this concept is the analysis of group participation by Alesina and La Ferrara (2000), where the population is heterogeneous and individual utility from joining a group depends positively on the share of group members of ones own type and negatively on the share of di? erent types.

A second way in which diversity can a? ect economic outcomes is by in? uencing the strategies that individuals play. Even when individuals have no taste for or against homogeneity, it may be optimal from an e? ciency point of view to transact preferentially with members of ones own type if there are market imperfections. For example, Greif (1993) argues that traders in Medieval times formed coalitions along ethnic lines in order to monitor agents by exchanging information on their opportunistic behavior. Ethnic 2 a? liation helped sustain a reputation mechanism in the presence of asymmetric information.

But strategies can be conditional on ones ethnic identity also in the presence of perfect information. La Ferrara (2003a) shows that when contracts cannot be legally enforced (and therefore have to be self-enforcing), membership in ethnic groups allows to enlarge the set of cooperative strategies that can be supported. The reason is that both punishment and reciprocity can be directed not only to the individual but to other members of his/her group. A similar reasoning is proposed by Fearon and Laitin (1996) to explain inter-ethnic cooperation. Finally, ethnic diversity may enter the production function.

Alesina Spolaore and Wacziarg (2000) employ a Dixit Stiglitz production structure where more variety of intermediate inputs, that can be interpreted as more variety of individual skills, increases total output. This model, however, does not identify a trade o? in the production function since more heterogeneity is always better than less. The costs of heterogeneity are outside the production function. Lazear (1999 a, b) also discusses how di? erent skills in a production unit may increase overall productivity. He identi? es a trade o? between the productive bene?

ts of diversity and the possible costs that may arise due to di? cult communication between people with di? erent languages, culture etc. There is an optimal degree of heterogeneity that is identi? ed by the optimal point of this trade o? given also the nature of the production unit and its technology. An empirical paper by O Reilly Williams and Barsade (1997) brings supportive evidence on these hypothesis. They analyze 32 project teams and ? nd that more diversity lead to more con? ict and less communication, but controlling for the latter it also leads to higher productivity.

Pratt (2000) raises related points in the context of team theory. In teams where jobs are complementary homogeneity has positive e? ects and the other way around. Ottaviano and Peri (2003) also investigate the pros and cons of diversity in production. Diversity and related amenities a? ect the value of land (rents) which enters the production function. 2. 2 2. 2. 1 Costs and bene? ts of diversity: a simple model Private goods, public goods and diversity We provide here an elementary model that helps to clarify the pros and cons of ethnic diversity and o?

Ers a useful perspective for a review of the empirical literature. Consider a community, say a country, with K di? erent types of individuals, for a total population of N individuals. For simplicity, every group has the same size s = N/K. Output produced in the country is given by: Y = Nf (x; K) (1) where x is the ? xed amount of input, say labor, equal for every person and type. We assume that fx > 0, fxx < 0, where subscripts denote partial derivatives. If variety in 3 production is good then we have fK > 0, fKK < 0. This is the simplest possible way of capturing a bene?

T from variety in production, since per capita income is increasing in the number of di? erent types in the population. We also assume complementarity, i. e. fxK > 0. 2 Output can be either consumed privately or used to produce a public good, g. Individual utility is separable in the private and public good and is given by: U i = u(ci ) + v(g, K) (2) where uc > 0, ucc < 0, vg > 0, vgg < 0. We also assume vK < 0, and vgK < 0, implying that the enjoyment of the public good is decreasing and less communication, but controlling for the latter it also leads to higher productivity.

Pratt (2000) raises related points in the context of team theory. In teams where jobs are complementary homogeneity has positive e? ects and the other way around. Ottaviano and Peri (2003) also investigate the pros and cons of diversity in production. Diversity and related amenities a? ect the value of land (rents) which enters the production function. 2. 2 2. 2. 1 Costs and bene? ts of diversity: a simple model Private goods, public goods and diversity We provide here an elementary model that helps to clarify the pros and cons of ethnic diversity and o?

Ers a useful perspective for a review of the empirical literature. Consider a community, say a country, with K di? erent types of individuals, for a total population of N individuals. For simplicity, every group has the same size s = N/K. Output produced in the country is given by: Y = Nf (x; K) (1) where x is the ? xed amount of input, say labor, equal for every person and type. We assume that fx > 0, fxx < 0, where subscripts denote partial derivatives. If variety in 3 production is good then we have fK > 0, fKK < 0. This is the simplest possible way of capturing a bene?

T from variety in production, since per capita income is increasing in the number of di? erent types in the population. We also assume complementarity, i. e. fxK > 0. 2 Output can be either consumed privately or used to produce a public good, g. Individual utility is separable in the private and public good and is given by: U i = u(ci ) + v(g, K) (2) where uc > 0, ucc < 0, vg > 0, vgg < 0. We also assume vK < 0, and vgK < 0, implying that the enjoyment of the public good is decreasing with the number of types in the population. These preferences can be rationalized in two ways.

One is that sharing a public good implies contacts between people, and contacts across types produce negative utility, as in Alesina and La Ferrara (2000). A di? erent rationalization follows Alesina and Spolaore (1997). They distinguish between di? erent kinds of public goods in a context where the public good chosen is the one preferred by the median voter. The larger the number of types in the population the larger the average distance between each type an the median one that chooses the public good. 3 The budget constraint implies: g = tNf (x, K) (3).

Where t is the income tax rate. Suppose that a benevolent government can choose the tax rate, for given number of types. The problem is: max N [u(c) + v(g, K)] s. t. Nc + g = Nf (x, K) g = tNf (x, K) The ? rst order condition that de? nes an interior solution for this problem is: Nvg (·) = uc (·). (4) This equation implies that the marginal bene? t of taxation in terms of production of public good (LHS) has to be equal to the marginal cost of taxation in terms of reduction of private consumption (RHS). Distortionary taxes on, say, the labor supply would not change the basic message.

Standard applications of the implicit function theorem and of the envelope theorem lead to the following result: This can be considered a reduced form simpli? cation of a production function with a variety of inputs a la Dixit-Stiglitz as used by Alesina, Spolaore and Wacziarg (2000). 3 In Alesina and Spolaore (1997) there are multiple kinds of public goods to be supplied with ? x quantities. More generally, both the type and the quantity of public goods could change. 2 4 sign {dt/dK} = sign Note that we are holding N constant to isolate the e?

Ects of more fragmentation without changing total population size. While the sign of (5) is generally uncertain, dt/dK < 0 as long as vgK is large enough in absolute value. The intuition for this condition is clear: as long as the marginal bene? t of public consumption goes down substantially with an increase in ethnic fragmentation, then a larger K means that the social planner will choose a smaller size of the public good in favor of more private good. The only force working against this e? ect is the decreasing marginal utility of the private good.

In what follows we refer to the case where dt/dK < 0 as our benchmark case. This benchmark implies that, as a country becomes more ethnically fragmented, it may become more productive but it will choose to have a smaller size of government (remember that t = g/Y , thus t represents the size of government). More generally private consumption will increase but public consumption will decrease. This is an empirical implication which we shall test below. 4 Another application of the implicit function theorem leads to the following result: sign {dt/dx} = sign 2 ? tN vgg ? (1 ? t)ucc .

(6) 2 ? tN vgg fK + NvgK ? (1 ? t)ucc fK . (5) Note that if dt/dx < 0, then, a fortiori, dt/dK < 0. However one could have dt/dx > 0 and dt/dK < 0, i. e. , it is perfectly possible that the size of government is increasing with the level of individual productivity x, and thus in GDP, but decreasing in fragmentation. We next allow the social planner to choose not only the level of taxation but also the optimal number of types, K, again holding the size of the country constant. The ? rst order condition for an interior solution with respect to K is: uc (·)(1 ? t)fK + vg (·)tNfK = ?

VK (·) (7) and the second order conditions are satis? ed. Condition (7) equals the marginal bene? ts of letting in an additional group in terms of increased productivity and tax revenues (LHS) to the marginal costs of having one more group to share the public good with (RHS). 5 An interesting comparative statics exercise regards the e? ect of an increase in x (individual level of input/productivity) on the optimal number of groups. Straightforward algebraic computations establish, under very general conditions, the following:6 Note of course that if fk < 0, then income per capita would.

Go down as fragmentation increases and the allocation of this lower total output between private and public consumption would depend on the marginal bene? ts of the two. 5 Note that if there were no bene? ts in production from variety (fK ? 0), then the solution would be at a corner with the minimum number of groups, possibly 1, that is, a fully homogeneous society. The ? rst order condition for the choice of t is of course unchanged. 6 Intuitively, these conditions require that the indirect e? ects of a a change in t caused by a change in K do not override the direct e? ect of a change in x on K.

Details are provided in the appendix. 4 5 Remark 1 If fxK is positive and su? ciently large, then dK/dx > 0. A higher level of per capita input raises the bene? ts of variety and increases the optimal number of groups if the cross partial fxK is large enough. In this case, as the level of individual output increases the productivity gains from variety go up as well, so the bene? t from more ethnic fragmentation are increasing with the level of per capita output. This is an empirically plausible implication: the bene? ts of skill di? erentiation are likely to be more relevant in more advanced and complex societies.

2. 2. 2 On the number of jurisdictions The same theoretical framework can be extended to analyze the optimal number of jurisdictions, along the lines of Alesina and Spolaore (1997, 2003). We can think of the optimal size of a jurisdiction (say a country) to emerge from the a trade o? : the bene? t form variety and the costs of heterogeneity. In the language of our model above we could think of a social planner choosing the size s with the goal of maximizing total welfare. The trade o? between bene? ts and costs of heterogeneity would deliver an optimal size. Needless to say the larger the e?

Ect of variety in production and the lower the utility costs of heterogeneity the larger the size of the jurisdiction chosen by the social planner. 7 Given our analysis above, should we then expect larger countries to be more productive because they have more variety? The answer depends on the structure of international trade. With sever trade restrictions, country size would be very important for productivity; on the other hand with free trade countries can be small, enjoy the bene? t of homogeneity as far as public goods provision is concerned but enjoy diversity in production ( and consumption) by means of international trade.

8 Note that some ethnic fractionalization in country may favor trade as well. For instance a certain ethnic minority in country A can be a link with a country B where that ethnic group is a majority, therefore facilitating trade between A and B. The extent in which ethnic and cultural relation facilitate trade and more generally economic integration is well established See for instance Huntington (1994) for an informal discussion and Casella and Rauch (2001, 2003) for models and empirical evidence.

The same kind of trade o? between economies of scale of being large and the cost of heterogeneity public policy decisions, is applied to discuss the formation of local governments within a country with speci? c reference to the US by Alesina Baqir and Hoxby (2004). They show how an An important question is under which condition the optimal solution would or would not be reproduced by the market without a social planner, a question explored in a variety of setting by Alesina and Spolaore (2003).

In general the answer is no and the equilibrium size of jurisdictions would vary as a function of various aspect of political institutions and available rules to change borders, a set of issue that we do not purse here. 8 One implication of this is that he e? ects of the size of countries on economic success is mediated by the extent of freedom of trade, a result empirically supported by Ades and Glaeser (1995), Alesina Spolaore and Wacziarg (2000) and Alcala and Ciccone ( 2004) amongst others.

7 6 increase in heterogeneity in a county in the US leads to a formation of a larger number of smaller localities (cities and school districts). 2. 2. 3 Summing up the implications of the theory The potential bene? ts of heterogeneity come from variety in production. The costs come from the inability to agree on common public goods and public policies. One testable implication is that more heterogenous societies may exhibit higher productivity in private goods production but lower taxation.