Beneficial inequality in the provision of municipal services: why rich neighborhoods should get plowed first.

• Author: Conley, John

1. Introduction

   Local governments play an important role in the day-to-day life of Americans. They provide education, garbage collection, police protection, and many other fundamental services that the population cannot do without. This is especially true for the United States, whose population is largely urbanized. A large literature in the tradition of Tiebout (1956) has developed, which explores the possibility that competition between jurisdictions may induce efficient provision of these goods and services. Much less attention has been devoted to the question of how localities choose to allocate goods internally. In an important early paper that considered this issue, Inman and Rubinfeld (1979) observed that the typical city shows potentially significant inequalities in the provision of municipal services across neighborhoods. There are a few neighborhoods with low crime rates, green parks, good schools, and clean streets, but most have occasional crime, decent streets, and schools financed at an adequate level. Of course, there are always some parts of a city with high crime rates, dirty and potholed streets, and poor schools. Putting this in quantitative terms, Inman and Rubinfeld (1979) determined that families with $10,000 yearly incomes received on average 25% more in services than families with $5000 incomes, whereas a family with a $20,000 yearly income received an additional 25% more than the $10,000 income family.

   This inequality is a bit mysterious if cities are ruled democratically. Intuitively, one might expect that lower income groups would not willingly tolerate an unfair allocation such as this. Of course, one could explain this by telling a political-economy story of how political donations, low voter turnout among the poor, or ignorance and apathy effectively disenfranchise the poor. The main point of this paper is to provide an explanation for this phenomenon that does not rely on this type of argument. We will show that, in fact, the poor often have an interest in supporting this type of inequality and are better off as a result. As a secondary point, we will also explore how the parameters of the economy affect the relative treatment of the rich and poor by local governments.

   We consider a model with a private good, a public good, and a public service (a publicly provided private good). There are two types of agents, rich and poor, who differ in income but have identical tastes. We assume the poor live in a jurisdiction called "the city" and form the majority of the population. The rich can choose to live in the city as well, but may instead choose to live in "the suburbs" apart from the poor. We assume that because of zoning, commuting costs, or some other unmodeled factor, the poor are unable to move to the suburbs. The public good and service are funded by a proportional income tax, and the public good is purely nonrival. The proportionality of this income tax (which may roughly proxy for sales taxes or property taxes) is a key modeling assumption. It precludes the city from using the tax system to discriminate either in favor of or against the rich.

   As we suggest above, there may be circumstances in which it is in the interest of the poor to treat the rich better than they treat themselves with respect to municipal services. Intuitively, what drives this is that the poor would prefer that the rich live in the city, as this allows them to capture their income as part of the tax base. The rich also potentially benefit from living in the city, since the larger population (the rich plus the poor) allows higher public good production at lower per capita cost. If there were nothing standing in their way, the poor would choose to impose very high income taxes on everyone and redistribute the resulting revenue in the form of high levels of public service targeted specifically at the poor. The rich, however, have the option of moving to the suburbs. To prevent this, the poor must make the rich at least as well off in the city as they would be on their own. Since tax rates and public goods consumption are the same by constraint, the only instrument the poor have available to provide the rich enough benefit to prevent their migration is the public service. (1) Thus, the poor may choose to give the rich extra public service to induce them to stay in the city and pay city taxes. The rich are at least as well off as they would be in the suburbs by constraint, and the poor are strictly better off. Thus, the poor should support such a differential allocation, and it results in a Pareto superior social allocation.

   We are, of course, not the first to look at the differential provision of public services within a jurisdiction. In addition to the work of Inman and Rubinfeld (1979), related papers include Gramlich and Rubinfeld (1982, and references therein); Behrman and Craig (1987); Craig (1987); Craig and Heikkila (1989); and Schwartz (1993). These last models look at the empirical distribution of a certain public output (for example, "safety" within a city) by examining the local government allocation of an input (the input for safety being "police"). For a very interesting application of a model quite close to the one proposed in this paper, see Rothstein and Te (2001), who consider a case in which the production costs are lower for the rich, and thus the poor have a relatively harder time attracting them into an integrated city.

   Most closely related to our model is the work of Craig and Holsey (1997) and Hoyt and Lee (1998). Craig and Holsey (1997) developed a framework that determined the efficient distribution of a publicly provided input within one jurisdiction, taking into account the congestion effects that may be present. They showed that the efficient distribution of publicly provided inputs depends on the individual tastes of each local resident and on each individual's ability to convert publicly provided inputs into public services output. (2)

   Hoyt and Lee (1998) took a somewhat different approach. In a framework with rich and poor agents, they developed a model that showed how fiscal zoning regulations can play a role in improving the welfare of a community. If such a policy tool is not available to the community (perhaps because it is illegal), the authors showed that an alternative policy with similar outcome (to sort out the poor) is for the rich community to overprovide a luxury private good (for example, a golf course). The provision of such high-income elasticity goods will make the jurisdiction less attractive to the poor, and so make the communities more homogeneous. Notice that Hoyt and Lee (1998) focused their attention on how to keep the two income groups separate. In contrast, our model identifies conditions under which it is possible for the rich and poor to benefit from living together.

   There is also a relationship between our analysis and the tax competition literature. Seminal papers in this line of research include Mintz and Tulkens (1986), Wilson (1986), Wildasin (1988) and Bucovetsky (1991). More recent extensions of the literature can be found in Bucovetsky (1995); Henderson (1994, 1995); Lee (1997); and Hindriks (1999). See Wilson (1999) and Wildasin (2003) (3) for surveys on tax competition. In such models, jurisdictions choose their tax rates optimally taking capital flows and their net return impact into account while viewing the tax rates chosen by other jurisdictions as parametric. In our model, the rich are the mobile factor instead of capital, and public services are the instrument used to attract the factor, rather than tax rates. Nevertheless, the basic insight--that the outside offers available to the mobile factor allow these factors to force jurisdictions to use the instruments available to induce them to move to the locality--is the same.

   The paper proceeds as follows. The next section introduces the general model. In section 3, we solve for the equilibrium in the general case and give some results. In section 4, we develop a more specific example of our model and provide additional results. Section 5 concludes the paper.

2. The Model

   We consider a model with a private consumption good x, a local public good y, and a public service s. The public service in this case is a purely rival private good that is provided exclusively by the government. We assume that the local public good is a nonexcludable and nonrival good also provided by the city government.

   We will analyze an economy with two types of people, the rich and the poor, which we will distinguish by the superscripts r and p, respectively, on utility functions and as subscripts elsewhere. We shall assume that rich and poor share the same preferences and differ only in their initial endowments of private goods. We denote these endowments [[omega].sub.r] and [[omega].sub.p], with [[omega].sub.r] > [[omega].sub.p]. Thus

   [U.sub.r](x, s, y) = [U.sup.p](x, s, y) = U(x, s, y) and [[omega].sub.r] > [[omega].sub.p] > 0.

   This utility function is assumed to be continuously differentiable, strongly monotonic, and strongly quasi-concave.

   There are [N.sub.p] poor and [N.sub.r] rich agents in the population. We shall also assume that there are more poor agents than rich ones. Thus [N.sub.p] > [N.sub.r]. The poor always live in a location we call the city. The rich may either live in the city or move to a different location called the suburbs. In the interest of simplicity, we leave unmodeled the factors that prevent the poor from following the rich. A more complete treatment would need to...