On the (Sequential) Majority Choice of Public Good Size and Location

In this paper, we lay the first building blocks of a positive theory of nation formation where national choices consist of the size and location of a public good. Individuals differ both in income and in their preferences for the public good location. Public expenditures are financed either by a lump sum tax or by a proportional income tax. We study both the simultaneous and the sequential determinations of the public good size and location. We show that, while the choice of the type of public good follows the traditional median logic, the majoritarian determination of the taxation rate need not coincide with the choice of a median income citizen. With lump sum financing, income heterogeneity plays no role and the sequential equilibrium consists of the median location together with the public good level most-preferred by the individual located at the median distance from the median. This policy bundle also constitutes an equilibrium with simultaneous voting in the special case of a uniform bivariate distribution of individuals' income and location. With proportional taxation, there is no policy equilibrium with simultaneous voting. We offer a complete characterization of the equations describing the sequential equilibrium in the general case and we show why and how our results depart from those obtained with the lump sum case. The public good level is lower than the one emerging under lump sum taxation when the income distribution is concave and when the correlation between individuals' income and location is positive but not perfect.