Efficient agglomeration of spatial clubs

We investigate here the agglomeration of spatial clubs in an efficient allocation of a club economy. The literature on agglomeration has focused largely on a primary agglomeration caused by direct attraction forces. We concentrate mainly on secondary and tertiary agglomerations caused by a primary agglomeration. Initially, scale economies in the provision of club goods (CGs) lead each CG to agglomerate in facilities of its club. This primary agglomeration causes a secondary concentration of population around these facilities, which in turn brings about a tertiary agglomeration of facilities of different clubs into centers in the midst of population concentration. The agglomeration of facilities occurs only if a secondary concentration of population takes place. We analyze in detail two specific patterns of agglomeration. One is the central location pattern in which the facilities of all clubs agglomerate perfectly in the middle of the complex. The second is a triple-centered complex in which the center in the middle of the complex consists of perfectly agglomerated facilities of different clubs, each with a single facility per complex. The remaining two centers also consist of facilities of different clubs, but clubs in these centers each have two facilities per complex, one in each center. Each of these two centers is located between a boundary and the middle of the complex closer to the middle of the complex than to the boundary. The facilities in these two centers form condensed clusters of facilities that may contain residential land in between the facilities. We then show that these agglomeration patterns also characterize agglomerations in general. The literature maintains that an efficiently behaving municipality increases its tax-base. This implies that it is in the municipality’s interest to achieve efficiency. The best way for a local government to achieve this desired efficiency is by partially intervening in market operations in order to internalize local externalities. Such an intervention should be limited to providing the city’s infrastructure, to taxing only residential land rents and clubs’ profits, to subsidizing the basic industry of the city, and to partially regulating land uses. Consequently, if the local governments of all complexes behave according to the above, the decentralization of the efficient allocation of the club economy would be attained.

Research highlights
► Agglomerations (into centers) of agglomerations (of club goods).
► Three stages (of causality) in agglomeration: primary agglomeration of club goods, secondary concentration of population and tertiary agglomeration of facilities.
► In a first best allocation the population distribution is never uniform and in a second best uniform population distribution an agglomeration of facilities is ineffective.
► There are two types of facility agglomeration: perfect agglomeration in the middle of a complex and imperfect agglomeration in clusters away from the middle of the complex where each cluster gravitates away from the center of its joint market area and towards the center of the symmetric complex.
► An efficient allocation can be decentralized by local governments intervention that is limited to taxation of land rents and club profits, subsidization of the basic industry and partial land use regulations.