A theory of spatial equilibrium: the existence of migration proof country partition in a uni-dimensional world

The existence of an immigration proof country partition is studied in a one-dimensional world of interval $[0,1]$. The allocation of population is described by the Radon measure which does not necessarily have density. We prove that the world can be divided into “countries” presented as generalized intervals. In particular, a “country” of zero size (length), but nonzero mass (of population) can appear. This is a specific spatial Tiebout equilibrium, in which the principle of migration consistency suggests that the inhabitants of frontier have no incentives to change jurisdiction, i.e. an inhabitant at every frontier point has equal costs for all permissible jurisdictions. The paper generalizes various results of 90s–2000s.