On the Existence of Spatial Equilibrium and Generalized Fixed Point Theorems

Valeriy Marakulin ()

Journal of the New Economic Association, 2019, vol. 42, issue 2, 12-34

Abstract: The problem of immigration-proof division into countries of a finite-dimensional area is studied. This is a kind of Tiebout equilibrium, in which the principle of migration consistency assumes that the border residents do not have incentives for the change of jurisdiction, i.e., at the point of their location costs of citizens for border countries are equal. It is assumed that a measurable population density is given and it is required that the cross-country boundary be represented by a continuous surface (curve). The proof of the existence of required division is based on the reducing of the problem to the searching of a fixed point. However, the conditions of classical theorems on fixed points of Brouwer-Kakutani or the "conical" Krasnoselskii's theorem are violated. This led us to the development of their generalization to the case of a mapping, possibly acting outside the domain. It is proved that a continuous mapping defined on a convex compact has a fixed point if it satisfies one of two boundary conditions: "compression" or "expansion". This result also is extended to point-to-set "Kakutani maps": applying it, we prove the existence of an immigration-consistent division into countries of any compact finite-dimensional area in very general setting..

Keywords: Brouwer-Kakutani fixed points theorems; compression and expansion conditions; country formation; migration-consistent (stable) partition (search for similar items in EconPapers)
JEL-codes: D70 H20 H73 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.econorus.org/repec/journl/2019-42-12-34r.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nea:journl:y:2019:i:42:p:12-34

DOI: 10.31737/2221-2264-2019-42-2-1

Access Statistics for this article

Journal of the New Economic Association is currently edited by Victor Polterovich and Aleksandr Rubinshtein

More articles in Journal of the New Economic Association from New Economic Association Contact information at EDIRC.
Bibliographic data for series maintained by Alexey Tcharykov ().