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A Pure Theory of Population Distribution When Preferences Are Ordinal

Holger Stark () and Grzegorz Kosiorowski
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Grzegorz Kosiorowski: Cracow University of Economics

No 15923, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: We model an environment in which individuals prefer to be in a space in which their rank is higher, be it a social space, a geographical space, a work environment, or any other comparison sphere which we refer to in this paper, and without loss of generality, as a region. When the individuals can choose between more than two regions, we inquire: (i) whether a steady-state distribution of the population is reached; (ii) how long it will take to reach a steady state; and (iii) if a steady state obtains, whether at the steady state social welfare is maximized. Despite the fact that when there are three or more regions the mobility paths are more intricate than when there are only two regions, we prove that a steady-state distribution of the population across the regions is reached; we identify the upper bound of the number of time periods that it will take to reach the steady-state distribution; and we show that the steady-state distribution maximizes social welfare. This last result is surprising: even though the individuals act of their own accord, they achieve the socially preferred outcome.

Keywords: inter-space mobility; three or more spaces; ordinal preferences; distaste for low rank; steady-state population distribution; social welfare (search for similar items in EconPapers)
JEL-codes: C61 C62 D50 D60 D62 I31 R13 R23 Z13 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2023-02
New Economics Papers: this item is included in nep-evo and nep-geo
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