Some applications of set-valued mappings in mathematical economics

Given a separable metrizable space X and a metric d on it a characterization of preferences R:X→2 X that admit d-Lipschitz utility functions is presented. Also characterized are choice functions that can be rationalized by d-Lipschitz and by continuous utility functions. The asymptotic behavior of a...

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Published inJournal of mathematical economics Vol. 20; no. 1; pp. 69 - 87
Main Author Levin, V.L.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 1991
Elsevier
Elsevier Sequoia S.A
SeriesJournal of Mathematical Economics
Subjects
Applications
Economic theory
Economics
Growth models
Mapping
Mathematical analysis
Mathematical economics
Utility functions
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Summary:Given a separable metrizable space X and a metric d on it a characterization of preferences R:X→2 X that admit d-Lipschitz utility functions is presented. Also characterized are choice functions that can be rationalized by d-Lipschitz and by continuous utility functions. The asymptotic behavior of a dynamical system determined by R is another subject of study in the paper. The trajectories of such a system are sequences χ=( χ( t)) ∞ t=0 with χ( t)∈ R( χ( t-1)), t=1,2,...Properties are examined of a certain global attractor which, in the particular case of compact X and Hausdorff-continuous R, was introduced by Rubinov (1980) as an analogue of a turnpike in models of growth.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0304-4068
1873-1538
DOI:10.1016/0304-4068(91)90018-O