 Smooth preferences, symmetries and expansion vector fieldsJournal of Economics, 2016, vol. 119, issue 2, No 5, 147-169 Abstract: Abstract Tyson (J Math Econ 49(4): 266–277, 2013) introduces the notion of symmetry vector field for a smooth preference relation, and establishes necessary and sufficient conditions for a vector field on consumption space to be a symmetry vector field. The structure of a such a condition is discussed on both geometric and economic grounds. It is established that symmetry vector fields do commute (i.e. have vanishing Lie bracket) for additive and joint separability. The marginal utility of money is employed as a normalization of the expansion vector field (Mantovi, J Econ 110(1): 83–105, 2013) which results in the fundamental (expansion-) symmetry vector field. Finally, a characterization of symmetry vector fields is given in terms of their action on the distance function, and a pattern of complete response is discussed for additive preferences. Examples of such constructions are explicitly worked out. Potential implications of the results are discussed. Keywords: Utility function; Symmetry; Separability; Vector field; Expansion path; Distance function (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:kap:jeczfn:v:119:y:2016:i:2:d:10.1007_s00712-016-0475-7 DOI: 10.1007/s00712-016-0475-7 Access Statistics for this article Journal of Economics is currently edited by Giacomo Corneo More articles in Journal of Economics from Springer |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.