Various Convexities and Some Relevant Properties of Consumer Preference Relations

Forrest Jeffrey Yi-Lin (), Tiglioglu Tufan (), Liu Yong (), Mong Donald () and Marta Cardin
Additional contact information
Forrest Jeffrey Yi-Lin: Slippery Rock University, Slippery Rock, USA
Tiglioglu Tufan: Alvernia University, Reading, USA
Liu Yong: Jiangnan University, Wuxi, China
Mong Donald: Slippery Rock University, Slippery Rock, USA

Studia Universitatis „Vasile Goldis” Arad – Economics Series, 2023, vol. 33, issue 4, 145-168

Abstract: The concept of convexity plays an important role in the study of economics and consumer theory. For the most part, such studies have been conducted on the assumption that consumer preferences are a binary relation that is complete, reflexive and transitive on the set X of consumption choices. However, each consumer is a biological being with multidimensional physiological needs so that possible consumptions from different dimensions cannot be compared by using preferences. By removing that unrealistic assumption, this paper examines how the various concepts of convex preferences and relevant properties can be re-established. We derive a series of 10 formal propositions and construct 6 examples to show that (a) a weighted combination of two possible consumptions is not necessarily comparable with any of the consumptions; (b) not every convergent sequence of a consumer’s preferred consumptions asymptotically preserves that consumer’s preference preordering; (c) not all preferences satisfy either positive multiplicativity or additive conservation; (d) three types of preference convexities – weak convexity, convexity and strong convexity – can all be introduced into general convex spaces. This paper concludes with some research topics of expected significance for future works.

Keywords: additive conservation; convex space; Euclidean space; half-space; positive multiplicativity; possible consumption; preorder; utility function (search for similar items in EconPapers)
JEL-codes: D11 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.2478/sues-2023-0021 (text/html)

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:vrs:suvges:v:33:y:2023:i:4:p:145-168:n:4

DOI: 10.2478/sues-2023-0021

Access Statistics for this article

Studia Universitatis „Vasile Goldis” Arad – Economics Series is currently edited by Florin Cornel Dumiter

More articles in Studia Universitatis „Vasile Goldis” Arad – Economics Series from Sciendo
Bibliographic data for series maintained by Peter Golla ().