Various Convexities and Some Relevant Properties of Consumer Preference Relations
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. Howeve...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-12-01
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| Series: | Studia Universitatis Vasile Goldis Arad, Seria Stiinte Economice |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/sues-2023-0021 |
| _version_ | 1797660972212551680 |
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| author | Forrest Jeffrey Yi-Lin Tiglioglu Tufan Liu Yong Mong Donald Cardin Marta |
| author_facet | Forrest Jeffrey Yi-Lin Tiglioglu Tufan Liu Yong Mong Donald Cardin Marta |
| author_sort | Forrest Jeffrey Yi-Lin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T18:37:43Z |
| format | Article |
| id | doaj.art-45fd1440a8114efaa1f219d58860506f |
| institution | Directory Open Access Journal |
| issn | 2285-3065 |
| language | English |
| last_indexed | 2024-03-11T18:37:43Z |
| publishDate | 2023-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Studia Universitatis Vasile Goldis Arad, Seria Stiinte Economice |
| spelling | doaj.art-45fd1440a8114efaa1f219d58860506f2023-10-12T14:09:07ZengSciendoStudia Universitatis Vasile Goldis Arad, Seria Stiinte Economice2285-30652023-12-0133414516810.2478/sues-2023-0021Various Convexities and Some Relevant Properties of Consumer Preference RelationsForrest Jeffrey Yi-Lin0Tiglioglu Tufan1Liu Yong2Mong Donald3Cardin Marta41Slippery Rock University, Slippery Rock, USA2Alvernia University, Reading, USA3Jiangnan University, Wuxi, China4Slippery Rock University, Slippery Rock, USA5Ca’ Foscari University of Venice, Venezia, ItalyThe 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.https://doi.org/10.2478/sues-2023-0021additive conservationconvex spaceeuclidean spacehalf-spacepositive multiplicativitypossible consumptionpreorderutility functiond11 |
| spellingShingle | Forrest Jeffrey Yi-Lin Tiglioglu Tufan Liu Yong Mong Donald Cardin Marta Various Convexities and Some Relevant Properties of Consumer Preference Relations Studia Universitatis Vasile Goldis Arad, Seria Stiinte Economice additive conservation convex space euclidean space half-space positive multiplicativity possible consumption preorder utility function d11 |
| title | Various Convexities and Some Relevant Properties of Consumer Preference Relations |
| title_full | Various Convexities and Some Relevant Properties of Consumer Preference Relations |
| title_fullStr | Various Convexities and Some Relevant Properties of Consumer Preference Relations |
| title_full_unstemmed | Various Convexities and Some Relevant Properties of Consumer Preference Relations |
| title_short | Various Convexities and Some Relevant Properties of Consumer Preference Relations |
| title_sort | various convexities and some relevant properties of consumer preference relations |
| topic | additive conservation convex space euclidean space half-space positive multiplicativity possible consumption preorder utility function d11 |
| url | https://doi.org/10.2478/sues-2023-0021 |
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