Convex preferences

In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. Comparable to the greater-than-or-equal-to ordering relation for real numbers, the notation below can be translated as: 'is at least as good as' (in preference satisfaction). Similarly, can be translated as 'is strictly better than' (in preference satisfaction), and Similarly, can be translated as 'is equivalent to' (in preference satisfaction). Use x, y, and z to denote three consumption bundles (combinations of various quantities of various goods). Formally, a preference relation on the consumption set X is called convex if whenever where and , then for every : i.e., for any two bundles that are each viewed as being at least as good as a third bundle, a weighted average of the two bundles is viewed as being at least as good as the third bundle. A preference relation is called strictly convex if whenever where , , and , then for every : i.e., for any two distinct bundles that are each viewed as being at least as good as a third bundle, a weighted average of the two bundles (including a positive amount of each bundle) is viewed as being strictly better than the third bundle. Use x and y to denote two consumption bundles. A preference relation is called convex if for any where then for every : That is, if a bundle y is preferred over a bundle x, then any mix of y with x is still preferred over x. A preference relation is called strictly convex if whenever where , and , then for every : That is, for any two bundles that are viewed as being equivalent, a weighted average of the two bundles is better than each of these bundles.

If there is only a single commodity type, then any weakly-monotonically-increasing preference relation is convex. This is because, if , then every weighted average of y and ס is also .

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés (7)

Cours associés (4)

Séances de cours associées (25)

MGT-454: Principles of microeconomics

The course allows students to get familiarized with the basic tools and concepts of modern microeconomic analysis. Based on graphical reasoning and analytical calculus, it constantly links to real eco

FIN-406: Macrofinance

This course provides students with a working knowledge of macroeconomic models that explicitly incorporate financial markets. The goal is to develop a broad and analytical framework for analyzing the

MGT-301: Foundations in financial economics

The aim of this course is to expose EPFL bachelor students to some of the main areas in financial economics. The course will be organized around six themes. Students will obtain both practical insight

Modélisation de choix MOOC: Introduction to Discrete Choice Models

Explore comment la modélisation des choix prédit le comportement humain et quantifie les préférences dans divers scénarios.

Rôle de l'État dans l'économie de marché MGT-454: Principles of microeconomics

Explore le rôle de l'État dans l'économie de marché, l'allocation des ressources, la redistribution des revenus et l'optimisation des consommateurs.

Théorie microéconomique des consommateurs MOOC: Introduction to Discrete Choice Models

Couvre les modèles de choix, les faisceaux de consommation, les contraintes budgétaires et les fonctions de la demande dans la théorie microéconomique des consommateurs.

In economics and other social sciences, preference refers to the order in which an agent ranks alternatives based on their relative utility. The process results in an "optimal choice" (whether real or theoretical). Preferences are evaluations and concern matter of value, typically in relation to practical reasoning. An individual's preferences are determined purely by a person's tastes as opposed to the good's prices, personal income, and the availability of goods. However, people are still expected to act in their best (rational) interest.

In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask how much better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility. For example, suppose George tells us that "I prefer A to B and B to C".