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Technical Results on Regular Preferences and Demand
| Content Provider | Semantic Scholar |
|---|---|
| Abstract | Preferences For the purposes of this note, a preference relation (or simply a preference) ≽ on a set X is a reflexive, total, transitive binary relation on X. Following Richter [3], I usually call this a regular preference. Mas-Colell, Whinston, and Green [2] call this a rational preference. There are times we wish to consider a weaker notion of preference that may be incomplete or non-transitive, but for now a preference is always reflexive, total, and transitive. 1 The binary relations ≻ and ∼ are the asymmetric and symmetric parts of ≽, defined by x ≻ y if x ≽ y and not y ≽ x and x ∼ y if x ≽ y &y ≽ x. The symmetric part ∼ of a preference relation is called the induced indifference relation, and is reflexive, transitive, and symmetric. That is, ∼ is an equivalence relation. The equivalence classes of ∼ are traditionally called indifference curves, even though in general they may not be " curves. " 2 The asymmetric part ≻ of ≽ is called the induced strict preference relation. It is transitive, irreflexive, and asymmetric. Recall that a function u : X → R is a utility for ≽ if x ≽ y ⇐⇒ u(x) ⩾ u(y). A preference relation ≽ on a set X has a satiation point x if x is a greatest element, that is, if x ≽ y for all y ∈ X. A preference relation is nonsatiated if it has no satiation point. That is, for every x there is some y ∈ X with y ≻ x. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://people.hss.caltech.edu/~kcb/Notes/Demand0-Preferences.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
