Convex preferences: Difference between revisions

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In [[economics]], '''convex preferences''' are a property of [[utility function]]s commonly represented in an [[indifference curve]] as a ''bulge toward'' the origin for normal goods. (A concave utility function appears to ''bulge away'' from the origin instead.) It roughly corresponds to [[marginal utility#The “law” of diminishing marginal utility|the "law" of diminishing marginal utility]] but uses modern theory to represent the concept.

Comparable to the greater-than-or-equal-to [[Order theory#Partially ordered sets|ordering]] relation <math>\geq</math> for real numbers, the notation <math>\succeq</math> below can be translated as: 'is at least as good as' (in [[preference]] satisfaction). Formally, if <math>\succeq</math> is a preference relation on the [[consumption set]] X, then <math>\succeq</math> is [[Convex set|convex]] if for any <math>x, y, z \in X</math> where <math>y \succeq x </math> and <math>z \succeq x </math>, then it is the case that <math>\theta y + (1-\theta) z \succeq x </math> for any <math> \theta \in [0,1] </math>.