In economics, convex preferences are a property of utility functions 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 the "law" of diminishing marginal utility but uses modern theory to represent the concept. Comparable to the greater-than-or-equal-to ordering relation <math>\geq</math> for real numbers, the notation <math>\succeq</math> below can be translated as: 'is at least as good as' . Formally, if <math>\succeq</math> is a preference relation on the consumption set X, then <math>\succeq</math> is convex if for any <math>x, 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 + z \succeq x </math> for any <math> \theta \in [0,1] </math>.

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  • In economics, convex preferences are a property of utility functions 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 the "law" of diminishing marginal utility but uses modern theory to represent the concept. Comparable to the greater-than-or-equal-to ordering relation <math>\geq</math> for real numbers, the notation <math>\succeq</math> below can be translated as: 'is at least as good as' . Formally, if <math>\succeq</math> is a preference relation on the consumption set X, then <math>\succeq</math> is convex if for any <math>x, 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 + z \succeq x </math> for any <math> \theta \in [0,1] </math>. <math>\succeq</math> is strictly convex if for any <math>x, z \in X</math> where <math>y \succeq x </math> and <math>z \succeq x </math>, and <math> y \neq z</math> then it is also true that <math>\theta y + z \succ x </math> for any <math> \theta \in </math>. It can be translated as: 'is better than relation' . An indifference curve displaying convex preferences thus means that the agent prefers, in terms of consumption bundles, averages over extremes (agents express a basic inclination for diversification). (en)
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  • In economics, convex preferences are a property of utility functions 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 the "law" of diminishing marginal utility but uses modern theory to represent the concept. Comparable to the greater-than-or-equal-to ordering relation <math>\geq</math> for real numbers, the notation <math>\succeq</math> below can be translated as: 'is at least as good as' . Formally, if <math>\succeq</math> is a preference relation on the consumption set X, then <math>\succeq</math> is convex if for any <math>x, 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 + z \succeq x </math> for any <math> \theta \in [0,1] </math>. (en)
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  • Convex preferences (en)
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