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Convex preferences
From Wikipedia, the free encyclopedia
Convex preferences refer to a property of utility functions commonly represented in an indifference curve as a bulge toward the origin. 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 
for real numbers, the notation 
below can be translated as: 'is as at least as good as' (in preference satisfaction). Formally, if is a preference relation on the consumption set X, then is convex if for any 
where 
and 
, then it is the case that 
for any ![\theta \in [0,1]](../../../math/4/7/a/47a3741e5d5e897fe367d00a31461023.png)
.
is strictly convex if for any where and , and 
then it is also true that 
for any 
. It can be translated as: 'is better than relation' (in preference satisfaction).
An indifference curve displaying convex preferences thus means that the agent prefers, in terms of consumption bundles, averages over extremes.
Mas-Colell, Andreu; Whinston, Michael; & Green, Jerry (1995). Microeconomic Theory. Oxford: Oxford University Press. ISBN 978-0-19-507340-9