Convex preferences: Difference between revisions

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{{Short description|Concept in economics}}

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 [[marginal utility#Diminishing marginal utility|diminishing marginal utility]] without requiring [[utility function]]s.

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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". This implies that the consumer prefers a variety of goods to having more of a single good. The concept roughly corresponds to the concept of [[marginal utility#Diminishing marginal utility|diminishing marginal utility]] without requiring [[utility function]]s.

== Notation ==

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== Examples ==

1. If there is only a single commodity type, then any weakly-monotonically- increasing preference relation is convex. This is because, if <math>y \geq x </math>, then every weighted average of ''y'' and ''ס'' is also <math>\geq x </math>.

2. Consider an economy with two commodity types, 1 and 2. Consider a preference relation represented by the following [[Leontief utility function]]:

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A set of [[Convex function|convex]]-shaped [[indifference curve]]s displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a [[convex set]].

Convex preferences with their associated convex indifference mapping arise from [[Quasi-convex function|quasi-concave]] utility functions, although these are not necessary for the analysis of preferences. For example, Constant Elasticity of Substitution (CES) utility functions describe convex, homothetic preferences. CES preferences are self-dual and both primal and dual CES preferences yield systems of indifference curves that may exhibit any degree of convexity.<ref>{{Cite journal |last=Baltas |first=George |date=2001 |title=Utility-consistent Brand Demand Systems with Endogenous Category Consumption: Principles and Marketing Applications |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1540-5915.2001.tb00965.x |journal=Decision Sciences |language=en |volume=32 |issue=3 |pages=399–422 |doi=10.1111/j.1540-5915.2001.tb00965.x|url-access=subscription }}</ref>

== See also ==