Convex preferences

In economics, convex preferences refer to a property of an individual's ordering of various outcomes which roughly corresponds to the idea that "averages are better than the extremes". 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 $\geq$ for real numbers, the notation $\succeq$ below can be translated as: 'is at least as good as' (in preference satisfaction). Formally, if $\succeq$ is a preference relation on the consumption set X, then $\succeq$ is convex if for any

$x,y,z\in X$ where $y\succeq x$ and $z\succeq x$,

then it is the case that

$\theta y+(1-\theta )z\succeq x$ for any $\theta \in [0,1]$. $\succeq$

is strictly convex if for any

$x,y,z\in X$ where $y\succeq x$ and $z\succeq x$, and $y\neq z$

then it is also true that

$\theta y+(1-\theta )z\succ x$ for any $\theta \in (0,1)$.

It can be translated as: 'is better than relation' (in preference satisfaction).

A convex shaped 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).

References

• Hal R. Varian. Intermediate Microeconomics A Modern Approach. New York: W.W. Norton & Company. ISBN 0-393-92702-4
• Mas-Colell, Andreu; Whinston, Michael; & Green, Jerry (1995). Microeconomic Theory. Oxford: Oxford University Press. ISBN 978-0-19-507340-9

See also

• Convex function
• Shapley–Folkman lemma
• Wold, Herman O.