In
economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and intera ...
, 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
diminishing marginal utility
In economics, utility is the satisfaction or benefit derived by consuming a product. The marginal utility of a good or service describes how much pleasure or satisfaction is gained by consumers as a result of the increase or decrease in consumpti ...
without requiring
utility function
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...
s.
Notation
Comparable to the greater-than-or-equal-to
ordering
Order, ORDER or Orders may refer to:
* Categorization, the process in which ideas and objects are recognized, differentiated, and understood
* Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of d ...
relation
for real numbers, the notation
below can be translated as: 'is at least as good as' (in
preference
In psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are central to decision theo ...
satisfaction).
Similarly,
can be translated as 'is strictly better than' (in preference satisfaction), and Similarly,
can be translated as 'is equivalent to' (in preference satisfaction).
Definition
Use ''x'', ''y'', and ''z'' to denote three consumption bundles (combinations of various quantities of various goods). Formally, a preference relation
on the
consumption set
The theory of consumer choice is the branch of microeconomics that relates Preference (economics), preferences to consumption expenditures and to supply and demand, consumer demand curves. It analyzes how consumers maximize the desirability of t ...
''X'' is called convex if whenever
:
where
and
,
then for every