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Convex preferences
 
 
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In economics
Economics

File:Ballard Farmers' Market - vegetables.jpgEconomics is the Social sciences that studies the Production theory basics, Distribution , and Consumption of Good and Service ....
, convex preferences are a property of utility functions commonly represented in an indifference curve
Indifference curve

In microeconomic theory, an indifference curve is a graph of a function showing different bundles of good , each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another....
 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
Marginal utility

In economics, the marginal utility of a Good or of a Service is the utility of the specific use to which an agent would put a given increase in that good or service, or of the specific use that would be abandoned in response to a given decrease....
 but uses modern theory to represent the concept.

Comparable to the greater-than-or-equal-to ordering
Order theory

Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another....
 relation for real numbers, the notation below can be translated as: 'is at least as good as' (in preference
Preference

Preference is a concept, used in the social sciences, particularly economics. It assumes a real or imagined "choice" between alternatives and the possibility of rank ordering of these alternatives, based on happiness, satisfaction, gratification, enjoyment, utility they provide....
 satisfaction).






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In economics
Economics

File:Ballard Farmers' Market - vegetables.jpgEconomics is the Social sciences that studies the Production theory basics, Distribution , and Consumption of Good and Service ....
, convex preferences are a property of utility functions commonly represented in an indifference curve
Indifference curve

In microeconomic theory, an indifference curve is a graph of a function showing different bundles of good , each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another....
 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
Marginal utility

In economics, the marginal utility of a Good or of a Service is the utility of the specific use to which an agent would put a given increase in that good or service, or of the specific use that would be abandoned in response to a given decrease....
 but uses modern theory to represent the concept.

Comparable to the greater-than-or-equal-to ordering
Order theory

Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another....
 relation for real numbers, the notation below can be translated as: 'is at least as good as' (in preference
Preference

Preference is a concept, used in the social sciences, particularly economics. It assumes a real or imagined "choice" between alternatives and the possibility of rank ordering of these alternatives, based on happiness, satisfaction, gratification, enjoyment, utility they provide....
 satisfaction). Formally, if is a preference relation on the consumption set X, then is convex
Convex set

In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object....
 if for any where and , then it is the case that for any .

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 (agents express a basic inclination for diversification).

See also

  • Convex function
    Convex function

    In mathematics, a real-valued function f defined on an interval is called convex, concave upwards, concave up or convex cup, if for any two points x and y in its domain C and any t in [0,1], we have...