偏好凸向原点的英文

偏好凸向原点的英文
## Convex Preferences and the Origin.
In economics, a preference relation is a binary
relation that represents an individual's preferences over a set of alternatives. A preference relation is said to be convex if it satisfies the following condition:
> For any three alternatives x, y, and z, if x is preferred to y and y is preferred to z, then x is preferred to any convex combination of y and z.
In other words, a preference relation is convex if, for any two alternatives x and y, the individual prefers any weighted average of x and y to any alternative that is not on the line segment connecting x and y.
Convex preferences have a number of important implications. First, they imply that the indifference curves of an individual are convex. An indifference curve
is a curve that represents all of the alternatives that an individual is indifferent between. If an individual's preferences are convex, then their indifference curves will be bowed outward, as in the following diagram:
[Image of a convex indifference curve]
Second, convex preferences imply that the demand curve of an individual is downward sloping. A demand curve is a curve that shows the relationship between the price of a good and the quantity of the good that an individual demands. If an individual's preferences are convex, then their demand curve will be downward sloping, as in the following diagram:
[Image of a downward sloping demand curve]
Third, convex preferences imply that the utility function of an individual is quasi-concave. A utility function is a function that represents an individual's preferences over a set of alternatives. If an individual's preferences are convex, then their utility function will be
quasi-concave, which means that the level sets of the
utility function will be convex.
Convex preferences are a common assumption in economic models. This is because convex preferences are consistent with a number of reasonable assumptions about human behavior. For example, convex preferences are consistent with the assumption that individuals are risk-averse.
## Applications of Convex Preferences.
Convex preferences have a number of applications in economics. For example, convex preferences can be used to explain why individuals demand more of a good when its price decreases. This is because, when the price of a good decreases, the individual can afford to purchase more of the good without giving up any other goods.
Convex preferences can also be used to explain why individuals are willing to pay more for a good when its quality increases. This is because, when the quality of a good increases, the individual's utility from consuming the
good increases.
Finally, convex preferences can be used to explain why individuals are more likely to choose a risky option when the expected value of the option is high. This is because, when the expected value of a risky option is high, the individual's expected utility from choosing the option is also high.
## Conclusion.
Convex preferences are a powerful tool for understanding human behavior. Convex preferences can be used to explain a wide range of economic phenomena, including the shape of indifference curves, the slope of demand curves, and the behavior of individuals under uncertainty.。