Chapter Four Utility 效用
Chapter Four Utility 效用
What Do We do in This Chapter? We create a mathematical measure of preference in order to advance our analysIS
What Do We Do in This Chapter? We create a mathematical measure of preference in order to advance our analysis
Utility Functions A preference relation that is complete, reflexive, transitive can be represented by a utility function
Utility Functions A preference relation that is complete, reflexive, transitive can be represented by a utility function
Utility functions a utility function U(x represents a preference relation if and only if xxx〈U(x)>ux) Xx U(x)<U(x”) x~x〈Ux)=Ux”)
Utility Functions A utility function U(x) represents a preference relation if and only if: x’ x” U(x’) > U(x”) x’ x” U(x’) < U(x”) x’ ~ x” U(x’) = U(x”). ~ f p p
Utility Functions Utility is an ordinal(i.e. ordering) concept E.g. if U(x)=6 and Uly)=2 then bundle x is strictly preferred to bundle y. But x is not preferred three times as much as is y
Utility Functions Utility is an ordinal (i.e. ordering) concept. E.g. if U(x) = 6 and U(y) = 2 then bundle x is strictly preferred to bundle y. But x is not preferred three times as much as is y
Utility Functions Indiff Curves all bundles in an indifference curve have the same utility level U(x1, X2=Constant is the equation of an indifference curve
Utility Functions & Indiff. Curves All bundles in an indifference curve have the same utility level. U(x1, x2)=Constant is the equation of an indifference curve
Utility Functions Indiff Curves 2 (2,3)x(2,2)~(4,1) U≡6 2 4 X
Utility Functions & Indiff. Curves U 6 U 4 (2,3) (2,2) ~ (4,1) x1 x2 p
Utility functions Indiff Curves The collection of all indifference curves for a given preference relation is an indifference map An indifference map is equivalent to a utility function
Utility Functions & Indiff. Curves The collection of all indifference curves for a given preference relation is an indifference map. An indifference map is equivalent to a utility function
Utility Functions f U is a utility function that represents a preference relation and f is a strictly increasing function, then v=f(U)is also a utility function representing
Utility Functions If –U is a utility function that represents a preference relation and – f is a strictly increasing function, then V = f(U) is also a utility function representing . ~ f ~ f
Goods Bads and Neutrals a good is a commodity unit which increases utility (gives a more preferred bundle a bad is a commodity unit which decreases utility(gives a less preferred bundle) a neutral is a commodity unit which does not change utility (gives an equally preferred bundle
Goods, Bads and Neutrals A good is a commodity unit which increases utility (gives a more preferred bundle). A bad is a commodity unit which decreases utility (gives a less preferred bundle). A neutral is a commodity unit which does not change utility (gives an equally preferred bundle)