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Unformatted text preview: Chapter Four Utility 效效 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 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”). ~ 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 U ≡ 6 U ≡ 4 (2,3) (2,2) ∼ (4,1) x 1 x 2 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 ◆ 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 ....
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 Spring '11
 Luyu
 Utility, Utility Functions

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