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Unformatted text preview: Chapter Four Utility 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

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