Macroeconomics Exam Review 67

Macroeconomics Exam Review 67 - (d) Suppose x z 1 x and x z...

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Unformatted text preview: (d) Suppose x z 1 x and x z 2 x with z 1 x = z 2 x . Then either z 1 x > z 2 x or z 1 x < z 2 x . Without loss of generality, assume z 2 x > z 1 x . Then monotonicity and transitivity imply x z 2 x z 1 x x which is a contradiction. Therefore z x is unique. Let x denote the scale of z x , that is z x = x 1 . For every x + , there is a unique z x x and the function : + given by ( x ) = x is well-defined. Moreover x 2 x 1 z x 2 z x 1 x 2 x 1 ( x 2 ) ( x 1 ) represents the preference order . 2.39 1. For every 1 , ( 1 , 2) ( 1 , 1) in the lexicographic order. If represents , is strictly increasing and therefore ( 1 , 2) > ( 1 , 1). There exists a rational number ( 1 ) such that ( 1 , 2) > ( 1 ) > ( 1 , 1)....
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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