Macroeconomics Exam Review 227

Macroeconomics Exam Review 227 - 5.5 We apply the reasoning...

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Unformatted text preview: 5.5 We apply the reasoning of Example 5.5 to each component. Formally, for each , let be the projection of along the axis ( ) = ( 1 , 2 ,..., 1 , , +1 ,..., ) maximizes ( ) over + , for which it is necessary that ( ) ( ) = 0 Substituting ( ) = [ x ] yields [ x ] [ x ] = 0 5.6 By Taylors Theorem (Example 4.33) ( x + dx ) = ( x ) + ( x ) dx + 1 2 dx ( x ) dx + ( dx ) dx 2 with ( dx ) as dx . Given 1. ( x ) = and 2. ( x ) is negative definite and letting...
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