Macroeconomics Exam Review 242

Macroeconomics Exam Review 242 - 5.39 Assume x ∈ ( x ∗...

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Unformatted text preview: 5.39 Assume x ∈ ( x ∗ ). That is, there exists ¯ such that x ∗ + x ∈ for every ∈ [0 , ¯ ]. For = 1 , 2 ,... , let = ¯ / . Then x = x ∗ + x ∈ , x → x ∗ and ( x − x ∗ ) / = ( x ∗ + x − x ∗ ) / = x . Therefore, x ∈ ( x ∗ ). 5.40 Let dx ∈ ( x ∗ ). Then there exists a feasible sequence { x } converging to x ∗ and a sequence { } of nonnegative scalars such that the sequence { ( x − x ∗ ) / } converges to dx . For any ∈ ( x ∗ ), ( x ∗ ) = 0 and ( x ) = [ x ∗ ]( x − x ∗ ) + ∪ ∪ x − x ∗ ∪ ∪ where → 0 as k → ∞ . This implies 1 ( x ) = 1 [ x ∗ ]( x − x ∗ ) + ∪ ∪ ( x − x ∗ ) / ∪ ∪ Since x is feasible...
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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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