Macroeconomics Exam Review 62

Macroeconomics Exam Review 62 - 2.17 Assume x is optimal,...

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Unformatted text preview: 2.17 Assume x is optimal, so that ( x ∗ ) ≥ ( x ) for every x ∈ Γ( ) This implies (using (2.39)) ( , ∗ 1 ) + ( x ∗′ ) ≥ ( , 1 ) + ( x ′ ) where x ′ = ( 1 , 2 ,... ) is the continuation of the plan x starting at 1 and x ∗′ = ( ∗ 1 , ∗ 2 ,... ) is the continuation of the plan x ∗ . In particular, this is true for every plan x ∈ Γ( ) with 1 = ∗ 1 and therefore ( , ∗ 1 ) + ( x ∗′ ) ≥ ( , ∗ 1 ) + ( x ′ ) for every x ′ ∈ Γ( ∗ 1 ) which implies that ( x ∗′ ) ≥ ( x ′ ) for every x ′ ∈ Γ( ∗ 1 ) That is, x ∗′ is optimal starting at ∗ 1 and therefore ( x ∗′ ) = ( ∗ 1 ) (Exercise 2.15). Consequently ( ) = ( x ∗ ) = ( , ∗ 1 ) + ( x ∗′ ) = ( , ∗ 1 ) + ( ∗ 1 ) This verifies (2.13) forThis verifies (2....
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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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