Macroeconomics Exam Review 83

Macroeconomics Exam Review 83 - 2. (a) Suppose that ( p , )...

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Unformatted text preview: 2. (a) Suppose that ( p , ) is not lhc. Then for every neighborhood of ( p , ), there exists ( p ′ , ′ ) ∈ such that ( p ′ , ′ ) ∩ = ∅ . In particular, for every open ball ( p , ), there exists a point ( p , ) ∈ ( p , ) such that ( p , ) ∩ = ∅ . (( p , )) is the required sequence. (b) By construction, ∥ p − p ∥ < 1 / → 0 which implies that → for every . Therefore (Exercise 1.202) ∑ ˜ → ∑ ˜ < and → and therefore there exists such that ∑ ˜ < which implies that ˜ x ∈ ( p , ) (c) Also by construction ( p , ) ∩ = ∅ which implies ( p , ) ⊆ and therefore ˜ x ∈ ( p , ) = ⇒ ˜ x / ∈...
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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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