Macroeconomics Exam Review 42

Macroeconomics Exam Review 42 - 1.207 The present value of...

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Unformatted text preview: 1.207 The present value of the payments is the th partial sum of the geometric series + + 2 + 3 + ... which (using (1.31)) is given by Present value = = − 1 − 1.208 By Exercise 1.93, there exists an open set ⊇ 1 such that ∩ 2 = ∅ . For every x ∈ 1 , there exists an open ball ( x ) such that ( x ) ⊆ and therefore ( x ) ∩ 2 = ∅ . The collection { ( x ) } of open balls is an open cover for 1 . Since 1 is compact there exists a finite subcover, that is there exists points x 1 , x 2 ,..., x in 1 such that 1 ⊆ ∪ =1 ( x ) Furthermore, for every x , there exists such that ( x ) = x + where is the unit ball. Let = min . = is the required neighborhood....
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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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