Macroeconomics Exam Review 49

Macroeconomics Exam Review 49 - 5. We have shown that conv...

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Unformatted text preview: 5. We have shown that conv conv , that is conv is closed. 6. conv is a closed and bounded subset of a finite dimensional space, and hence conv is compact (Proposition 1.4 and Exercise 1.215). 1.226 1. is bounded. Therefore, there exists some such that x = max < for every x . That is so that x = { x = ( 1 , 2 ,... , ) : for every } Therefore . 2. Exercise 1.177. 3. is the convex hull of a finite set and hence is compact (Exercise 1.225) 4. is a closed subset of a compact set and hence is compact (Exercise 1.110). 1.227 A polytope is the convex hull of a finite set. Any finite set is compact. 1.228 The unit simplex 1 in is the convex hull of the unit vectors e 1 , e 2 ,..., e , that is 1 = conv { e 1 , e 2 ,..., e } = { ( 1...
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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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