Macroeconomics Exam Review 28

Macroeconomics Exam Review 28 - 1.162 Let be a collection...

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Unformatted text preview: 1.162 Let be a collection of convex sets and let x , y belong to . for every , x , y and therefore x + (1 ) y for all 0 1 (since is convex). Therefore x + (1 ) y . 1.163 Fix some output . Assume that x 1 , x 2 ( ). This implies that both ( , x 1 ) and ( , x 2 ) belong to the production possibility set . If is convex ( , x 1 ) + (1 )( , x 2 ) = ( + (1 ) , x 1 + (1 ) x 2 ) = ( , x 1 + (1 ) x 2 ) for every [0 , 1]. This implies that x 1 + (1 ) x 2 ( ). Since the choice of was arbitrary, this implies that ( ) is convex for every . 1.164 Assume 1 and 2 are convex sets. Let = 1 + 2 . Suppose x , y belong to ....
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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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