Macroeconomics Exam Review 167

# Macroeconomics Exam Review 167 - Now 1 since ( x 1 ) = ( x...

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Unformatted text preview: Now 1 since ( x 1 ) = ( x 2 ). To show that 1 is a face of , assume that x +(1 ) y 1 for some x , y . Then = ( x + (1 ) y ) = ( x ) + (1 ) ( y ) = . Since x , y , this implies that ( x ) = ( y ) = so that x , y 1 . Therefore 1 is a face. We have shown that, if contains two distinct elements, there exists a smaller face 1 , contradicting the minimality of . We conclude that comprises a single element x . 3. = { x } which is an extreme point of . 3.208 Let = ( ) be a supporting hyperplane to . Without loss of generality assume ( x ) for every x (3.62) and there exists some x such that ( x ) = That is is maximized at 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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