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Unformatted text preview: 1.89 Assume is bounded, and let = ( ). Choose any . For all , ( , ) < + 1. Therefore, ( , + 1). is contained in the open ball ( , + 1). Conversely, assume is contained in the open ball ( ). Then for any , ( , ) ( , ) + ( , ) < 2 by the triangle inequality. Therefore ( ) < 2 and the set is bounded. 1.90 Let ( ). For every , ( , ) < and therefore ( , ) ( , ) + ( , ) < + = 2 so that 2 ( ). 1.91 Let y . For any > 0, let y = y be the production plan which is units less in every commodity. Then, for any y ( y ) ( y , y ) < for every and therefore...
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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.
- Fall '10