Macroeconomics Exam Review 76

Macroeconomics Exam Review 76 - 2.78 Choose any and...

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Unformatted text preview: 2.78 Choose any and > 0. Since is continuous, there exists 1 such that ( , ) < 1 = ( ) ( ) < / 2 Similarly, there exists 2 such that ( , ) < 2 = ( ) ( ) < / 2 Let = min { 1 , 2 } . Then, provided ( , ) < ( + )( ) ( + )( ) = ( ) + ( ) ( ) ( ) ( ) ( ) + ( ) ( ) < This establishes + is continuous at . Since was arbitrary, + is continuous for every . The continuity of is shown similarly. 2.79 Choose any . Given 0 < 1, there exists > 0 such that ( ) ( ) < and ( ) ( ) < whenever ( ,...
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