Macroeconomics Exam Review 220

Macroeconomics Exam Review 220 - 4.70 For , ( ) = ( ) and...

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Unformatted text preview: 4.70 For , ( ) = ( ) and (4.32) becomes ( ( 2 ) ( 1 )( 2 1 ) for every 1 , 2 . This is equivalent to ( 2 )( 2 1 ) ( 1 )( 2 1 )0 or 2 > 1 = ( 2 ) ( 1 ) is strictly convex if and only if the inequalities are strict. 4.71 is increasing if and only if = 0 (Exercise 4.35). is strictly increasing if = > 0 (Exercise 4.36). 4.72 Adapting the previous example ( ) = ( 1) 2 = = 0 if = 1 i f = 2 , 4 , 6 , indeterminate otherwise Therefore, the power function is convex if is even, and neither convex if 3 is odd....
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