Macroeconomics Exam Review 220

Macroeconomics Exam Review 220 - 4.70 For ⊆ ℜ ∇ = ′...

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Unformatted text preview: 4.70 For ⊆ ℜ , ∇ ( ) = ′ ( ) 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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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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