NotesECN741-page58

NotesECN741-page58 - ECN 741: Public Economics Fall 2008 z...

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ECN 741: Public Economics Fall 2008 1 = E ± λ z t ,z t +1 )(1 - δ + F K ( K * t +1 z t ) ,Y * t z t ,z t +1 ) , ¯ z t ,z t +1 )) | ¯ z t ² Note that (using Jensen’s inequality) λ z t ,z t +1 ) = β u 0 ( c * t ( θ t , ¯ z t )) ³ E ´ 1 u 0 ( c * t +1 ( θ t +1 , ¯ z t ,z t +1 )) µ µ µ µ θ t +1 , ¯ z t ,z t +1 ¶· - 1 < β E ± u 0 ( c * t +1 ( θ t +1 , ¯ z t ,z t +1 )) µ µ θ t +1 , ¯ z t ,z t +1 ² u 0 ( c * t ( θ t , ¯ z t )) and therefore u 0 ( c * t ( θ t , ¯ z t )) < β E ± u 0 ( c * t +1 ( θ t +1 , ¯ z t ,z t +1 ))(1 - δ + F K ( K * t +1 z t ) ,Y * t z t ,z t +1 ) , ¯ z t ,z t +1 )) µ µ θ t +1 , ¯ z t ,z t +1 ² Example 1: suppose Θ is singleton. Then λ z t ,z t +1 ) = βu 0 ( c * t +1 z t ,z t +1 )) u 0 ( c * t z t )) and therefore 1 = E ´ βu 0 ( c * t +1 z t ,z t +1 )) u 0 ( c * t z t )) (1 - δ + F K ( K * t +1 z t ) ,Y * t z t ,z t +1 ) , ¯ z t ,z t +1 )) | ¯ z t Example 2: suppose Z is singleton. Then λ t +1 = β u 0 ( c * t ( θ t )) ³ E ´ 1 u 0 ( c * t +1 ( θ t +1 )) µ µ µ µ θ t +1 ¶· - 1 1 = λ t +1 (1 - δ + F K ( K * t +1 ,Y * t )) and therefore β (1 - δ + F K ( K * t +1 ,Y * t )) u 0 ( c * t ( θ t )) = E ´ 1 u 0 ( c * t +1 ( θ t +1 )) µ µ µ µ θ t +1 and therefore (using Jensen’s inequality)
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This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.

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