NotesECN741-page52

NotesECN741-page52 - and be multipliers on the IC and...

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ECN 741: Public Economics Fall 2008 Note that P m ( w ) is strictly concave, P m ( w ) P ( w ) . Also, note that only the first term depends on w . Therefore P 0 m ( w ) = 1 - ˆ λ E ± 1 v 0 ( v ( y ( w,θ 0 )) + w 0 - w ) ² and lim w →-∞ P 0 m ( w ) = 1 . Therefore, lim w →-∞ P 0 ( w ) lim w →-∞ P 0 m ( w ) = 1 . Hence, we proved that lim w →-∞ P 0 ( w ) = 1 . In the next lemma we show that 1 - P ( w 0 ( w,θ )) can be bounded above and bellow for all θ . Let’s rewrite the problem ( 51 ) again P ( w ) = max c,y,w 0 X θ π ( θ ) ± u ( c ( θ,w )) - v ( y ( θ,w )) θ - ˆ λc ( θ,w ) + ˆ λy ( θ,w ) + ˆ βP ( w 0 ( θ,w )) ² (52) sub. to u ( c ( θ,w )) - v ( y ( θ,w )) θ + βw 0 ( θ,w ) u ( c ( θ 0 ,w )) - v ( y ( θ 0 ,w )) θ + βw 0 ( θ 0 ,w ) θ,θ 0 X θ π ( θ ) ± u ( c ( θ,w )) - v ( y ( θ,w )) θ + βw 0 ( θ,w ) ² w Suppose only high type’s incentive constraint binds. Let
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Unformatted text preview: and be multipliers on the IC and promise keeping (and let ( H ) = ) FOC w.r.t c ( w, ) 1- 1 u ( c ( w, H )) + + = 0 (1- ) 1- 1 u ( c ( w, L )) + - = 0 FOC w.r.t w ( w, ) P ( w, H ) + + = 0 (1- ) P ( w, L ) + (1- ) - = 0 52...
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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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