NotesECN741-page46

NotesECN741-page46 - ECN 741 Public Economics Fall 2008 at...

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ECN 741: Public Economics Fall 2008 at w = w * t ( ¯ θ t ) (note: I imposed the βR = 1 assumption here) K ( w ) = min c,y,W X θ π ( θ )[ c ( θ,w ) - y ( θ,w ) + βK ( w 0 ( θ,w ))] sub. to u ( c ( θ,w )) - v ± y ( θ,w ) θ ² + βw 0 ( θ,w ) u ( c ( θ 0 ,w )) - v ± y ( θ 0 ,w ) θ ² + βw 0 ( θ 0 ,w ) θ,θ 0 X θ π ( θ ) ³ u ( c ( θ,w )) - v ± y ( θ,w ) θ ² + βw 0 ( θ,w ) ´ w The second constraint is called “promise keeping” constraint. Proposition 10 K ( w ) is strictly increasing and strictly convex (assumptions on v ( · ) is needed). Also. Let w and ¯ w be the lowest and highest possible values for promised utility. Then, lim w w K 0 ( w ) = 0 and lim w ¯ w K 0 ( w ) = lim w ¯ w K ( w ) = 0 . Let μ ( θ,θ 0 ) be multiplier on incentive constraint and φ the multiplier on promise keeping. First order condition with respect to c ( θ,U ) is u 0 ( c ( θ,w )) X θ 0 μ ( θ,θ 0 ) - X θ 0 μ ( θ 0 ) + π ( θ )
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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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