NotesECN741-page53

NotesECN741-page53 - ECN 741 Public Economics Fall 2008 FOC...

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ECN 741: Public Economics Fall 2008 FOC w.r.t y ( w,θ ) - π θ H + π ˆ λ 1 v 0 ( y ( w,θ H )) - φ π θ H - μ θ H = 0 - (1 - π ) θ L + (1 - π ) ˆ λ 1 v 0 ( y ( w,θ L )) - φ (1 - π ) θ L + μ θ H = 0 combining these FOC’s together with envelope condition P 0 ( w ) = - φ we get E [1 - P 0 ( w 0 ( w,θ ))] = β ˆ β (1 - P 0 ( w )) + 1 - β ˆ β and ˆ λ E ± 1 v 0 ( y ( w,θ )) ² = (1 + φ ) E ± 1 θ ² = 1 + φ Assume that we know y ( w,θ H ) > y ( w,θ L ) and w 0 ( w,θ H ) > w 0 ( w,θ L ) . Now we can prove the next lemma. Lemma 3 The following inequalities hold (1 - P 0 ( w )) β ˆ β ³ 1 + θ H θ L - θ L ´ + 1 - β ˆ β 1 - P 0 ( w 0 ( w,θ )) (1 - P 0 ( w )) β ˆ β θ H + 1 - β ˆ β Proof. From the FOC for y ( w,θ H ) we get (1 +
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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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