NotesECN741-page54

NotesECN741-page54 - ECN 741: Public Economics Fall 2008...

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ECN 741: Public Economics Fall 2008 after rearranging terms 1 - P 0 ( w 0 ( w,θ L )) < 1 - P 0 ( w 0 ( w,θ H )) (1 - P 0 ( w )) β ˆ β θ H + 1 - β ˆ β Using similar argument we can show that μ 1 - π (1 + φ )(1 - θ L ) θ H θ L and P 0 ( w 0 ( w,θ L ) ≤ - φ β ˆ β ± 1 + θ H θ L - θ L ² + β ˆ β ± θ H θ L - θ L ² = P 0 ( w ) β ˆ β ± 1 + θ H θ L - θ L ² + β ˆ β ± θ H θ L - θ L ² and hence 1 - P 0 ( w 0 ( w,θ H )) > 1 - P 0 ( w 0 ( w,θ L )) (1 - P 0 ( w )) β ˆ β ± 1 + θ H θ L - θ L ² + 1 - β ˆ β Now let w → -∞ , then P 0 ( w ) 1 and lim w →-∞ P 0 ( w 0 ( w,θ )) = β ˆ β < 1 So w 0 ( w,θ ) can never stay at misery level. For more detailed arguments and complete proof of the existence of stationary distribution see Farhi and Werning
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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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