NotesECN741-page37

NotesECN741-page37 - L ) H = First, note that there is no...

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ECN 741: Public Economics Fall 2008 Consider a relaxed planning problem with only type H ’s I.C. constraint max π ( θ H ) ± u ( c ( θ H )) - v ² y ( θ H ) θ H ³´ + π ( θ L ) ± u ( c ( θ L )) - v ² y ( θ L ) θ L ³´ sub. to. u ( c ( θ H )) - v ² y ( θ H ) θ H ³ u ( c ( θ L )) - v ² y ( θ L ) θ H ³ ; π ( θ H ) μ π ( θ H )[ c ( θ H ) - y ( θ H )] + π ( θ H )[ c ( θ H ) - y ( θ H )] = 0 ; λ we will characterize the solution to this problem and then we will verify that at the solution the I.C. constraint of type L is slack. (1 + μ ) u 0 ( c ( θ H )) = λ ² 1 - μ π ( θ H ) π ( θ L ) ³ u 0 ( c ( θ L )) = λ (1 + μ ) 1 θ H v 0 ² y ( θ H ) θ H ³ = λ 1 θ L v 0 ² y ( θ L ) θ L ³ - μ π ( θ H ) π ( θ L ) 1 θ H v 0 ² y ( θ
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Unformatted text preview: L ) H = First, note that there is no distortion for type H u ( c ( H )) = 1 H v y ( H ) H Also, observe that c ( H ) > c ( L ) note that incentive compatibility implies v y ( H ) H -v y ( L ) H = u ( c ( H ))-u ( c ( L )) > and therefore y ( H ) > y ( L ) 37...
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