NotesECN741-page24

NotesECN741-page24 - ECN 741 Public Economics Fall 2008 C(st K(st g(st = F(K(st1 L(st st t(1)K(st1 Make our usual change of variable i i U i(hi(C L

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ECN 741: Public Economics Fall 2008 C ( s t ) + K ( s t ) + g ( s t ) = F ( K ( s t - 1 ) ,L ( s t ) ,s t ,t ) + (1 - δ ) K ( s t - 1 ) Make our usual change of variable W ( C,L ; ϕ,μ,λ ) X i π i ( λ i U i ( h i ( C,L ; ϕ )) + μ i ± U m C ( C,L ; ϕ ) h i c ( C,L ; ϕ ) + U m L ( C,L ; ϕ ) h i y ( C,L ; ϕ ) ² and rewrite the problem as max X t,s t ,i λ i π i β t Pr ( s t ) W ( C ( s t ) ,L ( s t ); ϕ,μ,λ ) - U i c ( C ( s 0 ) ,L ( s 0 ); ϕ ) X i π i μ i ± R 0 k i 0 - T ² sub. to C ( s t ) + K ( s t ) + g ( s t ) = F ( K ( s t - 1 ) ,L ( s t ) ,s t ,t ) + (1 - δ ) K ( s t - 1 ) First order conditions are F L ( K ( s t - 1 ) ,L ( s t ) ,s t ,t ) = - W C ( C ( s t ) ,L ( s t ); ϕ,μ,λ ) W L ( C ( s t ) ,L ( s t ); ϕ,μ,λ ) W C ( C ( s t ) ,L ( s t ); ϕ,μ,λ ) = β X s t +1 | s t W C ( C ( s t +1 ) ,L ( s t +1 ); ϕ,μ,λ ) R * ( s t +1 ) Pr ( s t +1 ) in which R * ( s t +1 ) = 1 + δ + F K ( K ( s t ) ,L ( s t +1 ) ,s t +1 ,t + 1) . FOC with respect to tax on initial capital X i μ i
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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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