NotesECN741-page6

NotesECN741-page6 - 1 + i = U i U l F l F i in other words...

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ECN 741: Public Economics Fall 2008 1.2 Elasticities and optimal taxes Suppose n = 2 . Consider the following Ramsey problem max c 1 ,c 2 ,l U ( c 1 ,c 2 ,l ) subject to 1. Implementability constraint U 1 c 1 + U 2 c 2 + U l l = 0 (6) 2. Feasibility F ( c 1 + g 1 ,c 2 + g 2 ,l ) = 0 (7) Let λ and γ be multipliers on implementability constraint (equation ( 6 )) and feasibility (equation ( 7 )). First order conditions are U i + λ ( U i + U 1 i c 1 + U 2 i c 2 + U li l ) = γF i i = 1 , 2 U l + λ ( U l + U 1 l c 1 + U 2 l c 2 + U ll l ) = γF l We can write these equations as 1 + λ - λH l = γ F l U l in which, H i = - ( U 1 i c 1 + U 2 i c 2 + U li l ) U i and H l = - ( U 1 l c 1 + U 2 l c 2 + U ll l ) U l . Note that from individual problem we have
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Unformatted text preview: 1 + i = U i U l F l F i in other words the optimal wedge must satisfy 1 + i = 1 + -H l 1 + -H i There you go! If H i > H j , then it is optimal to tax good i more than good j . The problem is that, it is not very helpful. Unfortunately, without imposing assumption on U we cannot say much more. Next we consider some special (yet, interesting) cases. 6...
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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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