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NotesECN741-page18 - ECN 741 Public Economics Fall 2008...

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ECN 741: Public Economics Fall 2008 Define W ( c 1 , c 2 , l 1 , l 2 , λ 1 , λ 2 ) = U 1 ( c 1 , l 1 ) + λ i ( U i c c i + U i l l i ) First order conditions λβ t U 2 cct c 2 t + U 2 ct + φ t = 0 φ t = φ t +1 (1 - δ + F kt +1 ) in steady state φ t +1 = βφ t and therefore 1 = β (1 - δ + F kt +1 ) and again, tax of capital is zero in the steady state. Exercise: In the above set up we have implicitly assumed that government can levy different taxes on different consumer types. How would you add the following restrictions to the problem 1. Tax on capital income has to be uniform across different types. Does the result hold with this restriction? Under what assumptions? 2. Tax on labor income has to be uniform across different types. Does the result hold? Under what assumptions?
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