NotesECN741-page18

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

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Unformatted text preview: ECN 741: Public Economics Fall 2008 Define i W (c1 , c2 , l1 , l2 , λ1 , λ2 ) = U 1 (c1 , l1 ) + λi Uc ci + Uli li First order conditions 2 2 λβ t Ucct c2t + Uct + φt = 0 φt = φt+1 (1 − δ + Fkt+1 ) in steady state φt+1 = βφt and therefore 1 = β (1 − δ + Fkt+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? 3. Tax on capital income cannot be more than 100 percent. Does the result hold? Under what assumptions? Dividend Taxes?!!! (an interesting example) Suppose we write the environment as in McGrattan and Prescott (2005) with corporate taxes and dividend taxes. Consumers can trade share of corporations, st , at price vt . Let dt be dividend and τdt be dividend tax. Consumers solve ∞ β t U (ct , lt ) max ct ,st+1 ,lt subject to ∞ t=0 ∞ pt [ct + vt (st+1 − st )] ≤ t=0 pt [(1 − τdt )dt st + (1 − τlt )wt lt ] t=0 s0 = 1 18 ...
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