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Unformatted text preview: ECN 741: Public Economics Fall 2008 Deﬁne
W (c1 , c2 , l1 , l2 , λ1 , λ2 ) = U 1 (c1 , l1 ) + λi Uc ci + Uli li First order conditions
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
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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- Fall '10