W e e W e [ ] d ( ) + y + + < ( ) b a f f (a) ( a )
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F Z ( a ) F + Z ( a ) F + Z ( ( a ) ( a )) F +( ) ( a ) a ( ) ( a ) Z ( a ) > F Z ( a ) ( a )) F R ( + )( y + ) ( a ) F R F ( a ) ( ( a ) > ( ) ( ) ( ) ( ) ( ) F F
( ) ( ) ( ) ( ) ( ) ( ) We e d e W( e) ( ) ( ) Z ( a ) ( a ) F ( + )( + ) Z ( a ) F Z ( a ) F +( + d) + ( ) F p F +( + ) ( + ) + + ( + )+ Z ( a ) F
Z + ( ( a ) ( a )) F ( + )( + + + ) Z ( a ) F y
e d d (W e d ) W ( a ) ( a ) a ( a ) ( a + # + a # # p f (a) ( a ) (a + # + )
a a s a s a f ( s a ) f (s a ) r s f s a s r r s s a f p p (p ) 2 p ( p ) p ( p ) p ( p ) p p ( p ) p ( p ) p ( p ) p 6 4 p p p p p p 3 7 5 p p p p p
p p p p p p p p ( ) g g l + c + c c g c l b a ( )
( ) [ ]
τ Marginal ax rae T (y ax ) τ l y l y Taxable income y ax ( a ) ( a ) ( ) ( a ) ( a) ( a ) ( ( a )) e (g c ) c
y e g c (d W) (b l ) W W d b l
Fracion of Liquidiy Consrained Houseolds 1 9 8 7 6 5 4 3 2 1 2 4 6 Age 8 1
( a ) + ( ) ( a )
Cange in op 1% labor ax revenue (in %) 15 Presen Value Sor Run Long Run 1 5-5 -1.6.65.7.75.8.85.9.95 1 Top marginal ax rae + {z} ( ) {z }
s s
Y ( a ) ( a + Y ( a )) ( a ) Y ( a Y ) ( a ) Y Z Y ( a ) + F + m  + + Y  + + ( a ) + +
a
7 6 Aggregae Welfare -1% Earners Long-Run Welfare Welfare effecs 5 4 3 2 1.6.65.7.75.8.85 Top marginal ax rae.9.95
Upper bend-poin 11 1 9 8 7 6 5 4 3 2 1.4.5.6.7.8.9 Top marginal ax rae Boom marginal ax rae.15.1.5 -.5 -.1 -.15 -.2.4.5.6.7.8.9 Top marginal ax rae
Canges in % of iniial equilbrium value 1 5-5 -1-15 Capial Privae Asses Public Deb -2 2 4 6 8 Year of Transiion Canges in % of iniial equilbrium value 2-2 -4-6 -8-1 Labor Supply Consumpion Oupu -12 2 4 6 8 Year of Transiion In % of ime endowmen 35 3 25 2 15 1 5 Labor Hours (oal) Labor Hours (op 1 %) 2 4 6 8 Year of Transiion Ineres rae (in %) 5.5 5 4.5 4 3.5 Ineres rae Wage rae 3 2 4 6-6 8 Year of Transiion 4 2-2 -4 Wage rae (cange in %)
Canges in % of iniial equilbrium value 15 1 5-5 -1-15 Consumpion Tax -2 Earnings Tax Capial Income Tax Toal Revenue -25 2 4 6 8 Year of Transiion Gini Index 1.9.8.7.6.5 Labor Earnings Weal.4 2 4 6 8 Year of Transiion
Welfare Effec (CEV) 15 1 5-5 -1-15 Welfare Effec (CEV) 15 1 5 low skilled/low sock low skilled/ig sock ig skilled/low sock ig skilled/ig sock -2-25 curren (-1% earners) curren (1% earners) fuure -5 5 1 Coor Enry Year 2 4 6 8 1 12 Coor Enry Year
1 8 Iniial Seady Sae Final Seady Sae 1 8 Iniial Seady Sae Final Seady Sae Marginal ax rae 6 4 2 Average ax rae 6 4 2-2 2 4 6 8 1 Fracion of median income -2 2 4 6 8 1 Fracion of median income
Difference in marginal ax rae 6 5 4 3 2 1-1 low skilled/low sock -2 low skilled/ig sock ig skilled/low sock ig skilled/ig sock -3 2 4 6 8 Fracion of median income Difference in average ax rae 6 5 4 3 2 1-1 -2 low skilled/low sock low skilled/ig sock ig skilled/low sock ig skilled/ig sock -3 2 4 6 8 Fracion of median income Difference in marginal ax rae 6 5 4 3 2 1-1 low skilled/low sock -2 low skilled/ig sock ig skilled/low sock ig skilled/ig sock -3 2 4 6 8 Fracion of median income Difference in average ax rae 6 5 4 3 2 1-1 -2 low skilled/low sock low skilled/ig sock ig skilled/low sock ig skilled/ig sock -3 2 4 6 8 Fracion of median income
Mean Consumpion (w/o Top Socks) 1.9.8.7.6.5.4.3.2.1 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age Mean Labor Hours (w/o Top Socks).4.35.3.25.2.15.1.5 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age
Variance log(consumpion) (w/o Top Socks).7.6.5.4.3.2.1 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age Variance log(labor Hours) (w/o Top Socks).25.2.15.1.5 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age Mean Consumpion 1.9.8.7.6.5.4.3.2.1 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age Mean Labor Hours.4.35.3.25.2.15.1.5 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age Variance log(consumpion).7.6.5.4.3.2.1 Iniial Seady Sae Period 1 of Transiion Final Seady Sae Variance log(labor Hours).25.2.15.1.5 Iniial Seady Sae Period 1 of Transiion Final Seady Sae 2 3 4 5 6 Age 2 3 4 5 6 Age
Cange in op 1% labor ax revenue (in %) 15 1 5-5 -1-15 Presen Value Sor Run Long Run -2.2.3.4.5.6.7 Top marginal ax rae Welfare effecs.2 -.2 -.4 -.6 -.8 Aggregae Welfare - 1% Earners Long-run Welfare -1.2.3.4.5.6 Top marginal ax rae
3.5 3 Frisc elasiciy.25 Frisc elasiciy.6 (Bencmark) Frisc elasiciy 1.5 Aggregae Welfare 2.5 2 1.5 1.5.6.65.7.75.8.85 Top marginal ax rae.9.95 g g g g Cange in Top 1% Tax Revenue 8 6 4 2-2 γ 2 (Bencmark) γ 1 Aggregae Welfare 3 2 1-1 -2 γ 2 (Bencmark) γ 1-4.5.55.6.65.7.75.8.85.9.95 Top marginal ax rae -3.5.55.6.65.7.75.8.85.9.95 Top marginal ax rae g g
Cange in Top 1% Tax Revenue 8 7 6 5 4 3 2 1 Bencmark Permanen Higes Sock.5.55.6.65.7.75.8.85.9.95 Top marginal ax rae Aggregae Welfare 3 2.5 2 1.5 1.5 -.5-1 -1.5-2 Bencmark Permanen Higes Sock -2.5.5.55.6.65.7.75.8.85.9.95 Top marginal ax rae
( a ) s a + s a [ ] ( a ) s a + s a ( + ) ( + ) > + ( a ) ( + ) + ( a ) + ( a )
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l ( a ) ( a ) ( a ) + ( + ) ( a )+ + ( ( a ) )+ i ( ( a ) ) ( ) ( a ) ( a ) ( a ) [ ( a )] g ( a ) g a[ ( a )] + c + c + by + Â + by + Â p ( ) ( + a ) p ( ) ( + a ) n n o ( a ) ( a ) o ( a ) ( a ) n n o ( a ) ( a ) o ( a ) ( a ) ( a ) ( a ) ( a ) ( a ) ( a ) > g l + a c l ( a ) ( ( a ) ) ( ( a ) ) ( + ) ( ) + ( a ) ( ( a ) ) ( ( a ) ) [( g) ] ( g) [( + c) ] ( + c)
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