Capital Gains Taxation under Different Tax Regimes

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arqus

Arbeitskreis Quantitative Steuerlehre

www.arqus.info

Diskussionsbeitrag Nr. 6 Caren Sureth / Dirk Langeleh

Capital Gains Taxation under Different Tax Regimes

September 2005

arqus Diskussionsbeiträge zur Quantitativen Steuerlehre arqus Discussion Papers on Quantitative Tax Research

ISSN 1861-8944

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Capital Gains Taxation under Different Tax Regimes

arqus

Arbeitskreis Quantitative Steuerlehre

www.arqus.info

Diskussionsbeitrag Nr. 6 Caren Sureth / Dirk Langeleh

Capital Gains Taxation under Different Tax Regimes

September 2005

arqus Diskussionsbeiträge zur Quantitativen Steuerlehre arqus Discussion Papers on Quantitative Tax Research

ISSN 1861-8944

∗

†

∗

†

1

2

3

4

5

6

I 0

t = 0

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γ

P t

t

0 ≤ γ ≤ 1

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= (1 + γi) D t .

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i

i

P 1 = iI 0 .

7

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t = 0

0 < t ≤ z

V z

t = z

V z

γ < 1

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∞

X

t=z+1

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= I 0 (1 + γi) z .

t = z

I 0

V 0 =

z

X

t=1

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T < ∞

i

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10

t = T

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T

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β

β ≤ 1

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= (1 + γi) D _t .

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P ₁ = iI ₀ .

i ⁱⁿ

i ^ex

V ₀

V _z

V _z

V _z =

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= I ₀ (1 + γi) ^z .

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D _t (1 + i) ⁻ ^t + V _z (1 + i) ⁻ ^z

= I ₀ .

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τ _c

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τ _B

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τ _g

0 ≤ τ _g < 1

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V _z ^τ =

(1 − ατ _c ) (1 − βτ ) D _t (1 + i _τ ) ⁻ ^(t ⁻ ^z) ,

D _t ^τ ^c = (1 − ατ _c ) D _t

= (1 − γ) (1 − ατ _c ) P _t

i _τ

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(1 − χατ _c ) i,

0 ≤ β ^F ≤ 1

β ^F = 0.5

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β ^F = 1

i _τ = (1 − τ) i.

R ^τ _t ^c = γ (1 − τ _c ) P _t

P _t+1 = P _t + i (1 − τ _c ) γP _t

= (1 + γi _τ _c ) P _t .

D _t+1 ^τ ^c = (1 + γi _τ _c ) D _t ^τ ^c .

γ < 1 ∧ γ < i _τ i τ c

V ₀ ^τ =

(1 − βτ ) D _t ^τ ^c (1 + i τ ) ⁻ ^t + V _z ^τ (1 + i τ ) ⁻ ^z − βτ g (V _z ^τ − I ₀ ) (1 + i τ ) ⁻ ^z

= I ₀ · (1 − βτ ) (1 − γ ) (1 − ατ _c )

(1 − τ) − γ (1 − τ _c ) 1 − βτ g · (1 + γi _τ _c ) ^z − ₍₁ − ⁽¹ βτ ⁻ )(1 ^τ) ⁻ − ^γ(1 γ)(1 ⁻ − ^τ ^c ατ ⁾ c )

(1 + i _τ ) ^z

= I ₀ · φ · 1 − βτ _g · (1 + γi _τ _c ) ^z − ¹ _φ (1 + i τ ) ^z

φ = (1 − βτ ) (1 − γ) (1 − ατ _c )

(1 − τ) − γ (1 − τ _c ) .

V ₀ ^τ T 1

β, β ^F = 1

V ₀ ^τ =

(1 − τ ) D _t (1 + i _τ ) ⁻ ^t + V _z ^τ (1 + i _τ ) ⁻ ^z

−τ g (V _z ^τ − I ₀ ) (1 + i τ ) ⁻ ^z

= I ₀ · ρ 1 − τ _g · (1 + γi _τ _c ) ^z − _ρ ¹ (1 + i _τ ) ^z

i τ < i τ _c

γ ≥ _i ⁱ ^τ

γ ≥ _i ⁱ ^τ

ρ = φ | α=0,β=1,β ^F =1 = (1 − τ ) (1 − γ)

(1 − τ ) − γ (1 − τ _c ) .

I ₀