2. Grundlagen der Steuerlehre - LMU

u(y) − u(y − T ) = ∆u absolut = const.
y T

u(y) − u(y − T )
u(y)
= ∆urelativ
u(y)
= const.
u ′ (y − T ) = const.

u(y) − u(y − T )
u(y)
= ∆urelativ
u(y)
= const.
u ′ (y − T ) = const.

u(y) − u(y − T )
u(y)
= ∆urelativ
u(y)
= const.
u ′ (y − T ) = const.

u(y) − u(y − T )
u(y)
= ∆urelativ
u(y)
= const.
u ′ (y − T ) = const.

→

T (y)
y
T (y)
t(y) =
y
T ′ dT (y)
(y) =
dy

T1(y) = ay
T ′ (y) = t(y) = a
T2(y) = ay − c 0 < a < 1 c > 0
T ′ (y) = a
t(y) = a − c
y

T1 T2

T(y)
0
T'(y)
t(y)
0
45 o
T1 T2
y
y

T (y) = max[a(y − c); 0]
a, c > 0 c

T (y) = max[a(y − c); 0]
a, c > 0 c

T (y) =
ay y > c
0 y ≤ c
a, c > 0

c

dt
dy =
⎧
⎨
⎩
< 0 regressiv
= 0 proportional
> 0 progressiv

t ′ (y) > 0 ⇔ yT ′ (y) − T (y)
y 2 > 0
⇔ T ′ (y) >
T (y)
y
= t(y)

T (y) = ty − b
T ′′ (y) > 0

T (y) = ty − b
T ′′ (y) > 0

T(y)
T(y 2)
(T(y 1)+T(y 2))/2
T((y 1+y2)/2)
T(y1)
y 1
(y1+y2)/2
y2
y

T ′′ (y)
t ′ (y)

α(y) = dT y
dy T =
α(y) = T ′ (y)
t(y) =
dT
T
dy
y
Grenzsteuerbelastung
Durchschnittssteuerbelast.
α(y) > ( T (y)/y

x(y) = y − T (y)
ρ(y) = dx y
dy x
ρ(y) < 1

x
L(0.3) = 0.1
y = y1, y2, ...
y1
y2 L1 > L2 i
◦
◦

T1(y)
T2(y)
T1 T2

Anteil am Gesamteinkommen
100%
L1
L2
100%
Anteil der
Einkommensbezieher

U0 < U1 < U2... U0 = 0
tj Uj < y < Uj+1
i−1
T (y) = ti(y − Ui) + tj(Uj+1 − Uj)
j=0

t2
t 1
t 0
U0
U 1
U2
T(y)
y

T ′′ (y) = const. ⇔ T (y) = ay 2 + by + c

http://upload.wikimedia.org/wikipedia/commons/c/cb/Historie_Einkommensteuer_D_Grenzsteuersatz.jpg

http://upload.wikimedia.org/wikipedia/commons/3/3e/Historie_Einkommensteuer_D_effektiver_Steuersatz.jpg

http://upload.wikimedia.org/wikipedia/commons/1/12/Historie_Steuers%C3%A4tze_ESt_USt_D.jpg

T (y2) − T (y1)
> 0 y2 = y1
y2 − y1
T (y2) − T (y1)
< 1 y2 = y1
y2 − y1

T (y2) − T (y1)
> 0 y2 = y1
y2 − y1
T (y2) − T (y1)
< 1 y2 = y1
y2 − y1

T (y2) − T (y1)
> 0 y2 = y1
y2 − y1
T (y2) − T (y1)
< 1 y2 = y1
y2 − y1

y1 y2

H(y1, y2) = T (y1 + y2)
I(y1, y2) = T (y1) + T (y2)
S(y1, y2) = 2T ((y1 + y2)/2)

E(y1, y2)
E(y1, y2) ≤ T (y1) + T (y2)
E(y1, y2) = T (y1) + T (y2)
E(y1, y2) = const.
y1, y2 y1 + y2 = const.

E(y1, y2)
T (y1) + T (y2)
⇒

⇒

⇒

(y1 + y2)/2
⇒

⇒
⇒

T(y)
T(y2)
(T(y 1)+T(y 2))/2
S(y 1,y 2)/2
T(y1)
y1
Δ/2
(y1+y2)/2
y2
y

y1 = ys − x y2 = ys + x
∆ = T (y1)+T (y2)−S(y1, y2) = T (y1)+T (y2)−2T (ys)
x
y1 < y2
d∆
dx = −T ′ (y1) + T ′ (y2) > 0

ys = 52.881
y1 + y2 = 105.762
T (y) = 0, 42y − 8.004
y1 = 0
y2 = 105.762
∆ = T (y2) − 2T (y2/2) =
= 0, 42y2 − 8.004 − 2(0, 42 y2
2
− 8.004) = 8.004

ys = 52.881
y1 + y2 = 105.762
T (y) = 0, 42y − 8.004
y1 = 0
y2 = 105.762
∆ = T (y2) − 2T (y2/2) =
= 0, 42y2 − 8.004 − 2(0, 42 y2
2
− 8.004) = 8.004

ys = 52.881
y1 + y2 = 105.762
T (y) = 0, 42y − 8.004
y1 = 0
y2 = 105.762
∆ = T (y2) − 2T (y2/2) =
= 0, 42y2 − 8.004 − 2(0, 42 y2
2
− 8.004) = 8.004