Optimal Taxation with Commitment in In
f
nite Horizon Models
Draws on Atkeson, Chari, and Kehoe (1999, FRBMinn QR). See also p.478—
88 of LS.
1
First Best
•
Planner solves
max
{
c
t
,C
t
,k
t
+1
}
∞
t
=0
∞
X
t
=0
β
t
U
(
c
t
,C
t
)
subject to
c
t
+
g
+
k
t
+1
=
F
(
k
t
t
)+(1
−
δ
)
k
t
(1)
•
First order conditions
C
t
:
−
U
C,t
=
U
c,t
F
C,t
(2)
k
t
+1
:
U
c,t
=
βU
c,t
+1
[
F
k,t
+1
+1
−
δ
](
3
)
•
First best has no distortion to the MB of working
F
C,t
or saving
F
k,t
+1
+
1
−
δ
.
2
Statement of the Competitive Equilibrium Prob
lem
•
Govt expenditure
g
is
f
nanced through proportional taxes on income from
capital (rate
θ
t
)andlabor(rate
τ
t
).
•
The government’s intertemporal budget constraint is
∞
X
t
=0
p
t
g
=
∞
X
t
=0
p
t
(
τ
t
w
t
C
t
+
θ
t
(
r
t
−
δ
)
k
t
)(
4
)
•
HH problem
max
{
c
t
,C
t
,k
t
+1
}
∞
t
=0
∞
X
t
=0
β
t
U
(
c
t
t
)
subject to
∞
X
t
=0
p
t
(
c
t
+
k
t
+1
)=
∞
X
t
=0
p
t
((1
−
τ
t
)
w
t
C
t
+
R
kt
k
t
5
)
where
R
kt
=1+(1
−
θ
t
)(
r
t
−
δ
)and
p
0
=1
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document•
The
f
rst order conditions for a HH are
c
t
:
β
t
U
c,t
=
λp
t
(6)
C
t
:
−
β
t
U
C,t
=
λp
t
(1
−
τ
t
)
w
t
(7)
k
t
+1
:
p
t
=
R
k,t
+1
p
t
+1
(8)
where
λ
is the multiplier on (5).
•
The
f
rm’s problem is
max
k
t
,C
t
F
(
k
t
,C
t
)
−
r
t
k
t
−
w
t
C
t
•
The
f
rst order conditions for the
f
rm are:
r
t
=
F
k,t
(9)
w
t
=
F
C,t
(10)
•
Let
π
t
=(
τ
t
,θ
t
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 CORBAE
 Government, Steady State

Click to edit the document details