E
CON
714: M
ACROECONOMIC
T
HEORY
II
TA: T
IM
L
EE
A
PRIL
9, 2010
Tax Announcements
(by Rody Manuelli)
Consider a simple
two planner
economy. The first planner picks taxes
(denoted by the flat tax rate
τ
) and makes transfers to the representative agent (denoted
v
). The second planner takes the tax rates and transfers
as given
. That is, even though
YOU
know the connection between tax rates and transfers, the second planner does not,
she takes the sequence of tax rates and transfers as given and beyond her control. The
problem she faces is
max
{
c
t
,
x
t
,
k
t
+
1
}
∞
t
=
0
∞
∑
t
=
0
β
t
u
(
c
t
)
subject to
c
t
+
x
t
≤
(
1

τ
t
)
f
(
k
t
) +
ν
t
,
k
t
+
1
≤
(
1

δ
)
k
t
+
x
t
,
k
0
≥
0
given,
(
c
t
,
x
t
,
k
t
+
1
)
≥
(
0, 0, 0
)
∀
t
≥
0.
Assume the functions
u
and
f
are nice and smooth.
1. Assume that 0
<
τ
t
=
τ
<
1 (constant tax rates), and that
v
t
=
τ
f
(
k
t
)
(remember
that we know this, but the second planner takes
v
t
as given at the time she maxi
mizes). Show that there exists a steady state, and that for any initial condition
k
0
>
0
the economy converges to the steady state.
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 Spring '08
 Staff
 Steady State, new steady state

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