ECN/APEC 7240
Spring 2010
Homework 4
Due 2/24/10
1)
We augment the Consumption RBC Model with CobbDouglas production and
CRRA utility by including government spending financed by lumpsum taxes.
Let
T
t
be
the tax at
t
with
τ
t
= ln
T
t
=
τ
t
0
+
τ
t
1
.
We assume that
τ
t
0
=
τ
0
+
gt
and
τ
t
1
is an AR(1)
process such that
,
1
1
1
1
τ
ε
φτ
τ
+
+
+
=
t
t
t
where
φ
∈
(

1,1) and
ε
t
τ
is i.i.d and uncorrelated with
ε
t
a
.
ζ
=
T
0
/
Y
0
is exogenous.
a)
What are the Euler equation and budget constraint for this model?
b)
How do
C
0
/
Y
0
,
K
0
/
Y
0
, and
r
0
depend on the exogenous parameters of the model?
c)
Derive the loglinearized Euler equation and budget constraint assuming now that
c
t
1
=
η
ck
k
t
1
+
η
ca
a
t
1
+
η
c
τ
τ
t
1
and similarly for
k
t
+1
1
and
y
t
1
.
d)
Does the introduction of the lumpsum tax change the equation that determines
η
ck
?
What about the equations that determine
η
ca
,
η
kk
,
η
ka
,
η
yk
, or
η
ya
?
2)
Consider the following discretetime model.
A continuum of identical households
with unit measure maximize
,
)
exp(
1
0
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 Spring '10
 Kutler
 Microeconomics, Equations, Utility, Trigraph, Euler equation, exogenous parameters, loglinearized Euler equation

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