Homework 7
Jonathan Heathcote
due in class on Tuesday April 25th
1. Model
Consider the simple RBC model that we discussed in class. A representative agent /
social plannner solves the following problem:
max
{
c
t
}{
k
t
+1
}
E
0
∞
X
t
=0
β
t
c
t
1
−
γ
1
−
γ
subject to
c
t
+
k
t
+1
=
e
z
t
k
θ
t
+(1
−
δ
)
k
t
z
t
+1
=
ρz
t
+
ε
t
+1
,ε
t
+1
∼
N
(0
,σ
2
ε
)
where
{
c
t
,z
t
,k
t
}
are time
t
values of consumption, the technology shock and capital
respectively.
2. Exercise
1. Write down the set of Euler equations and other equations that characterize
equilibrium.
2. Compute the steady state of this economy and report it. Use the following
parameter values:
β
=0
.
99
,δ
=0
.
02
,θ
=0
.
3
,γ
=2
,ρ
=0
.
95
.
3. Linearize the system of equations by taking
f
rst order Taylor series approxima
tions to them around the steady state.
4. Solve the system of equations by following the steps outlined in class. Report:
(i) Eigenvectors and eigenvalues for your linearized system
(ii) A decision rule for the choice variable (
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 '05
 would
 Economics, Thermodynamics, Taylor Series, Jonathan Heathcote

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