07 Jun Homework # 2 Dirk Krueger 1 The Deterministic Neoclassical Growth Model: Theory and Computation
Question
Homework # 2
Dirk Krueger
1
The Deterministic Neoclassical Growth Model:
Theory and Computation
Consider the social planner problem associated with the neoclassical growth
model
max 1
t
ln(ct )
sh is
ar stu
ed d
vi y re
aC s
ou
ou rc
rs e
eH w
er as
o.
co
m
fct ;kt+1 gt=0
1
X
s.t.
ct + kt+1
t=0
Akt
ct ; kt+1
0
k0 given
1. Write down the Euler conditions and the transversality condition for this
problem. Compute the steady state values of c and k:
2. Write down the functional equation associated with this problem. Guess
that the value function has the form
v(k) = a0 + a1 ln(k)
Calculate the value function (i.e. nd a0 ; a1 ) and the policy function.
3. Try to approximate v(k) : Guess that v0 (k) = 0 for all k and use the
iterative updating rule
vn+1 (k) =
max
0 k0 Ak
fln (Ak
k 0 ) + vn (k 0 )g
Th
Calculate analytically the functions v1 ; v2 ; v3 and compare your result with
2:
4. Let = 0:3; = 0:6 and A = 1. Let capital take values on the discrete
grid K = f0:04; 0:08; 0:12; 0:16; 0:2g: Make the original guess v0 (k) = 0 for
all k and perform the rst three steps of the value function iteration for
all k 2 K
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