Aubhik Khan
8 October 2010
Economics 806
Assignment 3
1. Do exercise 3.6 (b) in Stokey and Lucas.
1. Do exercise 3.8 in Stokey and Lucas.
2. Do exercise 3.13 (a) and 3.13 (b) in Stokey and Lucas.
3. Solve the following version of the one-sector growth mod
HW 5
1 (a) Planners Problem:
, nt
cfw_ct , kt+1
t=0
= arg max
X
t u(ct , 1 nt )
t=0
subject to
ct + kt+1 (1 )kt + Akt nt1
nt [0, 1]
ct > 0
k0 given
Taking first order conditions w.r.t.
ct : D1 u(ct , 1 nt ) = t
1 1
kt+1 : t = [Akt+1
nt+1 + (1 )]t+1
nt :
HW 4
1 (a) A date-0 competitive equilibrium is a sequence of prices cfw_pt , rt , wt
t=0 and quantities
cfw_ct , c0,t , c1,t , kt+1 , k0,t+1 , k1,t+1 , nt , n0,t , n1,t t=0 such that
(1) Households maximize utility:
For h = 0, 1,
cfw_ch,t , nh,t , k
HW1
Stokey & Lucas Problems
2.1 The fact that f : R+ R+ is continuously differentiable, strictly increasing and strictly concave
comes directly from the definition of f as
f (k) = F (k, 1) + (1 )k
with 0 < 1, and F satisfying the properties mentioned abov
Economics 806
HW 6
1 (a) Define the following notation, ci0 is the date-0 consumption of household i, i = 1, 2, and
ci1 (zj ) is its consumption in date-1 when the aggregate state is zj , j = 1, 2. Let bi define the
bond-purchases of household i in period
Aubhik Khan
30 September 2010
Economics 806
Assignment 2
1. Do exercise 2.3 in Stokey and Lucas.
2. (The method of successive approximations). Consider the sequence problem.
V (k0 ) =
max
fct ;kt+1 g1
t=0
ct ; kt+1
t
log (c)
(1)
t=0
subject to
ct + kt+1
1
HW2
Stokey & Lucas Problem
2.3 (a) We can write the value function using the optimal path for capital given by (8) as
X
v(k0 ) =
t log(kt kt )
t=0
X
log(1 )
+
t log kt
=
(1 )
t=0
The optimal policy function, written as a function of the initial capital
Aubhik Khan
Economics 806
9 November 2010
Assignment 5
1. Consider the neoclassical growth model without uncertainty but where the represetative
household values leisure. Production is Cobb-Douglas in capital and labour, with yt =
Akt n1t
and capital evol
Aubhik Khan
15 October 2010
Economics 806
Assignment 4
1. There are two types of households, in equal proportion, indexed as h = 0; 1. Households of
type 0 have a l > 0 units of time endowed in even periods, and no time endowment in odd periods. Household