Problem Set #1
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Due: February 2
1) Consider the optimal growth problem from class, with u (c) = ln (c) and n = 0, and compare
the following two situations. In the baseline case, the island
Problem Set #2
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Due: February 14
1) Consider the optimal growth problem with the CIES utility function
u (c) =
c1 1
1
and the Cobb-Douglas production function Y (t) = BK (t) N (t)1 , where
Practice Questions for Final Exam
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Second Exam from Fall 2004
Question I. (25 points) Consider the model of human capital. Output is produced according to
the production function Y = K (huL
Practice Questions for Midterm Exam
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Midterm Exam from Fall 2004
Part I. (45 points) Consider the Robinson Crusoe model. The harvest function is given by
Y (t) = F [K (t), N (t)] ,
where F
Solutions to Problem Set #2
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
1) Consider the optimal growth problem with the CIES utility function
c1 1
u (c) =
1
and the Cobb-Douglas production function Y (t) = BK (t) N (t)1 , where B >
Problem Set #3
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Due: February 23
1) Consider the following problem
max
cfw_c(t)
k (t)
k (0)
k (t)
c (t)
=
=
Z
0
c (t)1 1 (n)t
dt
e
1
subject to
F (k (t) , A (t) c (t) ( + n) k (t) ,
k0 ,
0
Problem Set #4
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
No Due Date
1) Consider the Ramsey model with productivity growth. Suppose the government imposes a
sales tax on rms: the representative rm must pay a fraction of its output
Problem Set #5
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Due: April 4
In this problem, you will examine the effect of aid for development when the differences between
economies are caused by differences in the efciency of the nanc
Problem Set #6
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Due: April 13
Consider the model of human capital. Output is produced according to the production function
Y = K (huL)1 , where 0 < < 1 and where u is the fraction of time t
Problem Set #7
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Due: April 27
Consider the Ak model, where there are externalities in production. As in class, the production
function of the representative rm is given by
Y = AK L1 K
1
,
w
Problem Set #8
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
No Due Date
Consider the Romer model, where output is produced using different types of capital according to
the production function
Z M (t)
1
Y (t) = AL (t)
Kj (t) dj.
0
Ho
Solutions to Problem Set #1
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
1) Consider the optimal growth problem from class, with u (c) = ln (c) and n = 0, and compare
the following two situations. In the baseline case, the island has
Solutions to Problem Set #3
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
1) Consider the following problem
max
cfw_c(t)
Z
0
c (t)1 1 (n)t
e
dt
1
subject to
(t) = F (k (t) , A (t) c (t) ( + n) k (t) ,
k
k (0) = k0 , and
k (t) , c (t)
Solutions to Problem Set #4
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Consider the Ramsey model with productivity growth. Suppose the government imposes a sales
tax on rms: the representative rm must pay a fraction of its output t
Solutions to Problem Set #5
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
In this problem, you will examine the effect of aid for development when the differences between
economies are due to differences in the efciency of the nancial
Solutions to Problem Set #6
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Consider the model of human capital. Output is produced according to the production function
Y = K (huL)1 , where 0 < < 1 and where u is the fraction of time th
Solutions to Problem Set #7
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Consider the Ak model, where there are externalities in production. As in class, the production
function of the representative rm is given by
Y = AK L1 K
1
,
wh
Solutions to Problem Set #8
Economic Growth
Spring 2005
Professor Todd Keister
keister@itam.mx
Consider the Romer model, where output is produced using different types of capital according to
the production function
Z M (t)
1
Y (t) = AL (t)
Kj (t) dj.
0
H