10
Chapter 10
2 A model with land and energy. The production function in this case is
Y = BK T E L1 :
_
Since T is a constant and E=E
= sE; taking logs and derivatives yields
ln Y
gY
= ln B + ln K + ln T + ln E + (1 ) ln L
= gB + gK sE + (1 )n;
where gX d

and solving for r = p
r
= 1; 000;
p
i.e.; to explain a variation of 10 in TFP we would need a variation in
the degree of capital utilization of 1,000, which is obviously unrealistic.
(b) Once more, let us call the fraction of both human and physical
capit

8
Chapter 7
1. Cost-benet analysis.
(a) Firstly we calculate the present value of the stream of prots assuming that the project yields prots forever. Applying the formula for
the innite series of a decreasing geometrical progression
a1
S=
1
where a denote

14
From the Mankiw-Romer-Weil (1992) model, we have the production function:
Y = K H (AL)1 .
Divide both sides by AL to get
y
=
A
!
k
A
" !
h
A
"
.
Using the () to denote the ratio of a variable to A, this equation can be rewritten as
.
y = k h
Now turn t

1
Homework 1
1. In 1900 GDP per capita in Japan (measured in 2000 dollars) was $1,433.
In 2000 it was $26,375. Calculate the growth rate of income per capita
in Japan over this century. Now suppose that Japan grows at the same
rate for 21st century. What

aging of the population on income per capita by trying to increase
the labour force participation ratio or increasing the retirement age
which, hopefully, will have the eect of decreasing the dependency
ratio.
4. The growth rate of aggregate productivity

(Analytically, suppose that the natural rate of unemployment is
the steady state,
1
=
1
=
0
0
1 1
1
(1
1)
(1
)
and
The rst e ect would be
= (1
2)
1
(1
2)
1
0
0
1 1
1
(1
(1
but eventually output per capita equals
2
=
0
1 1
(1
Again you were not required to

3. Unemployment and growth. Consider how unemployment would affect the Solow growth model. Suppose that output is produced according
to the production function =
[(1
) ]1 , where
is the natural
rate of unemployment. There is no technological progress. Ass

(a) What is the relation between an increase in productivity and an increase in income per capita?
The natural log of income per capita equals
ln i = ln y + ln l ln d:
Taking its derivative with respect to time, we obtain its growth rate
i_
y_
l_ d_
= +

CS1010: Programming Methodology
http:/www.comp.nus.edu.sg/~cs1010/
What did we cover last week?
Part I
Introduction
Logging into the UNIX system (sunfire)
Problem solving process
Writing algorithms in pseudo-codes
Part II: Overview of C Programming
1. Gen

UNIVERSITY OF SASKATCHEWAN
ECON 414.3 (02)
Winter 2016
Lectures
Time: TTh 2:30-3:50
Room: Geol 265
Professor
Cristina Echevarria
O ce: 817 Arts
Phone: 966-5211
http:/homepage.usask.ca/~ece220/
Please, bookmark this page. All the relevant information will

(b) Let us start by calculating the marginal products:
MPK
=
MPE
=
MPL =
(K + (BE) ) 1 K 1 (AL)1
(K + (BE) ) 1 (BE)1 B(AL)1
(1 )(K + (BE) )= (AL) A
The shares then are
=
MPK K
(K + (BE) ) 1 K (AL)1
K
=
=
Y
K + (BE)
(K + (BE) ) (AL)1
E
=
MPE E
(K + (

Thus, if r = 0:04
=1
0:04 0:021
= 0:1364 = 13:64%
0:04 0:018
=1
0:08 0:021
= 0:0484 = 4:84%:
0:08 0:018
and if r = 0:08
5 Robustness of the growth-drag calculations.
(a) The share of capital is calculated as a residual; therefore,
= 1 0:6 0:05 0:05 = 0

where = B0 K01 R0 L
:
0
To maximize PDV in sE ;
s1
[r g + (sE + n)] sE
P DV
E
=
=0
2
s
[r g + (sE + n)]
which is the same as
s1
[r g + (sE + n)] sE
E
s1
E
=
[r g + (sE + n)]
[r g + (sE + n)]
0
= sE
= sE =
sE
1
(1 ) [r g + (sE + n)] = sE
(1 ) [r g + n] =

Substituting into 11
d0
:
(12)
r
Therefore, if the rates of return to capital r were equalized across
countries, the investment rate would only depend on n; i.e., dierences in I, the social infrastructure would not lead to dierences in
investment rates.

You just show in part c. that
is a constant. Therefore
=
is a constant and we know that
(
+
)
(
)
=0+0=0
(e) Wages exhibit sustained growth
You need to show that, in the
of the Solow model with technological progress, the rate of growth of is a constant.

3
Homework 3
1. We have seen in class Kaldors stylized facts of growth in developed countries. The Cobb-Douglas production function is used to replicate fact a.
In this exercise, you are asked to show that the steady state in the Solow
model with technolo

15
Finally, we can write the equation in terms of output per worker as
y (t) =
!"
sK
n+g+d
# "
sH
n+g+d
1
# $ 1
A(t).
Compare this expression with equation (3.8),
y (t) =
%
sK
n+g+d
&
1
hA(t).
In the special case = 0, the solution of the Mankiw-Weil-Romer

investors may need to pay bribes. Let us call the appropriation
rate; the part of the return to capital that goes to investors.
Then investors require a M P K equal to r= : the lower the
appropriation rate, the higher the M P K demanded by investors
and,

Quantitative Methods in Economic Analysis
EC 2104
Roy Chen
Lecture 3
August 28, 2012
Administrative Stuff
all
IDear
created
a discussion forum on IVLE
Tutorials will start next week. Please get in touch with Dr Roy Chen by today.
TAs
have been assigned

EC 2104 Quantitative Methods for Economic Analysis
Problem Set 5
The material covered in this problem set may be tested on the midterm, which takes place on
October 2.
1. Find the following:
df
for f (x, y) = x2 y + ey , with x(t) = t t and y(t) = t2 .
dt

EC 2104 Quantitative Methods for Economic Analysis
Problem Set 7
Students will solve selected problems from the following questions during tutorial sessions the week
of October 22, 2012.
1. For each of the following functions, use the second derivative te

Quantitative Methods in Economic Analysis
EC 2104
Roy Chen
Lecture 12
November 12, 2012
Administrative Issues
Final exam will take place Thursday November 29, 1PM -
3PM
Covers entire module, but with an emphasis on the material
after the midterm
8 MCQs

EC 2104 Quantitative Methods for Economic Analysis
Problem Set 3
Students will solve selected problems from the following questions during tutorial sessions the week
of September 10, 2012.
1. Find the local and global maximum and minimum point(s) for the

EC 2104 Quantitative Methods for Economic Analysis
Problem Set 2
Students will solve selected problems from the following questions during tutorial sessions the week
of September 3, 2012.
1. Find f 0 (x) for the following f (x):
(a) 5x2 + ex
ex
(b)
ln x
2

Quantitative Methods in Economic Analysis
EC 2104
Roy Chen
Lecture 2
August 21, 2012
Outline
Readings: SH, Chapters 5-6
Shifting Graphs
Composite Functions
Inverse Functions
Limits
Derivatives
Shifting Graphs
If you know the graph of f (x), you also